Quantum Fields and Strings

String theory is starting to provide novel all-loop precision tools for the computation of scattering amplitudes in the high energy (HE) limit of N=4 SYM theory. After a review of some key insights and results for hexagon amplitudes, I will describe ongoing developments addressing higher numbers of external gluons.

I will discuss how to classify (up to discrete identifications) all rigid 4D N=2 supersymmetric backgrounds in both Lorentzian and Euclidean signatures that preserve eight real supercharges. These include backgrounds such as warped S_3×R, warped AdS_3×R, and AdS_2×S^2, as well as some more exotic geometries. I will also address how to construct all supersymmetric two-derivative actions involving hypermultiplets and vector multiplets in these backgrounds.

We study 5d and 6d SCFTs with eight supercharges by using 5-brane web diagrams in Type IIB string theory. There are two important properties of the web diagram. One is that it enables us to compute the exact partition function of the 5d theory on the 5-brane web. Even though the web diagram is not dual to a toric geometry, we develop a technique to compute the partition function by using the topological vertex. The other is that a new class of the 5-brane web diagram is conjectured to imply that the corresponding 5d theory has a 6d superconformal fixed point at high energies. Such a web diagram is called Tao web diagram. By using the Tao web diagram, we conjecture new 5d theories whose UV completion is a 6d SCFT. Moreover, we can show that a brane configuration realizing the 6d SCFT may reduce to the Tao web diagram, giving a direct way of identifying the 6d description of the 5d theory. This construction also indicates various dualities of the 5d theories.

Similarly to the probability distribution of energy in physics, the probability distribution of money among the agents in a closed economic system is also expected to follow the exponential Boltzmann-Gibbs law, as a consequence of entropy maximization.  Analysis of empirical data shows that income distributions in the USA, European Union, and other countries exhibit a well-defined two-class structure.  The majority of the population (about 97%) belongs to the lower class characterized by the exponential ("thermal") distribution.  The upper class (about 3% of the population) is characterized by the Pareto power-law ("superthermal") distribution, and its share of the total income expands and contracts dramatically during booms and busts in financial markets.  Globally, data analysis of energy consumption per capita around the world shows decreasing inequality in the last 30 years and convergence toward the exponential probability distribution, in agreement with the maximal entropy principle. Similar results are found for the global probability distribution of CO2 emissions per capita.  All papers are available at http://physics.umd.edu/~yakovenk/econophysics/.  For recent coverage in Science magazine, see http://www.sciencemag.org/content/344/6186/828

I will propose a proof for a monotonicity theorem, or c-theorem, for a three-dimensional Conformal Field Theory (CFT) on a space with a boundary, and for a two-dimensional defect coupled to a higher-dimensional CFT. The proof is applicable only to renormalization group flows that are localized at the boundary or defect, such that the bulk theory remains conformal along the flow, and that preserve locality, reflection positivity, and Euclidean invariance along the defect. The method of proof is a generalization of Komargodski’s proof of Zamolodchikov’s c-theorem. The key ingredient is an external “dilaton” field introduced to match Weyl anomalies between the ultra-violet (UV) and infra-red (IR) fixed points. Reflection positivity in the dilaton’s effective action guarantees that a certain coefficient in the boundary/defect Weyl anomaly must take a value in the UV that is larger than (or equal to) the value in the IR. This boundary/defect c-theorem may have important implications for many theoretical and experimental systems, ranging from graphene to branes in string theory and M-theory.

Based on results in quantum gravity we conjecture a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom. Chaos can be diagnosed using an out-of-time-order correlation function closely related to the commutator of operators separated in time. We conjecture that the influence of chaos on this correlator can develop no faster than exponentially, with Lyapunov exponent λL ≤ 2πkBT/\hbar. We give a precise mathematical argument, based on plausible physical assumptions, establishing this conjecture. 

The concept of quantum entanglement entropy is playing a key role in understanding the mechanism underlying holography. In this talk we will discuss how entanglement can capture non-trivial geometric properties of the bulk spacetime. The goal is to exploit the interplay between anomalies and entanglement entropy, and for concreteness we will focus on AdS3/CFT2.  Anomalies play as well a key role in RG flows, and in this context we will see how entanglement, anomalies and geometry conspire to capture dynamically the correct physics.

A classical Einstein-Rosen bridge changes the topology of spacetime,allowing (for example) electric field lines to penetrate it. It has recently been suggested that in the bulk of a theory of quantum gravity, the quantum entanglement of ordinary perturbative quanta should be viewed as creating a quantum version of an Einstein-Rosen bridge between the quanta, or a “quantum wormhole”. For this “ER=EPR” correspondence to make sense it then seems necessary for a quantum wormhole to allow (for example) electric field lines to penetrate it. I will discuss (within low-energy effective field theory) whether or not this happens.

We review recent versions of the information paradox, framed in the context of the AdS/CFT correspondence. We describe how they can be resolved using "state dependent" bulk to boundary maps for the black hole interior in AdS/CFT. We argue that this feature is necessary not only for single sided black holes but also for the eternal black hole.

We resolve some potential ambiguities in this map. We extend this construction of the black hole interior to entangled systems and show how a version of the ER=EPR conjecture emerges naturally in this process. Finally, we comment on the possible semi-classical origins of state-dependence.

Main properties of generalized contraction methods of Lie algebras, known also as expansion methods, are briefly introduced. Between some of their physical applications, one might study the nature of solutions in theories constructed with those expanded algebras. In particular, as we are interested in solutions that could be relevant in the context of AdS/CFT and Holographic Superconductors, we would like to study the holographic QFT dual to Chern-Simons gravity for an expansion of AdS algebra. As a first step, we studied charged static spherically symmetric BH solutions of a CS theory for the most simple extension of AdS symmetry: AdS×U(1). It is shown that in this kind of higher dimensional gravity, degeneracy in some sectors of the space of solutions can appear. In fact, arbitrary functions remain undetermined after the field equations are imposed. This is related to an increase in local symmetries and it is shown that the knowledge of these "accidental symmetries" can help to formulate a simple criterion that avoids unwanted degenerate ansatze. Finally, main properties of Pure Lovelock gravity are presented and some issues about black hole solutions this theory are also discussed.

In this talk I will discuss the non-equilibrium response of Chern insulators [1]. Focusing on the Haldane model, we study the dynamics induced by quantum quenches between topological and non-topological phases. A notable feature is that the Chern number, calculated for an infinite system, is unchanged under the dynamics following such a quench. However, in finite geometries, the initial and final Hamiltonians are distinguished by the presence or absence of edge modes. We study the edge excitations and describe their impact on the experimentally-observable edge currents and magnetization. We show that, following a quantum quench, the edge currents relax towards new equilibrium values, and that there is light-cone spreading of the currents into the interior of the sample. I will briefly comment on a complementary project to understand non-equilibrium charge transport using gauge-gravity duality and hydrodynamics.

[1] M. D. Caio, N. R. Cooper, M. J. Bhaseen, Quantum Quenches in Chern Insulators, arXiv:1504.01910