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 of the so-called two-particle-irreducible effective action, paying particular attention to the role of the sources that appear in its definition. Working in the context of a zero-dimensional quantum field theory, we will be able to accompany this derivation with a graphical and pedagogical exposition of the behaviour of the effective action, and its various ingredients. We will then be able to show that we have much greater control over the effective action than has perhaps previously been realised, and we will be able to use the sources to map between different realisations of the effective action and to preserve symmetry properties in its truncations. Most significantly, by associating the two-point source of the effective action with the regulator of the renormalisation group evolution, we will arrive at an exact flow equation that differs from the well-known Wetterich-Morris-Ellwanger equation. We conclude by commenting on the potential implications of our results for fundamental physics and highlight possible future directions.