String Theory Seminar  

Breakthroughs in numerical relativity (around 2005) have allowed a tremendous progress in solving the two body problem in general relativity. It is now possible to follow the inspiral, merger and ringdown phases of a binary black hole spacetime, extract accurate wave forms for the gravitational radiation emitted and learn new phenomena, like black hole kicks. It has also been possible to study high energy black hole scattering, and obtain the ratio of energy converted into gravitational radiation and the cross section for black hole formation. In this talk I shall describe the very first steps to apply the same type of techniques to high energy physics scenarios suggested by string theory: namely TeV gravity, the AdS/CFT duality and the study of the non-linear evolution of higher dimensional unstable black hole spacetimes.

Video Talk by Ludwig Faddeev @ IGST 2008

Video Talk by Boris Pioline @ Strings 2008

Video Talks by Freddy Cachazo and Simeon Hellerman @ Strings 2008

In this work, we propose a new non-Abelian generalization of the Born-Infeld Lagrangian. It is based on a geometrical property of the Abelian Born-Infeld Lagrangian in its determinantal form. Our goal is to extend the Abelian second type Born-Infeld action to the non-Abelian form preserving this geometrical property, which permits us to compute the generalized volume element as a linear combination of the components of metric and the Yang-Mills energy-momentum tensors. Under the BPS-like condition, the action proposed reduces to that of the Yang-Mills theory, independently of the gauge group. New instanton-wormhole solution and static and spherically symmetric solution in curved spacetime for an SU(2) isotopic ansatz are solved and the N = 1 supersymmetric extension of the model is performed. The uniqueness of the theory from the physical and geometrical point of view is discussed in the light of new results obtained.

Critical gravitational collapse has been a central subject in numerical general relativity for a long time. In this talk I will review the basic ideas of critical gravitational collapse and discuss the possible relevance of this phenomenon in the context of holography. In particular, I will discuss critical formation of trapped surfaces resulting from the collision of gravitational waves in AdS and its holographic implications.

Video Talks by Andrew Strominger and Ashoke Sen @ Strings 2008;

Video Talks by Marcos Mariño and Nathan Berkovits @ Strings 2008;

I describe four dimensional $N=2$ supersymmetric gauge theory in the Omega-background with the two dimensional $N=2$ super-Poincaré invariance. I explain how this gauge theory provides the quantization of the classical integrable system underlying the moduli space of vacua of the ordinary four dimensional $N=2$ theory. This four dimensional gauge theory in its low energy description has two dimensional twisted superpotential which becomes the Yang-Yang function of the integrable system. I present the thermodynamic-Bethe-ansatz like formulae for this Yang-Yang function and for the spectra of commuting Hamiltonians following the direct computation in gauge theory. Particular examples of the many-body systems include the periodic Toda chain, the elliptic Calogero-Moser system, and their relativistic versions. Gauge theory gives a complete characterization of the $L^2$-spectrum for these integrable systems.

Video Talks by Matthias Staudacher and Romuald Janik @ Strings 2008;

This talk is about recent and on-going work on classical string solutions relevant for the AdS/CFT correspondence. The focus is on properties which change when translating from the old N=4 super-Yang-Mills case (with strings on ${\mathrm{AdS}}_{5}x{S}^5$) to the recent case involving the super-Chern-Simons-matter theory of ABJM and strings on ${\mathrm{AdS}}_{4}x{\mathrm{CP}}^3$. The two cases have many similar features, but always with extra complications in the new one.

I will discuss a general formalism to compute non-perturbative corrections to the low energy effective action in Calabi-Yau compactifications with N=2 supersymmetry. I will describe how a detailed analyis of the instanton effects can support some recent conjectures on the quantum structure of the hypermultiplet moduli space.

