Yannick Kluth: Fixed Points of Quantum Gravity from Dimensional Regularisation
We investigate β-functions of quantum gravity using dimensional regularisation. In contrast to minimal subtraction, a non-minimal renormalisation scheme is e...
Recent posts
Jan Ambjorn: Relating CDT and FRG
CDT is a lattice theory of quantum gravity. It is shown how to identify the IR and the UV limit of this lattice theory with similar FRG limits.
Benjamin Knorr: Unearthing the intersections: positivity bounds, weak gravity conjecture, and asymptotic safety landscapes from photon-graviton flows
We compute the asymptotic safety landscape stemming from ultraviolet-complete photon-graviton flows in a field theoretic setup, and we confront it with the w...
Thomas Thiemann and Renata Ferrero: Asymptotically safe – canonical quantum gravity junction
The asymptotically safe (ASQG) and the canonical (CQG) approach to quantum gravity share to be both non-perturbative programmes. However, apart from that the...
Frank Saueressig: Almost-Gaussian Scaling in Asymptotic Safety – Yes? – No? - Maybe?
For more than a decade, we are used to the idea that evaluating Wetterich’s equation for polynomial f(R)-truncations yields 3 relevant directions. Moreover, ...
Anna Tokareva: Background-induced complex mass states of graviton: quantization and tensor power spectrum
I start from the assumption that the theory of gravity can be formulated in terms of 4-dimensional action, and there are only 2 graviton polarization states,...
Jian Wang: Global Flows of Foliated Gravity-Matter Systems
Asymptotic safety is a promising mechanism for obtaining a consistent and predictive quantum theory for gravity. The ADM formalism allows to introduce a (Euc...
Diego Buccio: Physical running of couplings in quadratic gravity
We argue that the well-known beta functions of quadratic gravity do not correspond to the physical dependence of scattering amplitudes on external momenta, a...
Christof Wetterich: Field transformations in functional flow equations
Field transformations for the quantum effective action lead to different pictures of a given physical situation, as describing a given evolution of the unive...
Agustín Silva: On harvesting physical predictions from asymptotically safe quantum field theories
Asymptotic safety is a powerful mechanism for obtaining a consistent and predictive quantum field theory beyond the realm of perturbation theory. It hinges o...
Yannick Kluth: Robustness of the derivative expansion in Asymptotic Safety
We analyse the renormalisation group flow of quantum gravity at sixth order in the derivative expansion within the background field approximation. Non-linear...
Marta Picciau: Quantum field theories of relativistic Luttinger fermions
We have constructed relativistic versions of Luttinger fermions in analogy to effective low-energy degrees of freedom of non-relativistic solid-state systems...
Benjamin Knorr: Momentum-dependent field redefinitions in Asymptotic Safety
We discuss general momentum-dependent field redefinitions in the context of quantum-gravitational scattering amplitudes in general, and Asymptotic Safety in ...
Tim Morris: Ultraviolet finite resummation of perturbative quantum gravity
If the metric is chosen to depend exponentially on the conformal factor, and if one works in a gauge where the conformal factor has the wrong sign propagator...
Bilal Hawashin: The Nordic-walking mechanism and its explanation of deconfined pseudocriticality from Wess-Zumino-Witten theory
Many phase transitions can be understood as the spontaneous breaking of a global symmetry of the microscopic system. This is well captured within the framewo...
Johanna Borissova: Suppression of spacetime singularities in quantum gravity
Spacetime singularities as predicted by general relativity signal the breakdown of our classical description of gravity and are expected to be absent in a fu...
Shouryya Ray: Light fermions in colour: why the quark mass is not the Planck mass
We investigate whether quantum gravity fluctuations can break chiral symmetry for fermions that are charged under a U(1) and an SU(Nc) gauge symmetry, and th...
Edoardo D’Angelo: Asymptotic Safety in Lorentzian quantum gravity
Recently, together with Drago, Pinamonti, and Rejzner, I introduced a functional Renormalization Group (RG) equation to explore non-perturbative and covarian...
Abhishek Chikkaballi: Naturally small neutrino mass with asymptotic safety and gravitational-wave signatures
We revisit the dynamical generation of an arbitrarily small neutrino Yukawa coupling in the Standard Model with trans-Planckian asymptotic safety and apply t...
