Quantum Fields and Strings

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.

The 4D rotating black hole described by the Kerr geometry possesses many of what was called by Chandrasekhar "miraculous" properties. Most of them are related to the existence of a fundamental hidden symmetry of a principal conformal Killing-Yano (PCKY) tensor. In my talk I shall demonstrate that hidden symmetry of the PCKY tensor plays exceptional role also in higher dimensions. Namely, I shall present the most general spacetime admitting the PCKY tensor and show that is possesses the following properties: 1) It is of the algebraic type D and admits the Kerr-Schild form 2) It allows a separation of variables for the Hamilton-Jacobi, Klein-Gordon, Dirac, and stationary string equations. 3) When the Einstein equations with the cosmological constant are imposed the metric describes the most general known (spherical) Kerr-NUT-AdS black hole spacetime. I will also discuss the generalization of Killing-Yano symmetries for spacetimes with natural "torsion 3-form", such as the black hole of D=5 minimal supergravity, or the Kerr-Sen solution of heterotic string theory, and comment on connection to special Riemannian manifolds admiting Killing spinors.

ABJM theory is a world-volume theory for an arbitrary number of M2-branes. One of the unique features of ABJM theory is its characteristic scaling behaviour, exhibited for example by the free energy and correlation functions of chiral primary operators. In more detail, ABJM theory has a holographic dual where thermodynamics at strong coupling is determined by a system of black M2-branes. The zero-coupling (black-body radiation) free energy disagrees with the strong coupling result. Even the scaling in the 't Hooft coupling is different (strongly suppressed at strong coupling). It is therefore important to check that the weak and strong coupling results converge as loop corrections are taken into account. The leading order computation indeed confirms that the first correction goes in the right direction.

We describe a classification of 4d N=2 superconformal theories obtained from the compactification of 6d N=(2,0) A_N theories on punctured Riemann surfaces. We show the basic building blocks to construct any such theory and its various S-dual frames. A host of new S-dualities and interacting (non-Lagrangian) superconformal theories are unconvered. We also compute various properties of these interacting superconformal theories.

I will discuss a novel approach to time-dependent background fields of string theory, which allows the identification of configurations which satisfy the conformal invariance conditions to all orders in the Regge slope parameter alpha'. I will present a graviton, dilaton and tachyon configuration which is a resummation of all orders in the Regge slope and is shown to satisfy the conformal invariance conditions order by order, to all orders in alpha', up to field redefinitions which do not change the dependence of the fields on the target space-time coordinates, due to a property termed as "homogeneity" of the Weyl anomaly coefficients. It describes an inflationary universe in the sigma-model frame, while in the Einstein frame it corresponds either to a de Sitter or to a power-law universe, depending on the values of the dilaton and the tachyon amplitudes. Possible ways to connect these different solutions, which may correspond to different epochs of the universe, will also be discussed.

Gauge/gravity duality, a concept which emerged from string theory, holds promise for revealing the secrets of certain strongly interacting real world condensed matter systems. Historically, string theorists presented their subject as a promising framework for a quantum theory of gravity. More recently, the AdS/CFT correspondence and gauge/gravity dualities have emerged as powerful tools for using what we already know about gravity to investigate the properties of strongly interacting field theories. I will cherry pick and discuss a few recent developments where black holes are used to calculate the thermodynamic and transport properties of quantum critical systems, superconductors, and superfluids.

N=8 supergravity in 4 dimensions exhibits a surprisingly favorable UV behavior -- it is known from explicit computations that the 4-point amplitudes in N=8 supergravity are finite up to 4-loop order. I explain how a "matrix-element approach" can be used to study candidate counterterms for UV divergences in this theory. This approach both demystifies the finiteness found in previous computations, and predicts finiteness of arbitrary n-point amplitudes in N=8 supergravity below the 7-loop order. It also points to the 7-loop 4-point amplitude as the first amplitude whose finiteness is not guaranteed by any known symmetry of the theory.