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
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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)