Matter Coupled AdS_3 Supergravities and Their Black Strings

TL;DR

This work constructs matter-coupled $AdS_3$ supergravities with $N=(2,0)$ (and an $N=(1,0)$ truncation) in 2+1 dimensions by coupling $n$ complex scalar multiplets to gauged $N=(2,0)$ supergravity, with scalars living on Kahler coset manifolds that can be compact or non-compact. The target-space geometry controls the global properties of supersymmetric string solutions: compact targets yield quantized radii and half-supersymmetric black strings that are asymptotically Minkowskian (including a special radius matching the Horne–Horowitz 2+1D string), while non-compact targets produce half-supersymmetric strings that are asymptotically $AdS_3$ but harbor naked singularities. An explicit consistent truncation to $N=(1,0)$ AdS$_3$ supergravity with the same matter content is also developed. Together, these results advance the AdS$_3$/CFT$_2$ program by offering concrete, solvable models of matter-coupled AdS$_3$ supergravity and their string-like solitons.

Abstract

We couple n copies of N=(2,0) scalar multiplets to a gauged N=(2,0) supergravity in 2+1 dimensions which admits AdS_3 as a vacuum. The scalar fields are charged under the gauged R-symmetry group U(1) and parametrize certain Kahler manifolds with compact or non-compact isometries. The radii of these manifolds are quantized in the compact case, but arbitrary otherwise. In the compact case, we find half-supersymmetry preserving and asymptotically Minkowskian black string solutions. For a particular value of the scalar manifold radius, the solution coincides with that of Horne and Horowitz found in the context of a string theory in 2+1 dimensions. In the non-compact case, we find half-supersymmetry preserving and asymptotically AdS_3 string solutions which have naked singularities. We also obtain two distinct AdS_3 supergravities coupled to n copies of N=(1,0) scalar multiplets either by the truncation of the (2,0) model or by a direct construction.