Related papers: Holography and Riemann Surfaces
Following a recent suggestion by Randall and Sundrum, we consider string compactification scenarios in which a compact slice of AdS-space arises as a subspace of the compactification manifold. A specific example is provided by the type II…
In the Labourie-Loftin parametrization of the Hitchin component of surface group representations into SL(3,R), we prove an asymptotic formula for holonomy along rays in terms of local invariants of the holomorphic differential defining that…
In this paper we construct smooth cuspidal automorphic forms related to integrable discrete series of a connected semisimple Lie group with finite center for classical and adelic situation as an application of the theory of Schwartz spaces…
Aspects of holography or dimensional reduction in gravitational physics are discussed with reference to black hole thermodynamics. Degrees of freedom living on Isolated Horizons (as a model for macroscopic, generic, eternal black hole…
The gauge/string dualities have drawn attention to a class of variational problems on a boundary at infinity, which are not well defined unless a certain boundary term is added to the classical action. In the context of supergravity in…
Let k be a non archimedean field. If X is a k-algebraic variety and U a locally closed semi-algebraic subset of X^{an} -- the Berkovich space associated to X -- we show that for l \neq char(\tilde{k}), the cohomology groups H^i_c (\bar{U},…
Metrics of constant negative curvature on a compact Riemann surface are critical points of the Liouville action functional, which in recent constructions is rigorously defined as a class in a Cech-de Rham complex with respect to a suitable…
We propose a novel codimension-n holography, called cone holography, between a gravitational theory in $(d+1)$-dimensional conical spacetime and a CFT on the $(d+1-n)$-dimensional defects. Similar to wedge holography, the cone holography…
To gain insight into how bulk locality emerges from the holographic conformal field theory, we reformulate the bulk to boundary map in as local a way as possible. In previous work, we carried out this program for Lorentzian AdS, and showed…
Motivated by the pseudo-entropy program, we study timelike subregion complexity within the holographic Complexity-equal-Volume framework, extending previous spatial constructions to Lorentzian boundary intervals. For hyperbolic timelike…
We study the Liouville action for quasi-Fuchsian groups with parabolic and elliptic elements. In particular, when the group is Fuchsian, the contribution of elliptic elements to the classical Liouville action is derived in terms of the…
We present a data-driven method for holographic bulk reconstruction that works even when the spacetime is not asymptotically AdS. Given the data of boundary Green functions within a finite frequency window, we iteratively adjust a bulk…
We prove a semisimplicity result for the boundary, in the corresponding Deligne-Mumford compactification, of a totally geodesic subvariety of a moduli space of Riemann surfaces. At the level of Teichm\"uller space, this semisimplicity…
In this thesis we study two different approaches to holography, and comment on the possible relation between them. The first approach is an analysis of the high-energy regime of quantum gravity in the eikonal approximation, where the theory…
These are lecture notes based on a series of lectures presented at the XIII Modave Summer School in Mathematical physics aimed at PhD students and young postdocs. The goal is to give an introduction to some of the recent developments in…
Real time holography is studied in the context of the embedding space formalism. In the first part of this paper, we present matching conditions for on-shell integer spin fields when going from Euclidean to Lorentzian signature on AdS…
We consider the holomorphic unramified mapping of two arbitrary finite bordered Riemann surfaces. Extending the map to the doubles $X_1$ and $X_2$ of Riemann surfaces we define the vector bundle on the second double as a direct image of the…
We study the conventional holographic recipes and its real-time extensions in the context of the correspondence between SYK quantum mechanics and JT gravity. We first observe that only closed contours are allowed to have a 2d space-time…
The volume of the region inside the bulk Ryu-Takayanagi surface is a codimension-one object, and a natural generalization of holographic complexity to the case of subregions in the boundary QFT. We focus on time-independent geometries, and…
We systematically study inhomogeneous Hamiltonians in two-dimensional conformal field theories within the framework of the AdS/CFT correspondence by relating them to two-dimensional curved backgrounds. We propose a classification of…