Non-Abelian supertubes

Abstract

A supertube is a supersymmetric configuration in string theory which occurs when a pair of branes spontaneously polarizes and generates a new dipole charge extended along a closed curve. The dipole charge of a codimension-2 supertube is characterized by the U-duality monodromy as one goes around the supertube. For multiple codimension-2 supertubes, their monodromies do not commute in general. In this paper, we construct a supersymmetric solution of five-dimensional supergravity that describes two supertubes with such non-Abelian monodromies, in a certain perturbative expansion. In supergravity, the monodromies are realized as the multi-valuedness of the scalar fields, while in higher dimensions they correspond to non-geometric duality twists of the internal space. The supertubes in our solution carry NS5 and 5 2 2 dipole charges and exhibit the same monodromy structure as the SU(2) Seiberg-Witten geometry. The perturbative solution has AdS 2 × S 2 asymptotics and vanishing four-dimensional angular momentum. We argue that this solution represents a microstate of four-dimensional black holes with a finite horizon and that it provides a clue for the gravity realization of a pure-Higgs branch state in the dual quiver quantum mechanics.

Interpolating between multi-center microstate geometries

“…Here we give a brief review of the harmonic solution, which represents multi-center blackhole/ring solutions in 4d/5d. Our purpose here is to introduce notation; for further detail, see [1][2][3][4][5][6][7] (for solutions with codimension-2 sources see also [22,23]).…”

“…1 Codimension-2 sources can be produced by the supertube transition [21] and harmonic functions will have non-trivial monodromies around a curve in R 3 . Some examples of codimension-2 harmonic solutions were studied in [22,23].…”

“…The construction proceeds in layers, in that one constructs the harmonic functions in the order of V, K I , L I , M . In the previous work [22,23], solutions with trivial V (i.e. V = 1) were studied.…”

Interpolating between multi-center microstate geometries

“…1 Codimension-2 sources can be produced by the supertube transition [21] and harmonic functions will have non-trivial monodromies around a curve in R 3 . Some examples of codimension-2 harmonic solutions were studied in [22,23].…”

Microstate geometries at a generic point in moduli space

“…Both types can also be combined, but this has not been done explicitly for the co-dimension one generic solutions [22][23][24][25], which are called superstrata. One may also consider solutions that are only smooth locally, but for which the patching between open sets would involve U-duality transformations [26][27][28][29].…”