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

Abstract

In this note we consider ${\cal N}=4$ SYM theories in 2+1 dimensions with gauge group $U(N)\times U(M)$ 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 $k=0$.