Exact Results in 5D from Instantons and Deconstruction

TL;DR

This paper develops instanton calculation rules for 5D theories on a circle, verifies them against known solutions, and demonstrates that deconstructed theories accurately reproduce non-perturbative effects of continuum extra dimensions, providing new insights and validation.

Contribution

It introduces and validates instanton calculus rules for 5D theories, and shows that deconstructed models can replicate non-perturbative effects of higher-dimensional theories.

Findings

Instanton calculations in 5D theories match known exact solutions.

Deconstructed theories reproduce continuum non-perturbative results.

Provides non-perturbative evidence supporting deconstruction of extra dimensions.

Abstract

We consider non-perturbative effects in theories with extra dimensions and the deconstructed versions of these theories. We establish the rules for instanton calculations in 5D theories on the circle, and use them for an explicit one-instanton calculation in a supersymmetric gauge theory. The results are then compared to the known exact Seiberg-Witten type solution for this theory, confirming the validity both of the exact results and of the rules for instanton calculus for extra dimensions introduced here. Next we consider the non-perturbative results from the perspective of deconstructed extra dimensions. We show that the non-perturbative results of the deconstructed theory do indeed reproduce the known results for the continuum extra dimensional theory, thus providing the first non-perturbative evidence in favor of deconstruction. This way deconstruction also allows us to make exact predictions in higher dimensional theories which agree with earlier results, and helps to clarify the interpretation of 5D instantons.