Black Probes of Schr\"{o}dinger Spacetimes

Abstract

We consider black probes of Anti-de Sitter and Schr\"{o}dinger spacetimes embedded in string theory and M-theory and construct perturbatively new black hole geometries. We begin by reviewing black string configurations in Anti-de Sitter dual to finite temperature Wilson loops in the deconfined phase of the gauge theory and generalise the construction to the confined phase. We then consider black strings in thermal Schr\"{o}dinger, obtained via a null Melvin twist of the extremal D3-brane, and construct three distinct types of black string configurations with spacelike as well as lightlike separated boundary endpoints. One of these configurations interpolates between the Wilson loop operators, with bulk duals defined in Anti-de Sitter and another class of Wilson loop operators, with bulk duals defined in Schr\"{o}dinger. The case of black membranes with boundary endpoints on the M5-brane dual to Wilson surfaces in the gauge theory is analysed in detail. Four types of black membranes, ending on the null Melvin twist of the extremal M5-brane exhibiting the Schr\"{o}dinger symmetry group, are then constructed. We highlight the differences between Anti-de Sitter and Schr\"{o}dinger backgrounds and make some comments on the properties of the corresponding dual gauge theories.