Quantum Fields and Strings

The gauge/gravity duality may give a nonperturbative formulation of superstring/M theory, and hence, if one can study the nonperturbative dynamics of the gauge theory, it would be useful to understand the nonperturbative aspects of superstring theory. Although researches in this direction were not successful for long time because of the notorious difficulties in lattice SUSY, however, recent progress made it possible; nonperturbative formulations free from the parameter fine-tuning were proposed, some of them are confirmed to work numerically, and nontrivial evidence for the validity of the gauge/gravity duality has been obtained. In these talks I review the state of the art in this field. I start with reviewing basics of the Monte-Carlo. Then I explain how to put supersymmetric theories on computer and show actual numerical results. 1st talk : basics of Monte-Carlo simulation. 2nd talk : 1d SYM (matrix quantum mechanics). 3rd talk : how to put 2d, 3d and 4d SYM on computer. In the talks I concentrate on basic ideas and omit technical details (e.g. algorithms to accelerate simulations). They will be explained after the talks if people are interested in. References: 1st talk : standard textbooks e.g. Heinz J. Rothe, "Lattice Gauge Theories: An Introduction", Third Edition, World Scientific. 2nd talk : 0706.1647 [hep-lat], 0707.4454 [hep-th], 0811.2081 [hep-th], 0811.3102 [hep-th], 0911.1623 [hep-th], 1012.2913 [hep-th]. 3rd talk : hep-lat/0302017, hep-lat/0311021, 1010.2948 [hep-lat] (2d SYM); hep-th/0211139 (3d SYM); 1004.5513 [hep-lat], 1009.0901 [hep-lat] (4d SYM)

We discuss the calculation of higher loop contributions to the anomalous dimensions of operators in N=6 Superconformal Chern-Simons theories. These lead us to conjecture the form of an interpolating function of the 't Hooft coupling that is not determined by integrability.

I will discuss the construction of a holographic dictionary for theories with non-relativistic conformal symmetry, relating the field theory to the dual spacetime. I will focus on the case of Lifshitz spacetimes, giving a definition of asymptotically locally Lifshitz spacetimes and discussing the calculation of field theory observables and holographic renormalization.

What is the gravity dual of a strongly interacting state of matter at zero temperature and finite charge density? The simplest candidates are extremal black holes. The presence of charged matter in the bulk can often mean that extremal black holes are not the ground state. In this talk I will discuss the physics of a class of solutions, essentially charged neutron stars, that can be thermodynamically preferred over extremal black holes.

Mass, a concept familiar to all of us, is also one of the deepest mysteries in nature. Almost all of the mass in the visible universe, you, me and any other stuff that we see around us, emerges from QCD, a theory with a negligible microscopic mass content. How does QCD and the family of gauge theories it belongs to generate a mass? This class of non-perturbative problems remained largely elusive despite much effort over the years. Recently, new ideas based on compactification have been shown useful to address some of these. Two such inter-related ideas are circle compactifications, which avoid phase transitions and large-N volume independence. Through the first one, we realized the existence of a large-class of "topological molecules", e.g. magnetic bions, which generate mass gap in a class of compactified gauge theories. The inception of the second, the idea of large-N volume independence is old. The new progress is the realization of its first working examples. This property allows us to map a four dimensional gauge theory (including pure Yang-Mills) to a quantum mechanics at large-N.

Correlation functions in the gauge-gravity correspondence (AdS/CFT) are dual to scattering amplitudes in anti-de Sitter space (AdS). In this talk, I will describe how techniques that were recently developed to study scattering amplitudes in flat space can be generalized to AdS leading to a new and efficient method of computing correlation functions in AdS/CFT. References: 1) S. Raju, "Generalized Recursion Relations for Correlators in the Gauge Gravity Correspondence", Phys.Rev.Lett. 106 (2011) 091601. http://arxiv.org/abs/arXiv:1011.0780 2) S. Raju, "Recursion Relations for AdS/CFT Correlators", http://arxiv.org/abs/arXiv:1102.4724

I will discuss a holographic model whose low-energy physics may be used to build a marginal Fermi liquid. The model has several interesting features, including (i.) it is embedded in string theory and we possess a Lagrangian description of the field theory, (ii.) it exhibits a first-order transition between the non-Fermi liquid phase and a normal Fermi liquid phase, and (iii.) the model involves a lattice of heavy defects interacting with a sea of propagating fields.

In this talk, I will first give an overview of holographic entanglement entropy. Next I will introduce recent our results on its applications to the quantum quenches and a holography for flat spacetime.

I will describe a method to compute from first principles the anomalous dimension of short operators in N=4 super Yang-Mills theory at strong coupling, where they are described in terms of superstring vertex operators in an anti-de Sitter background. I will focus on the Konishi multiplet, dual to the first massive level of the superstring, and compute the one-loop correction to its anomalous dimension at strong coupling, using the pure spinor formalism for the superstring.