Quantum Fields and Strings

As an alternative to the Holographic Renormalization procedure, we

introduce a regularization scheme for AdS gravity based on the addition

boundary terms which are a given polynomial of the extrinsic and 

intrinsic curvatures (Kounterterms).

Since these terms are closely related to either topological invariants 

or Chern-Simons densities in the corresponding dimension, they can be 

easily generalized to other gravity theories (Einstein-Gauss-Bonnet, 

Lovelock, etc.).

Finally, a general prescription on how to obtained the standard 

counterterm series in AdS gravity is given.​ 

Via the AdS/CFT correspondence, fundamental constraints on the entanglement structure of quantum systems translate to constraints on spacetime geometries that must be satisfied in any consistent theory of quantum gravity. In this talk, we describe some of the constraints arising from strong subadditivity and from the positivity and monotonicity of relative entropy. Our results may be interpreted as a set of energy conditions restricting the possible form of the stress-energy tensor in consistent theories of Einstein gravity coupled to matter."

The moduli space of k G instantons on C^2, where G is a classical gauge group, has a well known HyperKahler quotient formulation known as the ADHM construction. The extension to exceptional groups is an open problem.
In string theory this is realized using a system of branes, and the moduli space of instantons is identified with the Higgs branch of a particular supersymmetric gauge theory with 8 supercharges.
A less known, and less studied aspect of moduli spaces of instantons is that they can be realized as the Coulomb branch of a supersymmetric gauge theory in 2+1 dimensions.
Recent developments on the understanding of the Coulomb branch gives us a nice solution to the problem where G is an exceptional group, thus allowing a systematic study of these moduli spaces which was unavailable so far.
I will discuss these developments, and present the corresponding quivers, and the Coulomb branch Hilbert Series - the main tool which lead to the recent progress.

Recent research has suggested deep connections between geometry and entropy. This connection was first seen in black hole thermodynamics, but has been more fully realized in the Ryu-Takayanagi proposal for calculating entanglement entropies in AdS/CFT. We suggest that this connection is even broader: entropy, and in particular compression, are the fundamental building blocks of emergent geometry. We demonstrate how spatial geometry can be derived from the properties of a recursive compression algorithm for the boundary CFT. We propose a general algorithm for constructing MERA-like tensor networks and elucidate connections to the mathematical field of integral geometry.