Conformal Invariance in the Leigh-Strassler deformed N=4 SYM Theory

TL;DR

This paper investigates conditions for conformal invariance in the Leigh-Strassler deformed ${ m N}=4$ SYM theory, constructing a family of finite theories up to several loops and exploring their properties and equivalences.

Contribution

It develops an algorithm for perturbative coupling adjustments to identify conformal Leigh-Strassler deformations up to high loop orders, including genuine and equivalent solutions.

Findings

Constructed conformal theories up to 3 loops non-planar and 4 loops planar.

Identified solutions equivalent to real beta-deformed ${ m N}=4$ SYM.

Proposed these solutions may hold at all loop orders.

Abstract

We consider a full Leigh-Strassler deformation of the ${\cal N}=4$ SYM theory and look for conditions under which the theory would be conformally invariant and finite. Applying the algorithm of perturbative adjustments of the couplings we construct a family of theories which are conformal up to 3 loops in the non-planar case and up to 4 loops in the planar one. We found particular solutions in the planar case when the conformal condition seems to be exhausted in the one loop order. Some of them happen to be unitary equivalent to the real beta-deformed ${\cal N}=4$ SYM theory, while others are genuine. We present the arguments that these solutions might be valid in any loop order.