Video Talks by Zvi Bern and Barton Zwiebach @ Strings 2007

Video Talks of Emparan and Witten @ Strings 2007

The random matrix theory can be used to solve a problem of enumerative geometry: counting maps of arbitrary genus, i.e. counting surfaces composed of polygons glued by their edges. This issue has been extensively investigated by physicists for its possible applications such as quantum gravity. Following the work of Eynard, it was possible to compute such generating functions for different matrix models using a unique recursive procedure: a topological recursion allowing to build the generating function of surfaces with fixed Euler characteristic out of generating functions of surfaces with bigger Euler characteristic. The blind application of the same procedure to more general problems of enumeration such as topological string theories, Weyl-Peterson volume of moduli space of surfaces or Kontsevich-Witten theorem, proved to be very successful: one just has to change the basis ingredient of the procedure to go from one problem to the other, a plane curve referred to as the spectral curve to reflect it originates from integrable properties of the model considered. In this non-technical talk, I will give an overview of this procedure and its applications in mathematics and physics. I will also give a foretaste of the numerous open questions arising from these works.

Video Talks of Beisert and Zarembo @ Strings 2007

Exploring the characteristic features of emergence and identifying how the macro phenomena could be affected by different classes of hypothetical micro-theories are the challenges we face in this new paradigm. Two central issues are nonlocality and stochasticity. Noise can seed emergent structures and determine macroscopic forms. Nonlocality appears when one tries to translate physics expressed in one set of collective variables suitable for one level of structure to another set. We begin with the notion of nonlocality commonly associated with EPR experiment. We present results in the evolution of entanglement between two oscillators analyzed in a field theoretical context. We then show how nonlocality is linked with stochasticity in nonequilibrium dynamics: Nonlocal dissipation and nonlocal fluctuations (colored noise) arise naturally in the open-system dynamics of Langevin and the effectively-open system dynamics of Boltzmann, and the dynamics of correlation (BBGKY) hierarchy. These features originate from the choice of coarse-graining measures and backreaction processes. We analyze these two key issues in the context of strongly correlated systems which we believe are generic properties in any theory for the microscopic structure of spacetime, viz, quantum gravity.

Quantum gravity is a theory for the microscopic structure of spacetime. We challenge a half-century old supposition and practice that quantizing general relativity will produce such a theory. In our view general relativity is an effective theory valid only at the long wavelength, low energy limits, and the metric and connection forms are collective variables. Quantizing them will only lead to the equivalent of phonon dynamics of crystal lattices, not quantum electrodynamics of electrons and photons. The challenge of this new paradigm is to find ways to unravel the underlying microscopic structures from observed macroscopic phenomena (many to one relation), not unlike deducing the molecular constituents from hydrodynamics and kinetic theory, or universalities of microscopic theories from critical phenomena. We explore this `bottom-up’ approach, focusing on the foundational issues in quantum-classical and micro-macro interfaces, using ideas of nonequilibrium statistical mechanics and techniques from quantum field theory for strongly correlated systems, identifying the relation of gravity with matter fields.

Recent progress in the theory of (super)gravity has made it possible to calculate the entropy of certain black holes beyond the area law of Bekenstein and Hawking in a large charge expansion. I will first review this in the context of string theory. I will then present my own recent and ongoing work on the following interrelated questions:

1. How to compute and understand exponentially suppressed contributions to the black hole entropy?
2. How to compute the density of states of a conformal field theory in a regime far away from the Cardy regime?
3. How does one understand the entropy when there is an issue of wall-crossing in the moduli space?

The answers involve an interplay of physics and mathematics - in particular, newly discovered number theoretic objects called mock modular forms.

It has been seen that semi-classical string solutions play a major role in the study of the string/gauge correspondence. Giant magons are a particular set of these solutions, which are intimately related to sine-Gordon solitons. Considered to be the basic solitons of classical strings in the ${\mathrm{AdS}}_5\times S^5$ background, giant magnons are the building blocks one can use to understand other string solutions. The theory of classical strings in both ${\mathrm{AdS}}_5\times S^5$ and ${\mathrm{AdS}}_4\times {\mathrm{CP}}^3$ backgrounds is integrable, and the problem of finding the spectrum of solutions can be described by a Riemann-Hilbert problem in the so called Algebraic Curve formalism. This talk will focus on the use of the Algebraic Curve formalism to study the spectrum of these string solitons, first in the simpler case of ${\mathrm{AdS}}_5\times S^5$, and then in the much richer ${\mathrm{AdS}}_4\times {\mathrm{CP}}^3$ case.