"Integrability" of RG flows and duality in three dimensions in the 1/N expansion

TL;DR

This paper investigates certain three-dimensional RG flows with g -> 1/g dualities, demonstrating their integrability and exact duality symmetries at each order of the 1/N expansion, and explicitly analyzing their fixed points and correlators.

Contribution

It introduces integrable RG flows with exact dualities in three dimensions, providing explicit solutions and correlator calculations at the 1/N order.

Findings

RG flows can be integrated at any coupling in 1/N expansion

Duality symmetries are exact at each 1/N order

Explicit correlator calculations at leading-log level

Abstract

I study some classes of RG flows in three dimensions that are classically conformal and have manifest g -> 1/g dualities. The RG flow interpolates between known (four-fermion, Wilson-Fischer, phi_3^6) and new interacting fixed points. These models have two remarkable properties: i) the RG flow can be integrated for arbitrarily large values of the couplings g at each order of the 1/N expansion; ii) the duality symmetries are exact at each order of the 1/N expansion. I integrate the RG flow explicitly to the order O(1/N), write correlators at the leading-log level and study the interpolation between the fixed points. I examine how duality is implemented in the regularized theory and verified in the results of this paper.