Supersymmetry enhancement by monopole operators

Abstract

We describe a method which allows one to study hidden symmetries in a large class of strongly coupled supersymmetric gauge theories in three dimensions. We apply this method to the ABJM theory and to the infrared limit of N = 4 SQCD with adjoint and fundamental matter. We show that the U (N ) ABJM model with Chern-Simons level k = 1 or k = 2 has hidden N = 8 supersymmetry. Hidden supersymmetry is also shown to occur in N = 4 d = 3 SQCD with one fundamental and one adjoint hypermultiplet. The latter theory, as well as the U (N ) ABJM theory at k = 1, are shown to have a decoupled free sector. This provides evidence that both models are dual to the infrared limit of N = 8 U (N ) super-Yang-Mills theory.

Redeeming bad theories

“…One could, in principle, search for these currents in the original theory by considering monopole operators. Such symmetry enhancement by monopole operators has been shown to exist in several examples [14,18,38]. The analysis in "bad" theories is complicated by the fact that the R-charges for monopole operators are corrected by (we assume) the very accidental symmetries we are searching for.…”

“…In a theory with N ≥ 2 supersymmetry and k = 0 these can be promoted to chiral operators whose quantum numbers, including the R-charge, can be systematically deduced from the UV theory [17,18]. The superconformal algebra implies that the dimension of these operators, or any chiral operator, in the IR theory is equal to their charge under a particular R-symmetry whose current sits in the same multiplet as the energy momentum tensor.…”

Dualities between $ \mathcal{N} = 8 $ superconformal field theories in three dimensions

“…The hidden symmetry currents are realized by monopole operators. This proposal has been proved using controlled deformation to weak coupling [6]; for other approaches see [14,13,15].…”

“…Thus this BLG theory has not one but two copies of N = 8 supersymmetry algebra, one acting on the free sector and one acting on the remainder. This quantum doubling of the N = 8 supercurrent multiplet is required by duality, because U(2) 1 × U(2) −1 theory also has such a doubling on the quantum level, as well as a free sector [6]. All these peculiar properties stem from the fact that the theory of N M2-branes in flat space must have a free N = 8 sector describing the center-of-mass motion.…”

“…In the "traditional" approach to the theory of N M2-branes via the U(N) N = 8 super-Yang-Mills theory, this decomposition is apparent on the classical level (one can decompose all fields into trace and traceless parts which then do not interact, with the trace part being free). In the ABJM description of the same system this decomposition arises only on the quantum level [6]. For N = 2 we also have a BLG description of the same system, and the existence of a free sector is again a quantum effect.…”