Compactifying 5d superconformal field theories to 3d

Abstract

Building on recent progress in the study of compactifications of 6d (1, 0) superconformal field theories (SCFTs) on Riemann surfaces to 4d mathcal{N} = 1 theories, we initiate a systematic study of compactifications of 5d mathcal{N} = 1 SCFTs on Riemann surfaces to 3d mathcal{N} = 2 theories. Specifically, we consider the compactification of the so-called rank 1 Seiberg {E}_{N_f+1} SCFTs on tori and tubes with flux in their global symmetry, and put the resulting 3d theories to various consistency checks. These include matching the (usually enhanced) IR symmetry of the 3d theories with the one expected from the compactification, given by the commutant of the flux in the global symmetry of the corresponding 5d SCFT, and identifying the spectrum of operators and conformal manifolds predicted by the 5d picture. As the models we examine are in three dimensions, we encounter novel elements that are not present in compactifications to four dimensions, notably Chern-Simons terms and monopole superpotentials, that play an important role in our construction. The methods used in this paper can also be used for the compactification of any other 5d SCFT that has a deformation leading to a 5d gauge theory.