Gauge Theories in $AdS_5$ and Fine-Lattice Deconstruction

TL;DR

This paper explores gauge theories in AdS_5 using lattice deconstruction, analyzing how gauge couplings behave beyond the coarse-lattice approximation and providing methods to compute low-energy couplings for various lattice spacings.

Contribution

It extends the analysis of gauge couplings in AdS_5 deconstructed theories to finer lattices, offering new calculations for the product of KK masses and low-energy couplings.

Findings

Logarithmic energy dependence of gauge couplings is nearly automatic in coarse-lattice deconstruction.

Power-law corrections to the gauge coupling are suppressed by curvature effects.

Perturbative analysis around the coarse-lattice limit reveals intermediate energy behavior.

Abstract

The logarithmic energy dependence of gauge couplings in AdS_5 emerges almost automatically when the theory is deconstructed on a coarse lattice. Here we study the theory away from the coarse-lattice limit. While we cannot analytically calculate individual KK masses for a fine lattice, we can calculate the product of all non-zero masses. This allows us to write down the gauge coupling at low energies for any lattice-spacing and curvature. As expected, the leading log behaviour is corrected by power-law contributions, suppressed by the curvature. We then turn to intermediate energies, and discuss the gauge coupling and the gauge boson profile in perturbation theory around the coarse-lattice limit.