Gustavo de Brito: Towards an interplay between causal sets and asymptotically safe quantum gravity
In this seminar, I will explore possible connections between the causal sets and asymptotic safety approaches to quantum gravity. In the first part of the se...
Antonio Panassiti: Dust collapse in Asymptotic Safety: a path to regular black holes
I will discuss how regular black hole spacetimes are obtained from an effective Lagrangian for Quantum Einstein Gravity. The interior matter is modeled as a ...
Maria Conti: The conformal sector of Quantum Einstein Gravity beyond the local potential approximation
The seminar will revolve around the analysis of the conformal sector of Quantum Einstein Gravity with an improvement due to the study of the role of the anom...
Jan Tränkle: Effective action and black hole solutions in asymptotically safe quantum gravity
Exploring quantum corrections to black hole geometries might offer a unique opportunity for observationally testing the asymptotic safety scenario in quantum...
Jian Wang: Foliated asymptotically safe gravity in the fluctuation approach
The gravitational asymptotic safety program envisions a high-energy completion of gravity based on a non-Gaussian renormalization group fixed point. A key st...
Arthur Ferreira Vieira: The fate of chiral symmetry in Riemann-Cartan geometry
We study the mechanism of chiral symmetry breaking for fermionic systems in a gravitational background with curvature and torsion. The analysis is based on a...
Andrzej Goerlich: Scalar fields in lattice quantum gravity
The Causal Dynamical Triangulations (CDT) model is a background-independent and diffeomorphism-invariant approach to quantum gravity that provides a lattice ...
Robert Shrock: Higher-Loop Studies of Beta Function Zeros in Infrared-Free Field Theories
We discuss higher-loop studies of beta functions and their zeros in various quantum field theories. We focus mainly on infrared-free theories. Some calculati...
Yannick Kluth: Spectral Functions of Gauge Theories with Banks-Zaks Fixed Point
In this talk, we investigate spectral functions of matter-gauge theories that are asymptotically free in the ultraviolet and display a Banks-Zaks conformal f...
Diego Buccio: Amplitudes and Renormalization Group Techniques: A Case Study
We explore the properties of a simple renormalizable shift symmetric model with a higher deriva- tive kinetic energy and quartic derivative coupling, that ca...
Rafael-Robson-Lino-dos-Santos: From quantum gravity to gravitational waves through cosmic strings
I will talk about our latest paper whose abstract is: “New physics beyond the Standard Model can give rise to stochastic gravitational wave backgrounds, for ...
Shouryya Ray: Suppression of proton decay in quantum gravity
The proton lifetime is technically a low-energy measurement, the proton’s rest mass being only 1 GeV. However, it is also extraordinarily large: 21 orders of...
Chiang-Mei Chen: Phase Structure of Quantum Improved Black Holes in Asymptotically Safe Gravity
In this talk, I will discuss the quantum improvement of black hole solutions in the context of asymptotic safety. We propose that the consistency of the firs...
Fabian Wagner: Shift-symmetric Horndeski gravity in the asymptotic-safety paradigm
Horndeski gravity is a popular contender for a phenomenological model of dynamical dark energy, and as such subject to observational constraints. My colleagu...
Renata Ferrero: Geometrization of Renormalization Group Histories: a novel (A)dS/CFT emerging from Asymptotic Safety
We discuss the geometrization of entire evolution histories by means of a single, (d+1)-dimensional manifold furnished with a fixed (pseudo-) Riemannian stru...
Marc Schiffer: On the weak-gravity bound for a shift-symmetric scalar field
The weak-gravity bound has been discovered in several asymptotically safe gravity-matter systems. It limits the strength of gravitational fluctuations that a...
Johanna Borissova: Towards quantum black-hole dynamics inspired by asymptotic safety
We propose a new method to account for quantum-gravitational effects in cosmological and black hole spacetimes. At the core of our construction is the “decou...
Rafael Robson Lino dos Santos : Are there ALPs in the asymptotically safe landscape?
We investigate axion-like particles (ALPs) in the context of asymptotically safe gravity-matter systems. The ALP-photon interaction, which facilitates experi...
Cristóbal Laporte: Evidence for a novel shift-symmetric universality class from the functional renormalization group
Wetterich’s equation provides a powerful tool for investigating the existence and universal properties of renormalization group fixed points exhibiting quant...
