We study the quantum connection in positive characteristic for conical symplectic resolutions. We conjecture the equivalence of the p-curvature of such connections with (equivariant generalizations of) quantum Steenrod operations of Fukaya and Wilkins. The conjecture is verified in a wide range of examples, including the Springer resolution, thereby providing a geometric interpretation of the p-curvature and a full computation of … Read More
Abstract:The double-scaled limit of the SYK model takes the number of fermions and their interaction number to infinity in a coordinated way. In this limit, two entangled copies of the SYK model have a bulk description of sorts known as the “chord Hilbert space.” We analyze a symmetry algebra acting on this Hilbert space, generated by the two Hamiltonians together … Read More
Abstract: Spacetime inversion symmetries such as parity and time reversal play a central role in physics, but they are usually treated as global symmetries. In quantum gravity there are no global symmetries, so any spacetime inversion symmetries must be gauge symmetries. In particular this includes CRT symmetry (in even dimensions usually combined with a rotation to become CPT), which in … Read More
Abstract: Two-dimensional chiral/holomorphic quantum field theories serve as an arena where exact algebraic techniques offer a great deal of control over the spectrum of the theory. The underlying algebraic structure, known as a vertex algebra or vertex operator algebra, has seen countless applications ranging from superstring theory and pure mathematics to statistical and condensed matter physics. In this talk I … Read More
Abstract: The construction of de Sitter vacua remains a core problem for string theory. A leading proposal, put forth 20 years ago by Kachru, Kallosh, Linde, and Trivedi, calls for the insertion of antibranes into a supersymmetric AdS vacuum with a conifold. In this talk, we provide evidence for the existence of such vacua. We begin by constructing the first … Read More
Abstract: Theories with spontaneously broken conformal symmetry are ubiquitous in models for new physics, with examples including composite Higgs and conformal dark sectors. These models require a mechanism to stabilize the scale of symmetry breaking. Moreover, the stabilization mechanism affects the phenomenology of the dilaton, the pseudo-Goldstone boson of broken scale invariance, as well as the conformal phase transition. I … Read More
Abstract: Fixed point Floer cohomology of a symplectic automorphism categorifies the Lefschetz trace formula. On the categorical side, twisted Hochschild homology of an automorphism on an A infinity category can be understood as a categorical trace. I will explain how the twisted open-closed maps are used to relate these two invariants in the setting of Fukaya categories of Landau-Ginzburg models. … Read More
Abstract: We show that a generic extremal black hole in AdS is singular. In four dimensions, the horizon is replaced by a mild null singularity. That leaves significant imprints on the BH thermodynamics at sufficiently low temperatures. In five dimensions, that singularity becomes more serious. In particular, it makes RN AdS an unstable IR fixed point. Many new fixed points … Read More
Abstract: Zhenbin Yang and I proposed that wormhole effects can turn very old black holes into white holes (firewalls). Checking the proposal has been difficult due to the lack of a good definition of the infalling observer. I will describe the setup and some of the subtleties. Bio: I am an Associate Professor at Stanford University.
Abstract: Like many physical objects, under smallperturbations, black holes possess the property of vibrating at discretecharacteristic frequencies (known as QNM frequencies). They are complex anddepend on the type of black hole and the boundary conditions imposed on theperturbation. As we anticipate “hearing” these frequenciesthrough new experiments more distinctly, it becomes essential to understandtheir mathematical structure better or, in other words, … Read More