A matrix model black hole: act II

Abstract: We construct a kappa-symmetric Green-Schwarz action for type IIA string theory on AdS_2. As a candidate holographic dual, we consider superconformal matrix quantum mechanics, given by the Marinari-Parisi model with vanishing or logarithmic superpotential. We derive that the super-eigenvalues form a consistent subsector, and that their dynamics reduces to that of the supersymmetric Calogero-Moser model. The classical string action and the matrix model both have an infinite set of conserved charges, that include an N=2 target space super-Virasoro symmetry. As a microscopic test of the duality, we reproduce the exact form of the Calogero interaction via a string worldsheet calculation.

Abstract: We study RR flux backgrounds in two dimensional type 0 string theories. In particular, we study the relation between the 0A matrix model and the extremal black hole in two dimensions. Using T-duality we find a dual flux background in type 0B theory and propose its matrix model description. When the Fermi level is set to zero this system remains weakly coupled and exhibits a larger symmetry related to the structure of flux vacua. Finally, we construct a two dimensional type IIB background as an orbifold of the 0B background.

Abstract: We present a detailed analysis of the thermodynamics of two dimensional black hole solutions to type 0A with q units of electric and magnetic flux. We compute the free energy and derived quantities such as entropy and mass for an arbitrary non-extremal black hole. The free energy is non-vanishing, in contrast to the case of dilatonic 2-d black holes without electric and magnetic fluxes. The entropy of the extremal black holes is obtained, and we find it to be proportional to q^2, the square of the RR flux. We compare these thermodynamics quantities with those from candidate matrix model duals.

Abstract: We investigate a deformed matrix model proposed by Kazakov this http URL. in relation to Witten's two-dimensional black hole. The existing conjectures assert the equivalence of the two by mapping each to a deformed c=1 theory called the sine-Liouville theory. We point out that the matrix theory in question may be naturally interpreted as a gauged quantum mechanics deformed by insertion of an exponentiated Wilson loop operator, which gives us more direct and holographic map between the two sides. The matrix model in the usual scaling limit must correspond to the bosonic SL(2,R)/U(1) theory in genus expansion but exact in \alpha'. We successfully test this by computing the Wilson loop expectation value and comparing it against the bulk computation. For the latter, we employ the \alpha'-exact geometry proposed by Dijkgraaf, Verlinde, and Verlinde, which was further advocated by Tseytlin. We close with comments on open problems.

Abstract: An exact conformal field theory describing a black hole in two-dimensional space-time is found as an SL(2,openR)/U(1) gauged Wess-Zumino-Witten model. For k=9/4, the conformal field theory can be regarded as a classical solution of the same system that is probed in the c=1 matrix model. The conformal field theory governing the space-time is regular at the Riemannian singularity, but it appears that generic perturbations blow up there. It is argued that the end point of the Hawking black-hole evaporation is the standard space-time of the c=1 matrix model, which should be regarded as an analog of the extreme Reissner-Nordstr\"om black hole of four-dimensional general relativity. The c=1 model is thus a model of the quantum mechanics of matter interacting with a black hole.

Abstract: I review some of the recent progress in two-dimensional string theory, which is formulated as a sum over surfaces embedded in one dimension.

Abstract: We consider unstable D0-branes of two dimensional string theory, described by the boundary state of Zamolodchikov and Zamolodchikov [36] multiplied by the Neumann boundary state for the time coordinate t. In the dual description in terms of the c = 1 matrix model, this D0-brane is described by a matrix eigenvalue on top of the upside down harmonic oscillator potential. As suggested by McGreevy and Verlinde [25], an eigenvalue rolling down the potential describes D-brane decay. As the eigenvalue moves down the potential to the asymptotic region it can be described as a free relativistic fermion. Bosonizing this fermion we get a description of the state in terms of a coherent state of the tachyon field in the asymptotic region, up to a non-local linear field redefinition by an energy-dependent phase. This coherent state agrees with the exponential of the closed string one-point function on a disk with Sen's marginal boundary interaction for t which describes D0-brane decay.

Abstract: We consider two dimensional supergravity coupled to $\hat c=1$ matter. This system can also be interpreted as noncritical type 0 string theory in a two dimensional target space. After reviewing and extending the traditional descriptions of this class of theories, we provide a matrix model description. The 0B theory is similar to the realization of two dimensional bosonic string theory via matrix quantum mechanics in an inverted harmonic oscillator potential; the difference is that we expand around a non-perturbatively stable vacuum, where the matrix eigenvalues are equally distributed on both sides of the potential. The 0A theory is described by a quiver matrix model.

Abstract: We show that after integrating over the zero mode in Liouville correlation functions, the remaining functional integral resembles a free theory and may be evaluated by formally continuing the central charge We apply this technique to the unitary minimal models coupled to gravity on the sphere, computing a number of three-point functions After taking into account the normalizations of operators and the functional integral, we find exact agreement between the Liouville three-point functions and the results from matrix models