A piece of cake: the ground-state energies in gamma_i-deformed N=4 SYM theory

TL;DR

This paper calculates the ground-state energies of specific operators in gamma_i-deformed N=4 SYM theory, revealing finite-size effects and conformal symmetry breaking through direct Feynman diagram analysis and comparison with integrability methods.

Contribution

It provides the first direct Feynman diagram calculation of these energies, confirming integrability results and highlighting scheme dependence and conformal symmetry breaking.

Findings

For L>=3, energies proportional to the 'cake' integral match integrability predictions.

At L=2, a finite rational result is obtained despite divergences in integrability equations.

The results show conformal invariance is broken due to scheme dependence and non-zero beta-function.

Abstract

In the non-supersymmetric gamma_i-deformed N=4 SYM theory, the scaling dimensions of the operators tr[Z^L] composed of L scalar fields Z receive finite-size wrapping and prewrapping corrections in the 't Hooft limit. In this paper, we calculate these scaling dimensions to leading wrapping order directly from Feynman diagrams. For L>=3, the result is proportional to the maximally transcendental `cake' integral. It matches with an earlier result obtained from the integrability-based Luescher corrections, TBA and Y-system equations. At L=2, where the integrability-based equations yield infinity, we find a finite rational result. This result is renormalization-scheme dependent due to the non-vanishing beta-function of an induced quartic scalar double-trace coupling, on which we have reported earlier. This explicitly shows that conformal invariance is broken - even in the 't Hooft limit.