Non-Abelian supertubes

Journal of High Energy Physics, Dec 2017

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 AdS2 × 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.

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Non-Abelian supertubes

HJE Non-Abelian supertubes Jose J. Fernandez-Melgarejo 0 1 3 4 6 7 Minkyu Park 0 1 3 6 7 Masaki Shigemori 0 1 2 3 5 6 7 0 Queen Mary University of London , Mile End Road, London, E1 4NS , U.K 1 E-30100 Murcia , Spain 2 Center for Gravitational Physics, Yukawa Institute for Theoretical Physics 3 Kitashirakawa-Oiwakecho , Sakyo-ku, Kyoto 606-8502 Japan 4 Departamento de F sica, Universidad de Murcia 5 Centre for Research in String Theory, School of Physics and Astronomy 6 Yukawa Institute for Theoretical Physics, Kyoto University 7 Kyoto University , Kitashirakawa-Oiwakecho, Sakyo-ku, Kyoto 606-8502 Japan A supertube is a supersymmetric con guration 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 ve-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 elds, while in higher dimensions they correspond to non-geometric duality twists of the internal space. The supertubes in our solution carry NS5 and 5 22 dipole charges and exhibit the same monodromy structure as the SU(2) Seiberg-Witten geometry. The perturbative solution has S2 asymptotics and vanishing four-dimensional angular momentum. We argue that this solution represents a microstate of four-dimensional black holes with a and that it provides a clue for the gravity realization of a pure-Higgs branch state in the dual quiver quantum mechanics. ArXiv ePrint: 1709.02388 Black Holes in String Theory; D-branes; Spacetime Singularities; Supergravity - AdS2 Models 1.1 1.2 1.4 2.1 2.2 2.3 2.4 3.1 3.2 3.3 3.4 4.1 4.2 4.3 4.4 1 Introduction and summary Background Main results Plan of the paper 1.3 Implication for black-hole microstates Non-Abelian supertubes Strategy The near region 3.5 The far region: the solution 4 Physical properties of the solution Geometry and charges Closed timelike curves Bound or unbound? An argument for a bound state The far region: coordinate system and boundary conditions 4.5 A cancellation mechanism for angular momentum 5 Future directions A Duality transformation of harmonic functions B Matching to higher order C Con gurations with only two moduli D Supertubes in the one-modulus class D.1 Condition for a 1/4-BPS codimension-3 center D.2 Pu ed-up dipole charge for general 1/4-BPS codimension-3 center D.3 Round supertube E Harmonic functions for the D2 + D6 ! 522 supertube { 1 { 2 Multi-center solutions with codimension 2 and 3 3 Explicit construction of non-Abelian supertubes 1.1 Introduction and summary Background The fact that black holes have thermodynamical entropy means that there must be many underlying microstates that account for it. Because string theory is a microscopic theory of gravity, i.e., quantum gravity, all these microstates must be describable within string theory, at least as far as black holes that exist in string theory are concerned. A microstate must be a con guration in string theory with the same mass, angular momentum and charge as the black hole it is a microstate of, and the scattering in the microstate must be well-de ned as a unitary process. The fuzzball conjecture [1{5] claims that typical microstates spread over a macroscopic distance of the would-be horizon scale. More recent arguments [ 6, 7 ] also support the view that the conventional picture of black holes must be modi ed at the horizon scale and replaced by some non-trivial structure. The microstates for generic non-extremal black holes are expected to involve stringy excitations and, to describe them properly, we probably need quantum string eld theory. However, for supersymmetric black holes, the situation seems much more tractable. Many microstates for BPS black holes have been explicitly constructed as regular, horizonless solutions of supergravity | the massless sector of superstring theory. It is reasonable that the massless sector plays an important role for black-hole microstates because the large-distance structure expected of the microstates can only be supported by massless elds [8]. It is then natural to ask how many microstates of BPS black holes are realized within supergravity. This has led to the so-called \microstate geometry program" (see, e.g., [9]), which is about explicitly constructing as many black-hole microstates as possible, as regular, horizonless solutions in supergravity. A useful setup in which many supergravity microstates have been constructed is vedimensional N = 1 ungauged supergravity with vector multiplets, for which all supersymmetric solutions have been classi ed [10, 11]. Thi (...truncated)


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José J. Fernández-Melgarejo, Minkyu Park, Masaki Shigemori. Non-Abelian supertubes, Journal of High Energy Physics, 2017, pp. 103, Volume 2017, Issue 12, DOI: 10.1007/JHEP12(2017)103