Haridev S R: RG studies of scalar-field models of long-range interactions

In this work, we study long-range interactions in non-gravitational field theories and their behaviour in the deep infrared. To model such effects, we consider a nonlocal scalar theory obtained by adding a (\phi \Box^{-1} \phi) term to the local action. Using the functional renormalisation group, we analyse its infrared fixed-point structure.

Within the LPA, we show that nonlocality modifies phase-transition patterns and can induce symmetry breaking. Extending the LPA beyond polynomial truncations, we examine the convexity property of the effective potential as (k \rightarrow 0) and find that the flow becomes singular for (\lambda^{2} > 0) before reaching the deep infrared.

In the LPA’ framework we find that the infrared-stable fixed point is the nonlocal Gaussian fixed point. We then generalise the model to (\phi \Box^{\sigma/2} \phi) and analyse how the infrared properties depend on (\sigma). With appropriate scaling choices, we show that the infrared behaviour remains unchanged up to (\sigma = d/2) and follows Sak’s prediction up to (\sigma = 2).

Finally, we study higher-derivative cases within the LPA, focusing on (\sigma = 4), which corresponds to isotropic Lifshitz criticality, and obtain results consistent with earlier work.