This series consists of talks in the area of Quantum Fields and Strings.
Entanglement entropy quantifies the amount of uncertainty of a quantum state. For quantum fields in curved space, entanglement entropy of the quantum field theory degrees of freedom is well-defined for a fixed background geometry. In this work, we propose a generalization of the quantum field theory entanglement entropy by including dynamical gravity.
Abstract: Large N matrix quantum mechanics are central to holographic duality but not solvable in the most interesting cases. We show that the spectrum and simple expectation values in these theories can be obtained numerically via a `bootstrap' methodology. In this approach, operator expectation values are related by symmetries -- such as time translation and SU(N) gauge invariance -- and then bounded with certain positivity constraints. We first demonstrate how this method efficiently solves the conventional quantum anharmonic oscillator.
We investigate putting 2+1 free and holographic theories on a product of time with a curved compact 2-d space. We then vary the geometry of the space, keeping the area fixed, at zero/finite temperature, and measure the Casimir/free energy respectively. I will begin by discussing the free theory for a Dirac fermion or scalar field on deformations of the round 2-sphere. I will discuss how the Dirac theory may arise in physical systems such as monolayer graphene. For small deformations we solve analytically using perturbation theory.
I will give an overview of holographic cosmology and discuss recent results and work in progress.
In holographic cosmology time evolution is mapped to inverse RG flow of the dual QFT. As such this framework naturally explains the arrow of time via the
monotonicity of RG flows. Properties of the RG flow are also responsible for the holographic resolution of the classic puzzles of hot big bang cosmology, such as the horizon problem, the flatness problem and the relic problem.
Hawking famously observed that the formation and evaporation of black holes appears to violate the unitary evolution of quantum mechanics. Nonetheless, it has been recently discovered that a signature of unitarity, namely the "Page curve" describing the evolution of entropy, can be recovered from semiclassical gravity. This result relies on "replica wormholes" appearing in the gravitational path integral, which are examples of spacetime wormholes studied more than 30 years ago and related to interactions with closed "baby" universes.
We compute the partition function of 2D Jackiw-Teitelboim (JT) gravity at finite cutoff in two ways: (i) via an exact evaluation of the Wheeler-DeWitt wave-functional in radial quantization and (ii) through a direct computation of the Euclidean path integral. Both methods deal with Dirichlet boundary conditions for the metric and the dilaton. In the first approach, the radial wavefunctionals are found by reducing the constraint equations to two first order functional derivative equations that can be solved exactly, including factor ordering.
The information paradox can be realized in two-dimensional models of gravity. In this setting, we show that the large discrepancy between the von Neumann entropy as calculated by Hawking and the requirement of unitarity is fixed by including new saddles in the gravitational path integral. These saddles arise in the replica method as wormholes connecting different copies of the black hole. We will discuss their appearance both in asymptotically AdS and asymptotically flat theories of gravity.
We look at the interior operator reconstruction from the point of view of Petz map and study its complexity. We show that Petz maps can be written as precursors under the condition of perfect recovery. When we have the entire boundary system its complexity is related to the volume / action of the wormhole from the bulk operator to the boundary. When we only have access to part of the system, Python's lunch appears and its restricted complexity depends exponentially on the size of the subsystem one loses access to.
I describe a novel way to produce states associated to geodesic motion for classical particles in the bulk of AdS that arise from particular operator insertions at the boundary
at a fixed time. When extended to black hole setups, one can understand how to map back the geometric information of the geodesics back to
the properties of these operators. In particular, the presence of stable circular orbits in global AdS are analyzed. The classical Innermost Stable Circular Orbit
I will explain that a geometric theory built upon the theory of complex surfaces can be used to understand wide variety of phenomena in five-dimensional supersymmetric theories, which includes the following: