Deconstruction, Lattice Supersymmetry, Anomalies and Branes

TL;DR

This paper investigates how anomalies and chiral symmetries manifest in deconstructed supersymmetric theories, connecting lattice models with string theory brane realizations and supergravity calculations.

Contribution

It demonstrates the emergence of chiral symmetries in the infrared of deconstructed N=2 supersymmetric theories and links lattice anomalies to supergravity computations in brane setups.

Findings

Chiral symmetries appear only in the infrared in deconstructed theories.

Anomalies are reproduced using lattice perturbation theory with Wilson fermions.

Brane realizations allow classical supergravity to compute anomalies.

Abstract

We study the realization of anomalous Ward identities in deconstructed (latticized) supersymmetric theories. In a deconstructed four-dimensional theory with N=2 supersymmetry, we show that the chiral symmetries only appear in the infrared and that the anomaly is reproduced in the usual framework of lattice perturbation theory with Wilson fermions. We then realize the theory on the world-volume of fractional D-branes on an orbifold. In this brane realization, we show how deconstructed theory anomalies can be computed via classical supergravity. Our methods and observations are more generally applicable to deconstructed/latticized supersymmetric theories in various dimensions.