Superconductors for superstrings on AdS ₅ × T ^1,1

Abstract

We construct a one-parameter family of five-dimensional $\mathcal{N} = 2$ supergravity Lagrangians with an SU(2, 1)/U(2) hypermultiplet. For certain values of the parameter, these are argued to describe the dynamics of scalar modes of superstrings on AdS ₅  × T ^1,1, and therefore to be dual to specific chiral primary operators of Klebanov-Witten superconformal field theory. We demonstrate that, below a critical temperature, the thermodynamics is dominated by charged black holes with hair for the scalars that are dual to the operator of lowest conformal dimension $\frac{3}{2}$. The system thus enters into a superconducting phase where $\left\langle {{\text{Tr}}\left[ {{A_k}{B_l}} \right]} \right\rangle$ condenses.