Álvaro Pastor Gutiérrez: The Asymptotically Safe Standard Model: From quantum gravity to dynamical chiral symmetry breaking
We present a comprehensive non-perturbative study of the phase structure of the asymptotically safe Standard Model. The physics scales included range from th...
Alessia Platania: Causality, unitarity and stability in quantum gravity: a non-perturbative perspective
Resumming quantum fluctuations at the level of the gravitational path integral is expected to result in non-local effective actions and thus in a non-trivial...
Enrico Sessolo: Naturally small Yukawa couplings from trans-Planckian asymptotic safety
In gauge-Yukawa systems embedded in the framework of trans-Planckian asymptotic safety we discuss the dynamical generation of arbitrarily small Yukawa coupli...
Yannick Kluth: Functional Renormalisation for f(Rμνρσ) Quantum Gravity
We derive new functional renormalisation group flows for quantum gravity, in any dimension. The key new achievement is that the equations apply for any theor...
Álvaro Pastor Gutiérrez: UV completion of extradimensional Yang-Mills theory for Gauge-Higgs unification
The SU(N) Yang-Mills theory in ℝ4×S1 spacetime is studied as a simple toy model of Gauge-Higgs unification. The theory is perturbatively nonrenormalizable bu...
Mathijs Fraaije: On the reconstruction problem in Quantum Gravity
Path integrals and the Wilsonian renormalization group provide two complementary computational tools for investigating continuum approaches to quantum gravit...
Benjamin Knorr: Safe essential scalar-tensor theories
We discuss the renormalisation group flow of all essential couplings of quantum gravity coupled to a shift-symmetric scalar field at fourth order in the deri...
Ivano Basile: Asymptotic safety and the swampland
We propose testing the paradigm of asymptotically safe gravity using swampland conjectures. As a first step in this direction, we explore the infrared regime...
Maximilian Becker: Background Independent Field Quantization with Sequences of Gravity-Coupled Approximants
We apply the new quantization scheme outlined in M. Becker and M. Reuter, Phys. Rev. D 102, 125001 (2020), to explore the influence which quantum vacuum fluc...
Edoardo D’Angelo: Wetterich equation on lorentzian manifolds
The Wetterich equation governs the renormalization flow of the effective action under the scaling of an IR cutoff. In this talk, I introduce a generalization...
Gustavo de Brito: Nonvanishing gravitational contribution to matter beta functions for vanishing dimensionful regulators
In this talk, I will explore the effect of quantum gravity on matter couplings within a Renormalization Group framework. In particular, I will focus on resul...
Christof Wetterich: The quantum gravity connection between inflation and quintessence
The scaling solution of the functional flow in dilaton quantum gravity leads to highly predictive cosmology. Inflation and quintessence can both be described...
Rudrajit Banerjee: The spatial Functional Renormalization Group and Hadamard states on cosmological spacetimes
A spatial variant of the Functional Renormalization Group (FRG) is introduced on (Lorentzian signature) globally hyperbolic spacetimes. Through its perturbat...
Chris Ripken: De Sitter scattering amplitudes in the Born approximation
A basic calculation in QFT is the construction of the Yukawa potential from a tree-level scattering amplitude. In the massless limit, this reproduces the 1/r...
Renata Ferrero: Relational Observables in Asymptotically Safe Gravity
One of the greatest issues for a quantum theory of gravitation is how to generalise the notion of local observable quantities. A viable approach is to constr...
Dalius Stulga: Provable properties of asymptotic safety in the f(R) approximation
In this talk I will describe how we can derive general properties of the fixed-point solutions to the flow equations in the f(R) approximation using a family...
Tom Steudtner: Explaining B-Anomalies with safe Z’ extensions
U(1)’ extensions of the SM with generation-dependent couplings to quarks and leptons are a popular explanation of anomalies in rare B-decays, such as the R_K...
Jian Wang : Scalar-tensor theories within asymptotic safety
In this work we use the Wetterich equation for the effective average action to investigate the RG flow of gravity supplemented by a real scalar field. We giv...
Saswato Sen: Asymptotic safety and freedom in higher derivative gravity
We compute non-perturbative flow equations for the couplings of quantum gravity in fourth order of a derivative expansion. The gauge invariant functional flo...
