${\cal N} = 2^*$ Yang-Mills on the Lattice

TL;DR

This paper develops a lattice formulation of ${ m extbf{N}}=2^*$ Yang-Mills theory, enabling nonperturbative studies to test the AdS/CFT correspondence beyond conformal cases.

Contribution

It introduces a local, gauge-invariant lattice construction of ${ m extbf{N}}=2^*$ Yang-Mills theory that preserves some supersymmetry and avoids fermion doubling.

Findings

Lattice formulation is gauge-invariant and local.

Preserves part of supersymmetry on the lattice.

Provides a tool for nonperturbative tests of AdS/CFT in non-conformal theories.

Abstract

The ${\cal N} = 2^*$ Yang-Mills theory in four dimensions is a non-conformal theory that appears as a mass deformation of maximally supersymmetric ${\cal N} = 4$ Yang-Mills theory. This theory also takes part in the AdS/CFT correspondence and its gravity dual is type IIB supergravity on the Pilch-Warner background. The finite temperature properties of this theory have been studied recently in the literature. It has been argued that at large $N$ and strong coupling this theory exhibits no thermal phase transition at any non-zero temperature. The low temperature ${\cal N} = 2^*$ plasma can be compared to the QCD plasma. We provide a lattice construction of ${\cal N} = 2^*$ Yang-Mills on a hypercubic lattice starting from the ${\cal N} = 4$ gauge theory. The lattice construction is local, gauge-invariant, free from fermion doubling problem and preserves a part of the supersymmetry. This nonperturbative formulation of the theory can be used to provide a highly nontrivial check of the AdS/CFT correspondence in a non-conformal theory.