A View of 2-DIM. String Theory and Black Holes

Modern Physics Letters A, 1992

We discuss the classical two-dimensional black hole in the framework of the non-perturbative formulation (in terms of non-relativistic fermions) of c=1 string field theory. We identify an off-shell operator whose classical equation of motion is that of tachyon in the classical graviton-dilaton black hole background. The black hole ‘singularity’ is identified with the Fermi surface in the phase space of a single fermion, and as such is a consequence of the semiclassical approximation. An exact treatment reveals that stringy quantum effects wash away the classical singularity.

String Theory, Gauge Theory and Quantum Gravity '93, 1994

Nuclear Physics B - Proceedings Supplements, 2002

The IKKT or IIB matrix model has been proposed as a non-perturbative definition of type IIB superstring theories. It has the attractive feature that space-time appears dynamically. It is possible that lower dimensional universes dominate the theory, therefore providing a dynamical solution to the reduction of space-time dimensionality. We summarize recent works that show the central role of the phase of the fermion determinant in the possible realization of such a scenario.

Physical Review D, 2007

The matrix model formulation of two dimensional string theory has been shown to admit time dependent classical solutions whose closed string duals are geodesically incomplete space-times with space-like boundaries. We investigate some aspects of the dynamics of fermions in one such background. We show that even though the background solution appears pathological, the time evolution of the system is smooth in terms of open string degrees of freedom, viz. the fermions. In particular, an initial state of fermions evolves smoothly into a well defined final state over an infinite open string time interval, while the time perceived by closed strings appears to end abruptly. We outline a method of calculating fermion correlators exactly using symmetry properties. The result for the two point function is consistent with the semiclassical picture.

Nuclear Physics B, 1994

We invesigate how the exact 2D black-hole solution for the critical string theory should be described, at least perturbatively with respect to the inverse mass of the black hole, within the framework of matrix model. In particular, we propose a working hypothesis on the basis of which we can present plausible candidates for the necessary non-local field redefinition of the tachyon field and the deformation of the usual c = 1 matrix model with µ = 0. We exhibit some marked difference in the properties of tachyon scattering of the deformed model from those of the usual c = 1 model corresponding to tachyon condensation. These results lead to a concrete proposal for the S-matrix for the tachyon

String Theory and Quantum Gravity'92

We apply the method of coadjoint orbits of \winf-algebra to the problem of non-relativistic fermions in one dimension. This leads to a geometric formulation of the quantum theory in terms of the quantum phase space ...

Arxiv preprint hep-th/9211085, 1992

We discuss the basic features of the double scaling limit of the one dimensional matrix model and its interpretation as a two dimensional string theory. Using the collective field theory formulation of the model we show how the fluctuations of the collective field can be interpreted as the massless "tachyon" of the two dimensional string in a linear dilaton background. We outline the basic physical properties of the theory and discuss the nature of the Smatrix. Finally we show that the theory admits of another interpretation in which a certain integral transform of the collective field behaves as the massless "tachyon" in the two dimensional string with a blackhole background. We show that both the classical background and the fluctuations are non-singular at the black hole singularity.

Nuclear Physics B, 2002

We construct and study a matrix model that describes two dimensional string theory in the Euclidean black hole background. A conjecture of V. Fateev, A. and Al. Zamolodchikov, relating the black hole background to condensation of vortices (winding modes around Euclidean time) plays an important role in the construction. We use the matrix model to study quantum corrections to the thermodynamics of two dimensional black holes.

International Journal of Modern Physics D, 1992

We examine the two-dimensional spacetimes that emerge from string theory. We find all of the solutions with no tachyons, and show that the only nontrivial solution is the black-hole spacetime. We examine the role of duality in this picture. We then explore the thermodynamics of these solutions which is complicated by the fact that only in two spacetime dimensions is it impossible to redefine the dilaton field in terms of a canonical scalar field. Finally, we extend our analysis to the heterotic string, and briefly comment on exact, as opposed to perturbative, solutions.

1997

In the Chern-Simons gauge theory formulation of the spinning (2+1) dimensional black hole, we may treat the horizon and the spatial infinity as boundaries. We obtain the actions induced on both boundaries, applying the Faddeev and Shatashvili procedure. The action induced on the boundary of the horizon is precisely the gauged $SL(2,R)/U(1)$ Wess-Zumino-Witten (WZW) model, which has been studied previously