In AdS/CFT the Engelhardt-Wall prescription states that the entanglement entropy of a boundary subregion is given by the generalized entropy of a minimal quantum extremal surface. Since quantum extremal surfaces are not constrained to one time slice proving certain consistency conditions such as strong subadditivity has remained an open problem. We formulate a quantum generalization of maximin surfaces and show … Read More
Abstract: In a recent paper (1912.05649), my collaborators and I showed that boundary-to-boundary scattering in AdS/CFT is only possible when boundary regions associated with the scattering process have order-1/G_N mutual information. From the perspective of quantum information theory, this happens because the boundary theory needs a macroscopic amount of entanglement to simulate the bulk scattering process. I will explain the … Read More
Originally the notion of Cohomological Hall algebra (COHA for short) was introduced in my joint paper with Maxim Kontsevich (arXiv: 1006.2706) for the purposes of motivic Donaldson-Thomas theory of 3-dimensional Calabi-Yau categories. A physicist can think informally of COHA as of quantized enveloping algebra of the Lie algebra of single-particle closed BPS states. From this point of view there should … Read More
Recently it has been shown that quantum fields can be regular on the inner, Cauchy horizon of a rotating BTZ black hole, which appears to indicate a failure of strong cosmic censorship. We argue that, instead, what these results imply is that the inner horizon remains non-singular when leading-order backreaction of the quantum fields is computed, but, after next-order backreaction … Read More
Abstract: I will discuss several models of evaporating AdS black holes. In all models, it is possible to use the holographic entanglement entropy prescription to compute the dependence of entropy on time. In two cases, the dynamics are unitary, and a semiclassical calculation is sufficient to show this. In the third toy model, the dynamics are manifestly non-unitary; in this … Read More
Abstract: A fundamental issue in the AdS/CFT correspondence is the wormhole growth paradox. Susskind’s conjectured resolution of the paradox was to equate the volume of the wormhole with the circuit complexity of its dual quantum state in the CFT. We study the ramifications of this conjecture from a complexity-theoretic perspective. Specifically we give evidence for the existence of computationally pseudorandom … Read More
We discuss aspects of magnetically charged black holes in the Standard Model. For black holes smaller than a tennis ball, the electroweak symmetry is restored in the near horizon region. The lowest Landau level for the charged fermions leads to a large number effectively light degrees of freedom, which greatly enhance the effects of Hawking radiation. They are interesting primordial … Read More
Abstract: We argue that given holographic CFT1 in some state with a dual spacetime geometry M, and given some other holographic CFT2, we can find states of CFT2 whose dual geometries closely approximate arbitrarily large causal patches of M, provided that CFT1 and CFT2 can be non-trivially coupled at an interface. Our CFT2 states are “dressed up as” states of … Read More
I will explore the idea that certain theories of gravity in Anti-de Sitter space are dual to an average over an ensemble of quantum theories, rather than to a specific quantum theory. I will describe an average over Narain’s family of two-dimensional conformal field theories which describe free bosons on a torus, and compute the partition function using the Siegel-Weil … Read More
Entropy and energy are found to be closely tied on our quest for quantum gravity. We point out an interesting connection between the recently proposed outer entropy, a coarse-grained entropy defined for a compact spacetime domain motivated by the holographic duality, and the Bartnik-Bray quasilocal mass long known in the mathematics community. In both scenarios, one seeks an optimal spacetime … Read More