String Theory: A Framework for Quantum Gravity and Various Applications

In this semi-technical review we discuss string theory (and all that goes by that name) as a framework for a quantum theory of gravity. This is a new paradigm in theoretical physics that goes beyond relativistic quantum field theory. We provide concrete evidence for this proposal. It leads to the resolution of the ultra-violet catastrophe of Einstein's theory of general relativity and an explanation of the Bekenstein-Hawking entropy (of a class of black holes) in terms of Boltzmann's formula for entropy in statistical mechanics. We discuss `the holographic principle' and its precise and consequential formulation in the AdS/CFT correspondence of Maldacena. One consequence of this correspondence is the ability to do strong coupling calculations in SU(N) gauge theories in terms of semi-classical gravity. In particular, we indicate a connection between dissipative fluid dynamics and the dynamics of black hole horizons. We end with a discussion of elementary particle physics and cosmology in the framework of string theory. We do not cover all aspects of string theory and its applications to diverse areas of physics and mathematics, but follow a few paths in a vast landscape of ideas. (This article has been prepared for the TWAS Silver Jubilee)Comment: 38 pages, 5 figures, Article for TWAS Jubilee Publication, References and Comments adde

Black Holes: A Window into A New Theory of Space Time

S. Chandrasekhar wrote in the prologue to his book on black holes, "The black holes of nature are the most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time." In this contribution I briefly discuss recent developments in fundamental theory and black holes that vindicate this statement in a modern perspective. I also include some of my reminiscences of Chandra.Comment: One reference correcte

A microscopic theory of black holes in string theory: thermodynamics and Hawking radiation

In quantum mechanics, black holes behave like black bodies and they emit thermal radiation which is called Hawking radiation. Black hole evaporation leads to the 'information paradox'. In general relativity these properties follow from the fact that a black hole has a horizon. We explain this deep mystery in terms of the quantum statistical mechanics of an underlying microscopic theory. The microscopic degrees of freedom, for the class of black holes we discuss, are given by the collective excitations of a configuration of D-branes which occur in string theory. This article introduces the issues involved and presents a summary of what has been achieved and what more needs to be done

Stringy Quantum Effects in 2-Dimensional Black-Hole

We discuss the classical 2-dim. 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 semi-classical approximation. An exact treatment reveals that stringy quantum effects wash away the classical singularity.Comment: 17p, TIFR/TH/92-63; (v3) tex error correcte

Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models

The Nambu-Goldstone (NG) bosons of the SYK model are described by a coset space Diff/$\mathbb{SL}(2,\mathbb{R})$, where Diff, or Virasoro group, is the group of diffeomorphisms of the time coordinate valued on the real line or a circle. It is known that the coadjoint orbit action of Diff naturally turns out to be the two-dimensional quantum gravity action of Polyakov without cosmological constant, in a certain gauge, in an asymptotically flat spacetime. Motivated by this observation, we explore Polyakov action with cosmological constant and boundary terms, and study the possibility of such a two-dimensional quantum gravity model being the AdS dual to the low energy (NG) sector of the SYK model. We find strong evidences for this duality: (a) the bulk action admits an exact family of asymptotically AdS$_2$ spacetimes, parameterized by Diff/$\mathbb{SL}(2,\mathbb{R})$, in addition to a fixed conformal factor of a simple functional form; (b) the bulk path integral reduces to a path integral over Diff/$\mathbb{SL}(2,\mathbb{R})$ with a Schwarzian action; (c) the low temperature free energy qualitatively agrees with that of the SYK model. We show, up to quadratic order, how to couple an infinite series of bulk scalars to the Polyakov model and show that it reproduces the coupling of the higher modes of the SYK model with the NG bosons.Comment: 2+33 pages (including Appendices), 3 figures; v2 has revised discussion of orbits in Section 2, typos corrected; v3 has a new appendix analysing the off-shell equations of motion; v4 is published version with some more typos corrected; v5 corrects some typesetting error