N=1 SQCD and the Transverse Field Ising Model

TL;DR

This paper establishes a correspondence between the 1-loop dilatation operator in N=1 SQCD within the conformal window and the transverse field Ising model, enabling exact solutions for operator dimensions.

Contribution

It demonstrates that the dilatation operator acting on scalar gauge-invariant operators maps to an integrable spin chain model, providing a new solvable approach to compute anomalous dimensions.

Findings

The 1-loop dilatation operator is equivalent to the transverse field Ising model.

Exact solutions for anomalous dimensions are obtained for both periodic and open boundary conditions.

The approach offers a new integrable systems perspective on operator dimensions in supersymmetric QCD.

Abstract

We study the dimensions of non-chiral operators in the Veneziano limit of N=1 supersymmetric QCD in the conformal window. We show that when acting on gauge-invariant operators built out of scalars, the 1-loop dilatation operator is equivalent to the spin chain Hamiltonian of the 1D Ising model in a transverse magnetic field, which is a nontrivial integrable system that is exactly solvable at finite length. Solutions with periodic boundary conditions give the anomalous dimensions of flavor-singlet operators and solutions with fixed boundary conditions give the anomalous dimensions of operators whose ends contain open flavor indices.