No Arabic abstract
This work is the first step in a two-part investigation of real-time replica wormholes. Here we study the associated real-time gravitational path integral and construct the variational principle that will define its saddle-points. We also describe the general structure of the resulting real-time replica wormhole saddles, setting the stage for construction of explicit examples. These saddles necessarily involve complex metrics, and thus are accessed by deforming the original real contour of integration. However, the construction of these saddles need not rely on analytic continuation, and our formulation can be used even in the presence of non-analytic boundary-sources. Furthermore, at least for replica- and CPT-symmetric saddles we show that the metrics may be taken to be real in regions spacelike separated from a so-called `splitting surface. This feature is an important hallmark of unitarity in a field theory dual.
We continue the study of real-time replica wormholes initiated in arXiv:2012.00828. Previously, we had discussed the general principles and had outlined a variational principle for obtaining stationary points of the real-time gravitational path integral. In the current work we present several explicit examples in low-dimensional gravitational theories where the dynamics is amenable to analytic computation. We demonstrate the computation of Renyi entropies in the cases of JT gravity and for holographic two-dimensional CFTs (using the dual gravitational dynamics). In particular, we explain how to obtain the large central charge result for subregions comprising of disjoint intervals directly from the real-time path integral.
Plasma balls are droplets of deconfined plasma surrounded by a confining vacuum. We present the first holographic simulation of their real-time evolution via the dynamics of localized, finite-energy black holes in the five-dimensional anti-de Sitter (AdS) soliton background. The dual gauge theory is four-dimensional, N=4 super Yang-Mills compactified on a circle with supersymmetry-breaking boundary conditions. We consider horizonless initial data sourced by a massless scalar field. Prompt scalar field collapse then produces an excited black hole at the bottom of the geometry together with gravitational and scalar radiation. The radiation disperses to infinity in the noncompact directions and corresponds to particle production in the dual gauge theory. The black hole evolves toward the dual of an equilibrium plasma ball on a time scale longer than naively expected. This feature is a direct consequence of confinement and is caused by long-lived, periodic disturbances bouncing between the bottom of the AdS soliton and the AdS boundary.
We give a pedagogical introduction of the stochastic variational method and show that this generalized variational principle describes classical and quantum mechanics in a unified way.
We construct a covariant closed string field theory by extending recent works on the covariant open string field theory in the proper-time gauge. Rewriting the string scattering amplitudes generated by the closed string field theory in terms of the Polyakov string path integrals, we identify the Fock space representations of the closed string vertices. We show that the Fock space representations of the closed string field theory may be completely factorized into those of the open string field theory. It implies that the well known Kawai-Lewellen-Tye (KLT) relations of the first quantized string theory may be promoted to the second quantized closed string theory. We explicitly calculate the scattering amplitudes of three gravitons by using the closed string field theory in the proper-time gauge.
This review represents a detailed and comprehensive discussion of the Thermal Field Theory (TFT) concepts and key results in Yukawa-type theories. We start with a general pedagogical introduction into the TFT in the imaginary- and real-time formulation. As phenomenologically relevant implications, we present a compendium of thermal decay rates for several typical reactions calculated within the framework of the real-time formalism and compared to the imaginary-time results found in the literature. Processes considered here are those of a neutral (pseudo)scalar decaying into two distinct (pseudo)scalars or into a fermion-antifermion pair. These processes are extended from earlier works to include chemical potentials and distinct species in the final state. In addition, a (pseudo)scalar emission off a fermion line is also discussed. These results demonstrate the importance of thermal effects in particle decay observables relevant in many phenomenological applications in systems at high temperatures and densities.