Manuel Reichert: Lorentzian quantum gravity and the graviton spectral function
We present the first direct and non-perturbative computation of the graviton spectral function in quantum gravity. This is achieved with the help of a novel ...
Focus Seminar: The graviton propagator in Asymptotic Safety (Benjamin Knorr, Alessia Platania, and Manuel Reichert)
The propagator stores important information about the causality and unitarity of a theory, and is related to the spectral function, if it exists. Studying th...
Kamila Kowalska: Implications for g-2 and dark matter from asymptotic safety
We use the framework of asymptotic safety above the Planck scale to constrain the parameter space of simple models of new physics that can accommodate the me...
Rafael Robson Lino dos Santos: The weak-gravity bound and the need for spin in asymptotically safe matter-gravity models
In this talk, we introduce the weak-gravity bound for scalar-gravity systems within the asymptotic-safety paradigm. The weak-gravity bound arises when gravit...
Kevin Falls: Essential Quantum Einstein Gravity
The non-perturbative renormalisation of quantum gravity is investigated allowing for the metric to be reparameterised along the RG flow, such that only the e...
Alessio Baldazzi: Essential renormalization group
We use the generalised flow of the Effective average action which incorporates field redefinitions along the RG flow. This equation allows for the implementa...
Focus Seminar: Black Holes in Asymptotic Safety (Frank Saueressig & Aaron Held)
Black holes are vital for a consistent description of gravitational wave events as well as the recent image of the Event Horizon Telescope. However, black ho...
Shouryya Ray: Towards a Higgs Mass Determination in Asymptotically Safe Gravity with a Dark Portal
There are reasons to believe that extensions to the Standard Model that tend to lower the Higgs mass are phenomenologically attractive. (For one thing, it wo...
Lisa Glaser: Ising Spins and Causal Sets
Causal sets are a theory that encodes space-time through the causal relations between events. This leads to a fundamentally Lorentzian, discrete, formulation...
Benjamin Knorr: The derivative expansion in asymptotically safe quantum gravity: general setup and quartic order
We present a general framework to systematically study the derivative expansion of asymptotically safe quantum gravity. It is based on an exact decoupling an...
Tobias Denz: Reconstructing the graviton
We reconstruct the Lorentzian graviton propagator in asymptotically safe quantum gravity from Euclidean data. The reconstruction is applied to both the dynam...
Ivano Basile: String Tension between de Sitter vacua and Curvature Corrections
Higher-derivative corrections to cosmological effective actions in string theory are largely constrained by T-duality, but have been computed hitherto only t...
Alex Mitchell-Lister: A continuum limit of quantum gravity at second order in perturbation theory
In this talk we discuss the most recent step in an approach to finding the continuum limit of quantum gravity using the exact renormalization group and the c...
Adrien Florio: Searching for continuous phase transitions in 5D SU(2) lattice gauge theory
We study the phase diagram of 5-dimensional SU(2) Yang-Mills theory on the lattice. We consider two extensions of the fundamental plaquette Wilson action in ...
Abdol Sabor Salek: A curvature bound from gravitational catalysis in thermal backgrounds
A suitable candidate for a UV-complete quantum theory of gravity needs to be compatible with the existence of chiral fermions. Studies of quantum fields in c...
Judah Unmuth-Yockey: Newtonian binding from lattice quantum
We consider a free scalar field on Euclidean dynamical triangulations. By studying the 1-particle and 2-particle correlation functions, we extract the bindi...
Raúl Carballo Rubio: Mass inflation and the semiclassical limit of quantum black holes
Geometries describing static non-singular black holes have been obtained in suitable limits of various quantum gravity frameworks, including asymptotic safet...
Seth Kurankyi Asante: Effective spin foam models for four dimensional quantum gravity
A number of approaches to four-dimensional quantum gravity, such as loop quantum gravity and holography, situate areas as their fundamental variables. These ...
Passant Ali: Constraints on discrete global symmetries in quantum gravity
The question whether global symmetries can be realized in quantum-gravity-matter-systems has far-reaching phenomenological consequences. During my talk I wil...
Renata Ferrero: Dynamical diffeomorphisms
We consider a class of models for dynamical dark energy: we construct a general effective dynamics for diffeomorphisms of spacetime, in a fixed external metr...
