Families of Conformal Fixed Points of N=2 Chern-Simons-Matter Theories

TL;DR

This paper demonstrates that a broad class of N=2 Chern-Simons-matter theories in three dimensions possess a continuous family of exactly marginal IR fixed points, confirmed through perturbative calculations up to 4 loops.

Contribution

It establishes the existence of a continuous family of IR fixed points in N=2 Chern-Simons-matter theories and verifies their stability via high-order perturbative beta function computations.

Findings

The family of fixed points persists at 4-loop order.

4-loop beta functions do not alter the dimension of the fixed point family.

Perturbative corrections to the Zamolodchikov metric are explicitly computed.

Abstract

We argue that a large class of N=2 Chern-Simons-matter theories in three dimensions have a continuous family of exact IR fixed points described by suitable quartic superpotentials, based on holomorphy. The entire family exists in the perturbative regime. A nontrivial check is performed by computing the 4-loop beta function of the quartic couplings, in the 't Hooft limit, with a large number of flavors. We find that the 4-loop beta function can only deform the family of 2-loop fixed points, and does not change the dimension of this family. We further present an explicit computation of a perturbative correction to the Zamolodchikov metric on this space of three-dimensional superconformal field theories.