New N=1 Superconformal Field Theories In Four Dimensions

TL;DR

This paper constructs a broad new class of four-dimensional N=1 superconformal field theories by coupling known T_N theories with vector multiplets, exploring their properties and consistency conditions.

Contribution

It introduces a novel family of SCFTs in four dimensions by coupling T_N theories with vector multiplets without superpotential, analyzing their viability.

Findings

Some theories are new strongly coupled SCFTs.

Certain constructions violate the a-theorem.

Not all proposed theories are consistent or viable.

Abstract

We construct a large new family of four-dimensional N=1 superconformal field theories by coupling Gaiotto's T_N theories to N=1 vector multiplets. In particular, we consider theories in which various T_N blocks are linked together via bifundamental and adjoint chiral superfields, with no superpotential. We find that while some of these constructions appear to give new strongly coupled SCFTs, others lead to violations of the a-theorem, and thus do not appear to be good interacting theories.