SUSY Moose Runs and Hops: An extra dimension from a broken deformed CFT

TL;DR

This paper explores supersymmetric moose models that exhibit emergent extra dimensions at conformal fixed points, with nonperturbative evidence showing relevant deformations and intricate RG flows, offering insights into higher-dimensional gauge theories and phenomenology.

Contribution

It introduces a class of deformed conformal field theories with emergent extra dimensions, supported by a-maximization and RG flow analysis, advancing understanding of lattice-like gauge theories and their fixed points.

Findings

Hopping terms are relevant deformations at fixed points.

RG flows connect multiple conformal fixed points.

Extra dimensional interpretation is supported at stable fixed points.

Abstract

We find a class of four dimensional deformed conformal field theories which appear extra dimensional when their gauge symmetries are spontaneously broken. The theories are supersymmetric moose models which flow to interacting conformal fixed points at low energies, deformed by superpotentials. Using a-maximization we give strong nonperturbative evidence that the hopping terms in the resulting latticized action are relevant deformations of the fixed point theories. These theories have an intricate structure of RG flows between conformal fixed points. Our results suggest that at the stable fixed points each of the bulk gauge couplings and superpotential hopping terms is turned on, in favor of the extra dimensional interpretation of the theory. However, we argue that the higher dimensional gauge coupling is generically small compared to the size of the extra dimension. In the presence of a brane the topology of the extra dimension is determined dynamically and depends on the numbers of colors and bulk and brane flavors, which suggests phenomenological applications. The RG flows between fixed points in these theories provide a class of tests of Cardy's conjectured a-theorem.