Towards Hamiltonian String Field Theory, and Dirichlet Walls
I will present preliminary work towards formulating string field theory in a Hamiltonian (equal time slice) formalism. This problem is closely related (via a Wick rotation) to the problem of finding consistent End-Of-The-World boundary conditions for string scattering, in which the metric satisfies Dirichlet boundary conditions (rather than Neumann). In defining the transition amplitudes, two fundamental problems arise: (i) string worldsheets have tadpoles which transgress across the boundary infinitely often, and (ii) when a string does cross the boundary, it can cross multiple times. However, I believe that both of these problems can be overcome (at least at tree level) by clever resummation tricks.
Entanglement and geometric transitions in topological string theory
In this talk, we revisit the computations of entanglement entropy in topological string theory from the point of view of quantum group operator algebras and the notion of a q-tracial state. In this setup, D brane amplitudes play the role of closed string wavefunctions, which belong to the large N Hilbert space of a worldvolume Chern Simons theory. We explain how closed strings factorize into ``subregion" open strings that live on a different background than the closed strings. The entangling of these open strings involves a geometric transition that produces the closed string background. We explain how this arises from a local notion of holography.
Entanglement entropy in string theory and the Lorentzian FZZ correspondence
Black Hole Entropy from String Entanglement
We discuss the notion of string entanglement in string theory, whichaims to study entanglement between worldsheet Hilbert spaces rather thanentanglement between spacetime Hilbert spaces defined on a time slice in spacetime. Applying this framework to the FZZ duality and its extension to a three-dimensional black hole, we argue that the thermal entropy of 2d and 3d black holes is accounted for by the string entanglement entropy between folded strings arising in the dual sine-Liouville CFT. We compute this via a worldsheet replica method and show that it decomposes into two parts, which we call the vertex operator contribution and the replica contribution. The former can be evaluated analytically and is shown to coincide with the black hole thermal entropies in the low temperature limit in large D dimensions. Although a computation of the latter is left as an open problem, we present evidence that it captures the remaining portion of the black hole entropy.
Stringy Information and de-Sitter Entropy
Emergent Mixed States for Baby Universes
Euclidean preparations have been proposed in the literature that may possibly create a baby universe entangled with an asymptotically Anti de Sitter world. Based on standard reasoning about wormholes, such constructions never have a large N limit. This avoids paradoxes that have been suggested in the literature.
(Based on joint work with J. Kudler-Flam.)
Horizon Edge Modes in Λ > 0 Quantum Gravity
One-loop studies of de Sitter thermodynamics revealed universal codimension-2 “edge” degrees of freedom on the cosmic horizon of a static patch. I will show how to determine their spectra for fields of arbitrary mass and spin. For the graviton, we identify these modes as geometric fluctuations of the cosmic horizon, an interpretation that also persists in the static Nariai black hole. For higher-spin gauge fields, the edge spectra reveal patterns of shift symmetries, pointing to a symmetry-breaking phenomenon.