The Black Hole S-Matrix from Quantum Mechanics

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Abstract

We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory \& \(c=1\) Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model\textemdash of waves scattering off inverted harmonic oscillator potentials\textemdash that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.

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Liouville Field Theory -- A decade after the revolution

Yu Nakayama (2004)

We review recent developments (up to January 2004) of the Liouville field theory and its matrix model dual. This review consists of three parts. In part I, we review the bosonic Liouville theory. After briefly reviewing the necessary background, we discuss the bulk structure constants (the DOZZ formula) and the boundary states (the FZZT brane and the ZZ brane). Various applications are also presented. In part II, we review the supersymmetric extension of the Liouville theory. We first discuss the bulk structure constants and the branes as in the bosonic Liouville theory, and then we present the matrix dual descriptions with some applications. In part III, the Liouville theory on unoriented surfaces is reviewed. After introducing the crosscap state, we discuss the matrix model dual description and the tadpole cancellation condition. This review also includes some original material such as the derivation of the conjectured dual action for the N = 2 Liouville theory from other known dualities and the comparison of the Liouville crosscap state with the c = 0 unoriented matrix model. This is based on my master's thesis submitted to Department of Physics, Faculty of Science, University of Tokyo on January 2004.