Two-point function of the energy-momentum tensor and generalised conformal structure

TL;DR

This paper computes the two-point function of the energy-momentum tensor in theories with generalized conformal structure at two loops in dimensions 3 and 5, confirming expected behaviors and exploring effects of additional couplings relevant for holographic cosmology.

Contribution

It provides a perturbative two-loop calculation of the energy-momentum tensor correlator in generalized conformal theories, including renormalization effects and analysis of additional couplings.

Findings

Confirmed the structure of two-point functions in generalized conformal theories.

Derived functions of the effective coupling $g$ at two-loop order.

Analyzed the impact of a $\

Abstract

Theories with generalised conformal structure contain a dimensionful parameter, which appears as an overall multiplicative factor in the action. Examples of such theories are gauge theories coupled to massless scalars and fermions with Yukawa interactions and quartic couplings for the scalars in spacetime dimensions other than 4. Many properties of such theories are similar to that of conformal field theories (CFT), and in particular their 2-point functions take the same form as in CFT but with the normalisation constant now replaced by a function of the effective dimensionless coupling $g$ constructed from the dimensionful parameter and the distance separating the two operators. Such theories appear in holographic dualities involving non-conformal branes and this behaviour of the correlators has already been observed at strong coupling. Here we present a perturbative computation of the two-point function of the energy-momentum tensor to two loops in dimensions $d= 3, 5$, confirming the expected structure and determining the corresponding functions of $g$ to this order, including the effects of renormalisation. We also discuss the d=4 case for comparison. The results for $d=3$ are relevant for holographic cosmology, and in this case we also study the effect of a $\Phi^6$ coupling, which while marginal in the usual sense it is irrelevant from the perspective of the generalised conformal structure. Indeed, the effect of such coupling in the 2-point function is washed out in the IR but it modifies the UV.