$\mathcal{N}=2^{\ast }$ Yang-Mills on the Lattice

Abstract

The $\mathcal{N}=2^{\ast }$ Yang-Mills theory in four dimensions is a non-conformal theory that appears as a mass deformation of maximally supersymmetric $\mathcal{N}=4$ 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 $\mathcal{N}=2^{\ast }$ plasma can be compared to the QCD plasma. We provide a lattice construction of $\mathcal{N}=2^{\ast }$ Yang-Mills on a hypercubic lattice starting from the $\mathcal{N}=4$ 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.

Comments: 8 pages, 0 figures. Talk presented at the 35th International Symposium on Lattice Field Theory, 18-24 June 2017, Granada, Spain