The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals

TL;DR

This paper computes the large N limit of free energy in 3D field theories with AdS duals, confirming supergravity predictions, the F-theorem, and invariance under Seiberg duality, while proposing a new approach for chiral theories.

Contribution

It introduces a new proposal for analyzing chiral-like theories' free energy and offers an alternative geometric expression, extending the understanding of large N limits in these theories.

Findings

Vector-like theories match supergravity results.

Large N free energy is invariant under Seiberg duality.

A new method restores symmetry in chiral theories' free energy.

Abstract

We compute the large N limit of the localized three dimensional free energy of various field theories with known proposed AdS duals. We show that vector-like theories agree with the expected supergravity results, and with the conjectured F-theorem. We also check that the large N free energy is preserved by the three dimensional Seiberg duality for general classes of vector like theories. Then we analyze the behavior of the free energy of chiral-like theories by applying a new proposal. The proposal is based on the restoration of a discrete symmetry on the free energy before the extremization. We apply this procedure at strong coupling in some examples and we discuss the results. We conclude the paper by proposing an alternative geometrical expression for the free energy.