Quantum Holography and New Symmetries in String Theory – QHNS

An outstanding challenge of modern physics is to unify General Relativity and Quantum Mechanics into a consistent framework. String theory is an important step towards this goal. It offers a coherent framework that overcomes the perturbative divergences that plagued previous attempts to quantize gravity and which naturally incorporates quantum gauge theories that can describe all other non-gravitational forces. Moreover, the study of black holes, dualities, and holography has led to substantial evidence about the nonperturbative consistency of the theory.

However, there are two major hurdles in making further progress.
1) Even though we have some idea about the dynamics of string theory, we do not know which phase (compactification) of the theory may correspond to the real world.
2) We do not possess a powerful enough microscope, such as a super-LHC, that can directly access the short distance UV structure of the theory.

To make further progress we need new ideas. A productive research strategy is to focus on universal features that must hold in all phases of the theory and to use statistical reasoning to learn indirectly about the UV properties from the IR properties. One such requirement is that thermodynamic IR properties of a black hole must have statistical interpretation in terms of an ensemble of quantum states. It is a universal and highly stringent requirement since it must hold in all phases and for all black holes. Much of earlier work on the subject has been in the limit when the size of the black hole (or the area of the event horizon) is large which corresponds to classical gravity. The subleading finite size quantum corrections to the entropy are extremely interesting precisely as an IR window into the UV physics. Our goal will be to study these finite size quantum corrections to probe the short distance structure of the theory. There is a natural extension of these questions to black branes (an extended membrane generalization of black holes) and the associated AdS/CFT holography which gives a broader context to frame this enquiry. With this physical guiding principle, our two main organizing principles will be `Quantum Holography’ and `New Symmetries’ as we explain below.

I) Quantum Holography: Holography is one of the most important physical insights to emerge from the study of black holes which implies that the number of degrees of freedom in a quantum theory of gravity scales with area and not with volume as one might naively expect. A concrete realization of holography within string theory has led to the remarkable quantum equivalence between a theory with gravity described by strings moving in Anti de Sitter (AdS) space and a theory without gravity described by conformal quantum field theory (CFT) in one less dimension.

While there is substantial nontrivial evidence for this `AdS/CFT Duality’ over the past decades, much of it is at the level of semi-classical gravity. Our goal will be to develop methods to study AdS/CFT duality at the quantum level.

II) New Symmetries: Recent studies have revealed unexpected new symmetries of string theory. In particular, the nonperturbative spectrum of microstates corresponding to stable black holes in string theory has revealed surprising hints of a symmetry based on Borcherds algebras--a vast generalization of Lie algebras that underlie known gauge symmetries of particle physics. For a large class of black holes, this spectrum of microstates exhibits a `hidden’ modular symmetry and a deep connection with the fascinating mathematics of mock modular forms. Our goal will be to understand the physical origin and implications of these new symmetries.

We will achieve these goals by creatively combining new techniques of localization, topological string theory, worldsheet methods and new mathematics such as mock modular forms. Recent work of the three PIs has already played a leading role in developing these techniques.