Lectures on Superconformal Quantum Mechanics and Multi-Black Hole Moduli Spaces

This review is based on lectures given at the 1992 Trieste Spring School on String Theory and Quantum Gravity and at the 1992 TASI Summer School in Boulder, Colorado.

We explore the relationship between classical quasinormal mode frequencies and black hole quantum mechanics in 2+1 dimensions. Following a suggestion of Hod, we identify the real part of the quasinormal frequencies with the fundamental quanta of black hole mass and angular momentum. We find that this identification leads to the correct quantum behavior of the asymptotic symmetry algebra, and thus of the dual conformal field theory. Finally, we suggest a further connection bet...

We summarize our work on spherically symmetric midi-superspaces in loop quantum gravity. Our approach is based on using inhomogeneous slicings that may penetrate the horizon in case there is one and on a redefinition of the constraints so the Hamiltonian has an Abelian algebra with itself. We discuss basic and improved quantizations as is done in loop quantum cosmology. We discuss the use of parameterized Dirac observables to define operators associated with kinematical varia...

The motion of a particle near the RN black hole horizon is described by conformal mechanics. Models of this type have no ground state with vanishing energy. This problem was resolved in past by a redefinition of the Hamiltonian which breaks translational time invariance but gives a normalizable ground state. We show that this change of the Hamiltonian is a quantum mechanical equivalent of the change of coordinates near the black hole horizon removing the singularity. The new ...

In these lectures we discuss N-extended conformal supergravity and its spectrum in four dimensions. These theories can be considered as the massless limit of Einstein-Weyl supergravity and by taking into account their enhanced gauge symmetries, we derive their massless spectrum, which in general contains a dipole-ghost graviton multiplet and an N-fold tripole-ghost gravitino multiplet.

It is well known that an identical pair of extremal Reissner-Nordstrom black holes placed a large distance apart will exert no force on each other. In this paper, I establish that the same result holds in a very large class of two-derivative effective theories containing an arbitrary number of gauge fields and moduli, where the appropriate analog of an extremal Reissner-Nordstrom black hole is a charged, spherically symmetric black hole with vanishing surface gravity or vanis...

In this paper we summarize "loop quantum gravity" (LQG) and we show how ideas developed in LQG can solve the black hole singularity problem when applied to a minisuperspace model.

Lectures given at International School of Physics ``Enrico Fermi'', Varenna, Villa Monastero, June 28-July 7 1994

We study string theory in the background of a two-dimensional black hole which is described by an $SL(2, R)/U(1)$ coset conformal field theory. We determine the spectrum of this conformal field theory using supersymmetric quantum mechanics and give an explicit form of the vertex operators in terms of the Jacobi functions. We also discuss the applicability of SUSY quantum mechanics techniques to non-linear $\sigma$-models.

These lectures notes are based on courses given at National Taiwan University, National Chiao-Tung University, and National Tsing Hua University in the spring term of 2015. Although the course was offered primarily for graduate students, these lecture notes have been prepared for a more general audience. They are intended as an introduction to conformal field theories in various dimensions, with applications related to topics of particular interest: topics include the conform...