This series consists of talks in the area of Superstring Theory.
We compute the exact two-sphere, disk and real projective plane partition functions of two-dimensional supersymmetric theories using the localization technique. From these new results, we will attack old and new important problems in the string theory on Calabi-Yau spaces, and D-branes and Orientifold planes therein.
The dilaton effective action plays a key role for the recent proof of the a-theorem by Schwimmer and Komargodski. In the presence of other massless modes, one may ask if this proof is affected. In particular, in renormalization group (RG) flows with N=1 supersymmetry, there is a natural massless partner of the dilaton, namely an axion field. I will discuss RG flows, the a-theorem, and the form of the N=1 supersymmetric dilaton-axion effective action and its physics.
We investigate far from equilibrium energy transport in strongly coupled quantum critical systems. Combining results from gauge-gravity duality, relativistic hydrodynamics, and quantum field theory, we argue that long-time energy transport after a local thermal quench occurs via a universal steady-state for any spatial dimensionality. This is described by a boosted thermal state. We determine the transport properties of this emergent steady state, including the average energy flow and its long-time fluctuations.
In this presentation, evidence is given that supersymmetrical theories may be exceptional in their ability to conserve information about space-time representations under the impact of dimensional compactification. This is the essence of the concept of ``SUSY Holography.''
The physics of black hole horizons is intimately connected to the physics of quantum liquids. In this talk I will review the connection and draw lessons about quantum turbulence from black hole dynamics and vice versa. For example, gravitational dynamics reveal that quantum turbulence can behave very differently from normal fluid turbulence in 2d, with long-wavelength excitations rapidly dissolving into small fluctuations and dissipating as in a 3d normal liquid.
After giving a brief overview of holographic entanglement entropy formulas, I will explore a curious feature they imply: when the bulk spacetime includes a black hole, the entanglement entropies often appear to depend on the spacetime geometry inside the horizon. I will ask whether this implies any loss of causality in the field theory. To answer this question, I will present a new general-relativity theorem concerning the causal structure of asymptotically AdS spacetimes, which implies an interesting relationship between bulk and boundary causal domains.
Motivated by the cluster structure of two-loop scattering amplitudes in N = 4 Yang-Mills theory we define cluster polylogarithm functions. We find that all such functions of weight 4 are made up of a single simple building block associated to the A2 cluster algebra. Adding the requirement of locality on generalized Stasheff polytopes, we find that these A2 building blocks arrange themselves to form a unique function associated to the A3 cluster algebra.
I will describe progress in deriving 3d gravity directly from 2d conformal field theory at large central charge 'c'. In a large class of CFTs, using general arguments like modular invariance, crossing symmetry, and the OPE expansion, the spectrum, the entanglement entropy, and certain partition functions can be computed to leading order in a 1/c expansion.
In arXiv:0908.4052, Nekrasov and Shatashvili pointed out that the N=2 instanton partition function in a special limit of the Omega-deformation parameters is characterized by certain thermodynamic Bethe ansatz (TBA) like equations.In this talk I will present an explicit derivation of this fact as well as generalizations to quiver gauge theories. The TBA equations derived entirely within gauge theory have been proposed to encode the spectrum of a large class of quantum integrable systems. I will conclude with some remarks on this correspondence.