N=1 SQCD and the Transverse Field Ising Model

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.

17 pages, 2 figures

References in corpus (2)

• Bounds on 4D Conformal and Superconformal Field Theories
• Quantum dimer model with Z_2 liquid ground-state: interpolation between cylinder and disk topologies and toy model for a topological quantum-bit

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