Klebanov-Witten flows in M-theory

TL;DR

This paper investigates renormalization group flows in three-dimensional superconformal gauge theories, using holographic duality to relate them to M-theory on specific geometries, and confirms the consistency through geometric and partition function analyses.

Contribution

It introduces a flavoring method to generate new theories and verifies the duality by comparing chiral rings and three-sphere partition functions.

Findings

The free energy decreases by a universal ratio of 16/27 during the flows.

The gauge theories' chiral ring structures match the dual geometries.

The three-sphere partition function confirms the holographic duality.

Abstract

We study renormalization group flows among three dimensional superconformal gauge theories which closely resemble the renowned Klebanov-Witten flow in four dimensions. In the large N limit, each theory appearing in the flow is holographically dual to M-theory on AdS4 times a toric Sasaki-Einstein seven-manifold. The theories are obtained through the so-called flavoring method, which adds some fundamental matter fields to the dimensionally reduced Klebanov-Witten theories. We reconfirm the matching between the gauge theories and the dual geometries by comparing the chiral ring structure. As a more refined test of the flows, we compute the three-sphere partition function of the gauge theories. The square of the free energy, inversely proportional to the volume of the seven-manifold, decreases by a universal ratio 16/27 for all flows considered in this paper.