Yannick Kluth: Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
In this talk, the fixed point structure of asymptotically safe quantum gravity is tested for actions containing squares of the Riemann tensor and the Ricci s...
Alessia Platania: Non-perturbative unitarity and fictitious ghosts in quantum gravity
According to the asymptotic-safety conjecture, a (non-perturbatively) renormalizable quantum field theory of gravity could be constructed based on the existe...
Enrico Sessolo: Flavor anomalies from asymptotically safe gravity
I will describe how the framework of asymptotically safe quantum gravity can be employed to derive novel predictions for some well-known new physics solution...
Jesse Daas: Asymptotically Safe Gravity with Fermions
In this talk the fixed point structure of gravity-fermion systems on a curved background spacetime will be discussed using the functional renormalization gro...
Jobst Ziebell: Asymptotically Safe QED
High-energy completeness of quantum electrodynamics (QED) can be induced by an interacting ultraviolet fixed point of the renormalization flow. We provide ev...
Martin Pauly: Safety in Darkness: Towards asymptotically safe dark matter models
Asymptotic safety might have significant predictive implications for dark matter models. I illustrate this in a toy model for the visible Higgs-Yukawa sector...
Jan Kwapisz: Asymptotic safety and quantum gravity amplitudes
Application of the Weinberg’s conditions of asymptotic safety to amplitudes and not to couplings of the effective action can help to uniquely define the runn...
Leslaw Rachwal: Effective action from FRG
We study the quantum gravitational system coupled to a charged scalar, Dirac fermions, and electromagnetic fields. We use the “exact” or “functional” renorma...
Kevin Falls: Background independent exact renormalisation
I will discuss a new flow equation for the Wilsonian effective action based on a gauge invariant UV regularisation of gauge theories and gravity. The regular...
Maximiliano Binder: Functional Renormalization Group Flow of Massive Gravity
We apply the functional renormalization group equation to a massive Fierz–Pauli action in curved space and find that, even though a massive term is a modif...
Frank Saueressig: Spectroscopy of the Reuter fixed point from the composite operator formalism
Determining the structure of the UV-critical hypersurface, spanned by renormalization group trajectories enjoying asymptotic safety, is a highly complex prob...
Alicia Castro: FRG Approach to the Continuum Limit of Matrix Models of Quantum Gravity with Preferred Foliation
In this talk I will present the analysis of a dually-weighted Matrix Model which implements a preferred foliation in its dual-graph. By using the FRGE, we st...
Yu Hamada: Scalegenesis and fermionic dark matters in the flatland scenario
Recent studies in the context of asymptotically safe quantum gravity imply that scalar quartic couplings and scalar masses vanish above the Planck scale due ...
Bertrand Delamotte: Convergence of the derivative expansion and results at order ∂6
The derivative expansion (DE) is the most commonly used approximation scheme of Wilson’s renormalization group (RG), at least when it is formulated in terms ...
Tom Steudtner: Exact asymptotic safety: new solutions and large-N equivalences
We explore 4d gauge-Yukawa theories with weakly coupled UV fixed points. Using Majorana fermions, new families of theories with perturbatively exact asymptot...
Manuel Reichert: Dark Matter meets Quantum Gravity
We search for an extension of the Standard Model that contains a viable dark matter candidate and that can be embedded into a fundamental, asymptotically saf...
Gustavo Pazzini de Brito: A link that matters: Towards phenomenological constraints on quantum gravity models
Constraining quantum gravity from observations is a challenge. In this seminar, I explore the idea that the interplay of quantum gravity with matter could be...
Axel Maas: The Fröhlich-Morcchio-Strocchi Mechanism and Quantum Gravity
Taking manifest invariance under both gauge symmetry and diffeomorphisms as a guiding principle physical objects are constructed for Yang-Mills-Higgs theory ...
Peter Millington: Exact flow equations from the regulator-sourced 2PI effective action
The effective action is a powerful tool for studying the non-perturbative behaviour of quantum field theories. In this talk, we will revisit the derivation ...
Frank Saueressig: Form Factors in Asymptotic Safety
By definition, form factors capture the momentum dependence of a theory’s n-point function. For example, they may encode corrections to the propagation of fi...
Marc Schiffer: d=4 as the critical dimensionality of asymptotically safe interactions
In my talk, I explore the question why our universe is four dimensional from an asymptotically safe vantage point. I present indications that asymptotically ...
