Dynamics of N $$ \mathcal{N} $$ = 4 supersymmetric field theories in 2 + 1 dimensions and their gravity dual

Abstract

In this note we consider N = 4 SYM theories in 2+1 dimensions with gauge group U(N )×U(M ) and k hypermultiplets charged under the U(N ). When k > 2(N −M ), the theory flows to a superconformal fixed point in the IR. Theories with k < 2(N − M ), on the other hand, flows to strong coupling. We explore these theories from the perspective of gravity dual. We find that the gravity duals of theories with k < (N − M ) contain enhancons even in situations where repulson singularities are absent. We argue that supergravity description is unreliable in the region near these enhancon points. Instead, we show how to construct reliable sugra duals to particular points on the Coulomb branch where the enhancon is screened. We explore how these singularities reappear as one moves around in Coulomb branch and comment on possible field theory interpretation of this phenomenon. In analyzing gauge/gravity duality for these models, we encountered one unexpected surprise, that the condition for the supergravity solution to be reliable and supersymmetric is somewhat weaker than the expectation from field theory. We also discuss similar issues for theories with k = 0.

The Infrared Physics of Bad Theories

“…For SU (N ) gauge group, the Coulomb branch is not a complete intersection, but it can be obtained as a hyperkähler quotient of the U (N ) Coulomb branch by the topological U (1) J symmetry that acts on monopole operators. 36 Secondly, it would be interesting to generalise our analysis to circular quivers with unitary gauge groups, which have holographic dual solutions exhibiting cascading RG flows and enhançons [27][28][29]. We expect that these cascading RG flows are explained by the physics of the symmetric vacuum in the dual 3d N = 4 circular quivers, analogously to the rôle of the baryonic root in explaining the holographic RG flows of [30,31] for 4d N = 2 circular quivers [32,33].…”

“…The structure of the moduli space of the bad SQCD theories studied in the previous section leads to a number of infrared effective theories that depend on the Coulomb vacuum. 28 The SQCD theory in a generic vacuum of the codimension r singular locus C N −r ≡ C (r) sing flows to the low energy theory T U (r),N f plus N − r additional free twisted hypermultiplets. In particular the effective theory at the most singular locus C * =…”

Gauging and decoupling in 3d N $$ \mathcal{N} $$ = 2 dualities

“…In fact, all the terms which appear in the magnetic superpotentials (see (45) and (47)) have charge +1 under any of the three Z 2 symmetries, and hence the gauging is consistent with the superpotential. There is one big difference from the electric case, however: the role of the Z M and ZM should be exchanged, as follows from the identification (44).…”

“…8 This is in sharp contrast with the case of 3d N = 4 supersymmetry, where the IR decoupling of the monopole operators can be checked locally at the quiver diagram, by verifying the inequality N f ≥ 2N c (cf. [44,45] for recent discussion in gravity dual).…”

Resolved gravity duals of N = 4 $$ \mathcal{N}=4 $$ quiver field theories in 2 + 1 dimensions

“…It would be interesting and desirable to identify the manifestation of conditions (1.1) and (1.2) in the gravity dual. This very issue was studied recently in [7], which provided the following general picture. A supergravity ansatz can be set up, and solved, for any choice of N , M , and k satisfying…”