This series consists of talks in the area of Superstring Theory.
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.
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.
I am going to discuss applications of String/M/F theory dualities to argue about the toroidal compactification to four dimensions of 6d (1,0) theories.
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.
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.
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.
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.