This series consists of talks in the area of Superstring Theory.
In this talk I will propose a general correspondence which associates a non-perturbative quantum mechanical operator to a toric Calabi-Yau manifold, and I will propose a conjectural expression for its spectral determinant. As a consequence of these results, I will derive an exact quantization condition for the operator spectrum. I will give a concrete illustration of this conjecture by focusing on the example of local P2.
Using holography, I will describe an approach for understanding the physics of a big bang singularity by translating the problem into the language of the dual quantum field theory. Certain two-point correlators in the dual field theory are sensitive to near-singularity physics in a dramatic way, and this provides an avenue for investigating how strong quantum gravity effects in string theory might modify the classical description of the big bang.
The talk will be based on a work in progress with Stefano Kovacs
(Dublin IAS) and Yuki Sato (Wits University). In a previous work
(arxiv:1310.0016) we have shown that,
in the M-theory regime (large N with the Chern-Simon level k fixed)
of the duality between ABJM theory and M-theory on AdS4 x S7/Zk,
certain monopole operators with large R charges on the gauge theory side
correspond to spherical membranes
(which is in general in non-BPS excited states) in the pp-wave matrix
The analogy between Multi-scale Entanglement Renormalization
Ansatz (MERA) and the spatial slice of three-dimensional anti-de
Sitter space (AdS3) has motivated a great interest in tensor networks
among holographers. I discuss a way to promote this analogy to a
rigorous, quantitative, and constructive relation. A key quantitative
ingredient is the way the strong subadditivity of entanglement entropy
is encoded in MERA and in a holographic spacetime. The upshot is that
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.).
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.
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.
The tt* equations define a flat connection on the moduli spaces of 2d, N=2 quantum field theories. For conformal theories with c=3d, which can be realized as nonlinear sigma models into Calabi-Yau d-folds, this flat connection is equivalent to special geometry for threefolds and to its analogs in other dimensions. I will show that the non-holomorphic content of the tt* equations in the cases d=1,2,3 is captured in terms of finitely many generators of special functions, which close under derivatives. The generators are understood as coordinates on a larger moduli space.