Related papers: Adding the algebraic Ryu-Takayanagi formula to the…
The notion of quantum symmetry has recently been extended to include reduced-dimensional transformations and algebraic structures beyond groups. Such generalized symmetries lead to exotic phases of matter and excitations that defy Landau's…
We study a class of quantum states involving multiple entangled CFTs in AdS$_3$/CFT$_2$, associated with multi-boundary black hole geometries, and demonstrate that the Ryu-Takayanagi (RT) formula for entanglement entropy can be derived…
Walczak formula is a very nice tool for understanding the geometry of a Riemannian manifold equipped with two orthogonal complementary distributions. Svensson [7] has shown that this formula simplifies to a Bochner type formula when we are…
We explore the holographic properties of non-perturbative vacuum decay in Anti-de Sitter ($\mathrm{AdS}$) geometries. To this end, we consider a gravitational theory in a metastable $\mathrm{AdS}_3$ state, which decays into an…
In holography there is a one-to-one correspondence between physical observables in the bulk and boundary theories. To define physical observables, however, regularisation needs to be implemented in both sides of the correspondence. It is…
This article reviews the progress in our understanding of the reconstruction of the bulk spacetime in the holographic correspondence from the dual field theory including an account of how these developments have led to the reproduction of…
We investigate the problem of holomorphic algebraizibility for real hypersurfaces in complex space. We introduce a new invariant of a (real-analytic) Levi-nondegenerate hypersurface called {\em the jet transcendence degree}. Using this…
We study holographic entanglement entropy in four-dimensional quantum gravity with negative cosmological constant. By using the replica trick and evaluating path integrals in the minisuperspace approximation, in conjunction with the…
An attempt is made to make precise the connection between Wilson's RG and "Holographic RG" by writing Wilson's RG in a holographic form. A functional formulation is given for the exact RG evolution of a scalar field in $d$ (flat)…
I derive a family of Ryu--Takayanagi formulae that are valid in the large $N$ limit of holographic quantum error-correcting codes, and parameterized by a choice of UV cutoff in the bulk. The bulk entropy terms are matched with a family of…
We consider holography for d-dimensional scale invariant but non-Lorentz invariant field theories, which do not admit the full Schrodinger symmetry group. We find new realizations of the corresponding (d+1)-dimensional gravity duals,…
Holography for UV-incomplete gauge theories is important but poorly understood. A paradigmatic example is $d=4$, $\mathcal{N}=4$ super Yang-Mills coupled to $N_f$ quark flavors, which possesses a Landau pole at a UV scale $\Lambda_{LP}$.…
Motivated by the theory of holographic quantum error correction in the anti-de Sitter/conformal field theory (AdS/CFT) correspondence, together with the kink transform conjecture on the bulk AdS description of boundary cocycle flow, we…
We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a universal construction of Calabi-Yau algebras in terms of a noncommutative symplectic DG algebra resolution.…
Holographic duality conjecture has been proposed to be a novel non-perturbative theoretical framework for the description of strongly correlated electrons. However, the duality transformation is not specified to cause ambiguity in the…
The Ryu-Takayanagi prescription can be cast in terms of a set of microscopic threads that help visualize holographic entanglement in terms of distillation of EPR pairs. While this framework has been exploited for regions with a high degree…
In this paper the whole geometrical set-up giving a conformally invariant holographic projection of a diffeomorphism invariant bulk theory is clarified. By studying the renormalization group flow along null geodesic congruences a…
This dissertation represents work on three different subjects relating to quantum gravity and the AdS/CFT correspondence. First, we review a holographic computation of the one-loop corrections to the Weyl anomaly on Ricci flat backgrounds…
We propose a formulation of the Equivariant Tamagawa Number Conjecture for modular motives with coefficients in universal deformation rings and Hecke algebras; something which seems to have been heretofore missing because the complexes of…
We give a pedagogical review of how concepts from quantum information theory build up the gravitational side of the AdS/CFT correspondence. The review is self-contained in that it only presupposes knowledge of quantum mechanics and general…