Alessia Platania: Dynamical renormalization of black-hole spacetimes
We construct a black-hole spacetime which includes the running of the gravitational coupling in a self-consistent way. Starting from a classical Schwarzschil...
Masatoshi Yamada: Higgs scalar potential in asymptotically safe quantum gravity
The effect of gravitational fluctuations on the quantum effective potential for scalar fields is a key ingredient for predictions of the mass of the Higgs bo...
Tim Morris: Trace anomaly and infrared cutoffs
The Effective Average Action is a form of effective action which depends on a cutoff scale suppressing the contribution of low momentum modes in the function...
Maximilian Becker: Geometric Operators in Asymptotic Safety
We consider geometric operators, such as the geodesic length and the volume of hypersurfaces, in the context of the Asymptotic Safety scenario for quantum gr...
Benjamin Knorr: RG flow with a covariant foliation
After a short introduction on how to set up a foliation in a covariant language, I will use this formalism to investigate the RG flow on foliated spacetimes....
Jan Kwapsiz: Asymptotic safety and Conformal Standard Model
There are many proposals how to extend the Standard Model, designed to deal with its fundamental inconsistencies. Since no new particles have been detected e...
Senarath de Alwis: Exact RG equations, Quantum Gravity and Ghosts
I derive an exact RG equation for the Wilsonian Effective Action, that is essentially a background field (and gauge invariant) version of the Polchinski equa...
Dine Ousmane Samary: Progress in the solving nonperturbative renormalization group for tensorial group field theory
This presentation aims at giving our new advance on the functional renormalization group applied to tensorial group field theory. It is based on a serie of o...
Johannes Lumma: Towards background independent quantum gravity with tensor models
We explore whether the phase diagram of tensor models could feature a pregeometric, discrete and a geometric, continuum phase for the building blocks of spac...
Marc Schiffer: How perturbative is quantum gravity?
We explore asymptotic safety of gravity-matter systems, discovering indications for a near-perturbative nature of these systems in the ultraviolet. Our resul...
Giulia Gubitosi and Chris Ripken: Consistent early and late time cosmology from the RG flow of gravity
We explain how the quantum gravity regime associated with Asymptotic Safety may set the initial conditions for a consistent cosmological evolution, from the ...
Carlos M. Nieto: In search of a UV completion of the Standard Model
Asymptotically safe extensions of the Standard Model have been searched for by adding vector-like fermions charged under the Standard Model gauge group and h...
Gustavo Pazzini de Brito: Asymptotic safety and field parametrization dependence in the f(R) truncation
We study the dependence on field parametrization in the context of the Asymptotic Safety scenario. The investigation is performed with the f(R)-truncation fo...
Gabriele Gionti: Hamiltonian Analysis of Asymptotically Safe Gravity
Recent results based on renormalization group approaches to Quantum Gravity suggest that the Newton’s and Cosmological constants should be treated as dynamic...
Manuel Reichert: Effective universality in quantum gravity
We investigate the asymptotic safety scenario for a scalar-gravity system. This system contains two avatars of the dynamical Newton coupling, a gravitational...
Benjamin Knorr: Towards reconstructing the quantum effective action of gravity
I will present a new method to constrain the quantum effective action of gravity, inspired by recent results from causal dynamical triangulations (CDT). Afte...
Vedran Skrinjar: Safe and free instantons
We will discuss the instanton dynamics of asymptotically safe and free quantum field theories featuring respectively controllable ultraviolet and infrared fi...
Riccardo Martini: A curvature bound from gravitational catalysis
Gravitational catalysis expresses an interplay between the curvature of the spacetime and fluctuation-induced mass generation of quantum matter. I will show ...
Johannes Lumma: Quantum gravity fluctuations flatten the Planck-scale Higgs-potential
In this talk, we will investigate asymptotic safety of a toy model of a singlet-scalar extension of the Higgs sector including two real scalar fields under t...
Frank Saueressig: Asymptotically safe f(R)-gravity coupled to matter
We use the functional renormalization group equation for the effective average action to study the non-Gaussian renormalization group fixed points (NGFPs) ar...
Rodrigo León Ardón: The path integral of unimodular gravity
We compute the one-loop effective action in unimodular gravity, starting from two different classical formulations of the theory. We find that the effective ...