Quantum Fields and Strings

There are several important conceptual and computational questions concerning path integrals in QM and QFT, which have recently been approached from new perspectives motivated by "resurgent asymptotics", a novel mathematical formalism that seeks to unify perturbative and non-perturbative physics. I will discuss the basic ideas behind the connections between resurgent asymptotics and physics, ranging from differential equations to phase transitions and QFT. I will also discuss the reconstruction problem: how to optimally reconstruct non-perturbative information from a finite amount of perturbative information.

 I will discuss how central extensions of charge algebras in gravitational theories with null boundaries arise from an anomalous transformation of the boundary term in the gravitational action. This parallels the way in which the holographic Weyl anomaly appears in AdS/CFT, with the ambiguity in the normalization of the null generator being the analogue of the choice of Weyl frame. I will discuss a way to define the gravitational charges unambiguously within the covariant phase space formalism. As an application, I will analyze the near-horizon Virasoro symmetries of black holes and give a systematic derivation of the central charges. I will show that the central extension computed by the charge algebra is directly related to the Bekenstein-Hawking entropy via the Cardy formula.

We show that a naïve application of the quantum extremal surface (QES) prescription can lead to paradoxical results and must be corrected at leading order. The corrections arise when there is a second QES (with strictly larger generalized entropy at leading order than the minimal QES), together with a large amount of highly incompressible bulk entropy between the two surfaces. We trace the source of the corrections to a failure of the assumptions used in the replica trick derivation of the QES prescription, and show that a more careful derivation correctly computes the corrections. Using tools from one-shot quantum Shannon theory (smooth min- and max-entropies), we generalize these results to a set of refined conditions that determine whether the QES prescription holds. We find similar refinements to the conditions needed for entanglement wedge reconstruction (EWR), and show how EWR can be reinterpreted as the task of one-shot quantum state merging (using zero-bits rather than classical bits), a task gravity is able to achieve optimally efficiently.

In this talk, we review an approach to describing cosmological physics using ordinary AdS/CFT, where the cosmological physics is the effective description of an end-of-the-world brane which cuts off the second asymptotic region of a two-sided black hole. The worldvolume geometry of the brane is an FRW big-bang/big-crunch spacetime. Infavorable circumstances, the brane acts as a Randall-Sundrum Planck brane so that gravity localizes. We describe a microscopic construction for such an end-of-the-world brane with localized gravity in AdS/CFT, starting from N=4 SYM theory. We suggest specific microscopic states of N=4 SYM theory that may encode the physics in a four-dimensional cosmological spacetime.

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. The generalized quantity named effective entropy, and its Renyi entropy generalizations, are defined by analytic continuation of a gravitational path integral on replica geometry with a co-dimension-2 brane at the boundary of region we are studying. We discuss different approaches to define the region in a gauge invariant way, and show that the effective entropy satisfies the quantum extremal surface formula. When the quantum fields carry a significant amount of entanglement, the quantum extremal surface can have a topology transition, after which an entanglement island region appears. Our result generalizes the Hubeny-Rangamani-Takayanagi formula of holographic entropy (with quantum corrections) to general geometries without asymptotic AdS boundary, and provides a more solid framework for addressing problems such as the Page curve of evaporating black holes in asymptotic flat spacetime. We apply the formula to two example systems, a closed two-dimensional universe and a four-dimensional maximally extended Schwarzchild black hole. We discuss the analog of the effective entropy in random tensor network models, which provides more concrete understanding of quantum information properties in general dynamical geometries. By introducing ancilla systems, we show how quantum information in the entanglement island can be reconstructed in a state-dependent and observer-dependent map. We study the closed universe (without spatial boundary) case and discuss how it is related to open universe.

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 then reproduce the known solution of large N single matrix quantum mechanics. Finally, we present new results on the ground state of large N two matrix quantum mechanics.

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. For large deformations we use novel numerical methods to compute these energies for specific deformations, including ones that drive the space to become singular. I will give evidence that the round sphere globally maximises the Casimir/free energy, which may imply geometric instabilities for spheres of such mono layer materials, although probably not graphene. We then discuss the analog for a holographic theory by studying its gravity dual. Here we use gravity techniques to analytically prove at zero temperature the round sphere maximises the Casimir energy. We discuss attempts to show the same for free energy at finite temperature. And finally I will report on on-going numerical gravity calculations of the Casimir energy for specific  deformations of the round sphere which yield an unexpected result.

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.

The holographic framework includes qualitatively new models describing a non-geometric  very early Universe, and such models provide an excellent fit to CMB data.  In the last part of the talk I will present on-going work with lattice gauge theorists aiming to compute on the lattice the QFT observables(the 2-point function of stress energy tensor) needed to compute holographically the cosmological  power spectrum in the regime where the dual QFT is non-perturbative.

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. I will discuss the connection between these new and old ideas and the consequences for the black hole information problem. A central lesson is that a Hilbert space in quantum gravity can be dramatically modified by nonperturbative topology-changing processes.

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. In the second approach we perform the path integral exactly when summing over surfaces with disk topology, to all orders in perturbation theory in the cutoff. Both results precisely match the recently derived partition function in the Schwarzian theory deformed by an operator analogous to the TT¯ deformation in 2D CFTs. This equality can be seen as concrete evidence for the proposed holographic interpretation of the TT¯ deformation as the movement of the AdS boundary to a finite radial distance in the bulk.

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.