I will describe on -going work towards understanding holography in two -dimensional deSitter space. The hologram we consider is an SYK-like spin model which lives on the future space-like boundary.
The long time behaviour of a quantum chaotic system may be described using a random matrix theory, which for certain systems is dual to a 2D gravity model that allows for the creation and annihilation of baby universes. In this talk I will present a field theory of closed topological strings, known as Kodaira-Spencer theory whose perturbative expansion reproduces the correlation functions of the matrix-theory and 2D gravity theory. To correctly describe the very long time behaviour of the correlation functions of the chaotic system one needs to include non-perturbative effects, which in this approach are described in terms of a field theory of open topological strings, known as holomorphic Chern-Simons theory. By including a second non-perturbative saddle one reproduces the characteristic plateau behaviour of the chaotic correlators caused by the discreteness of the energy eigenvalues.
The main purpose of this talk is to urge us to more carefully consider how random matrix models capture theories of 2D gravity. The key is to emphasize a Wignerian view alongside the more standard ’t Hooftian approach used in this area. A central observation is that without doing so, the usual narratives about the physics are incomplete. The results prompt a proposal for a complete overhaul of how we think about the subject, and an immediate consequence is a new proposed duality that makes holography for JT gravity (and probably other 2D gravities) much more like traditional holography in other dimensions. This provides a simple solution to the factorization puzzle, and opens up some interesting avenues of research.
I will explore different aspects of unitarity in expanding cosmologies. First, I will argue that time evolution in quantum mechanics is always isometric, in the sense of preserving inner products, but not necessarily unitary. Evidence for this hypothesis can be seen in several technically and conceptually distinct examples. I will also discuss models of emergent unitary in low-dimensional gravity, and explain connections to recent work on wormholes and the factorization paradox in AdS/CFT.
In holographic duality an eternal AdS black hole is described by two copies of the boundary CFT in the thermal field double state. We provide explicit constructions in the boundary theory of infalling time evolutions which can take bulk observers behind the horizon. The constructions also help to illuminate the boundary emergence of the black hole horizons, the interiors, and the associated causal structure. A key element is the emergence, in the large N limit of the boundary theory, of a type III_1 von Neumann algebraic structure from the type I boundary operator algebra and the half-sided modular translation structure associated with it.
In renormalization group (RG) flow, the low energy states form a code subspace that is protected against the local short-distance errors. we will discuss the similarities and differences between this approximate error correction code and the classical and quantum codes that appear in the degenerate vacua of local many-body quantum systems. We will consider continuous MERA as a concrete example and discuss how well the low-energy operators are protected. We will argue that at large N and large gap the approximate error correction code becomes exact.
We analytically compute the quantum field theory entanglement and Renyi entropies of the Dirac fermions on 2 dimensional torus in the presence of background gauge fields. Chemical potential, current source, and topological Wilson loop are unified in a single framework by exhausting all the ingredients of the electromagnetic vertex operators of Zn orbifold conformal field theory. Surprisingly, in infinite space, these entropies become exact and depend only on the Wilson loop. By employing different normalizations for different topological sectors, we manage to get non-singular entanglement entropy. On a circle, we resolve to find the entropies subtly dependent on the chemical potential at zero temperature, which is useful for probing the ground state energy levels of quantum systems.
We consider the backreaction of the winding zero mode on the cigar geometry. We focus on the case of the $SL(2,R)_k/U(1)$ cigar associated with e.g. the near-horizon limit of k NS5 black-branes. We solve the equations of motion numerically in the large k limit as a function of the amplitude of the winding mode at infinity. We find that there is a critical amplitude $A_c=\exp(-\gamma/2)$ that admits a critical solution. In string theory, the exact CFT description of the $SL(2,R)_k/U(1)$ cigar, fixes completely the winding amplitude, $A_s$, at infinity. We find that in the large $k$ limit there is an exact agreement $A_c=A_s$. The critical solution is a cigar with a puncture at its tip; consequently, the black hole entropy is carried entirely by the winding condensate. We comment on the Lorentzian interpretation of the solution.
The revolutionary discovery of gravitational waves has opened an unprecedented experimental window into the Universe. The fact that the relevant physics is often out of equilibrium offers a golden opportunity for holography to make a unique impact on astrophysics and cosmology. I will review recent progress in this direction, with a focus on cosmological phase transitions. In particular, I will describe a recently discovered GW-production mechanism. I will also discuss a new holographic framework to describe strongly coupled matter coupled to dynamical gravity. If time permits, I will briefly mention possible applications to thermal inflation, primordial black holes, (p)reheating, baryogenesis, turbulence, cosmic strings and spacetime singularities. No prior knowledge of string theory or holography required.
