Holography of the BTZ Black Hole, Inside and Out

We propose a 1+1 dimensional CFT dual structure for quantum gravity and matter on the extended 2+1 dimensional BTZ black hole, realized as a quotient of the Poincare patch of AdS$_3$. The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincare patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon. While most of our checks are within gravitational effective field theory, we arrive at a fully non-perturbative CFT proposal to probe the UV-sensitive approach to the singularity.Comment: 52 pages, 15 figures. v2: Clarifications made throughout paper. Derivation of (new) Section 8 corrected. Results and conclusions unchanged. References adde

The large charge expansion and AdS/CFT

The scaling dimensions of charged operators in conformal field theory were recently computed in a large charge expansion. We verify this expansion in a dual AdS model. Specifically, we numerically construct solitonic boson star solutions of Einstein-Maxwell-Scalar theory in AdS$_4$ and find that its mass at large charge reproduces the universal form of the lowest operator dimension in the large U(1) charge sector of the dual 2+1 dimensional CFT

The large charge expansion at large N

The scaling dimensions of charged operators in conformal field theory have recently been predicted to exhibit universal behavior in the large charge limit. We verify this behavior in the 2+1 dimensional CPN model. Specifically, we numerically compute the scaling dimensions of the lowest dimension monopole operators with charges Q = 1, 2, ... , 100 to subleading order in large N. The coefficients of the large Q expansion are extracted through a fit, and the predicted universal O(1) contribution is verified to the subpercent level.Comment: 7 pages plus appendix, bibliography, et

4D Scattering Amplitudes and Asymptotic Symmetries from 2D CFT

We reformulate the scattering amplitudes of 4D flat space gauge theory and gravity in the language of a 2D CFT on the celestial sphere. The resulting CFT structure exhibits an OPE constructed from 4D collinear singularities, as well as infinite-dimensional Kac-Moody and Virasoro algebras encoding the asymptotic symmetries of 4D flat space. We derive these results by recasting 4D dynamics in terms of a convenient foliation of flat space into 3D Euclidean AdS and Lorentzian dS geometries. Tree-level scattering amplitudes take the form of Witten diagrams for a continuum of (A)dS modes, which are in turn equivalent to CFT correlators via the (A)dS/CFT dictionary. The Ward identities for the 2D conserved currents are dual to 4D soft theorems, while the bulk-boundary propagators of massless (A)dS modes are superpositions of the leading and subleading Weinberg soft factors of gauge theory and gravity. In general, the massless (A)dS modes are 3D Chern-Simons gauge fields describing the soft, single helicity sectors of 4D gauge theory and gravity. Consistent with the topological nature of Chern-Simons theory, Aharonov-Bohm effects record the "tracks" of hard particles in the soft radiation, leading to a simple characterization of gauge and gravitational memories. Soft particle exchanges between hard processes define the Kac-Moody level and Virasoro central charge, which are thereby related to the 4D gauge coupling and gravitational strength in units of an infrared cutoff. Finally, we discuss a toy model for black hole horizons via a restriction to the Rindler region.Comment: 66 pages, 8 figures; v2: version to appear in JHE

Non-Perturbative Methods in Quantum Field Theory and Quantum Gravity

This thesis considers non-perturbative methods in quantum field theory with applications to gravity and cosmology. In particular, there are chapters on black hole holography, inflationary model building, and the conformal bootstrap

3D reconstruction of syn-tectonic strata deposited during the inversion of salt-related structures : insights from the Llert syncline (South-central Pyrenees)

The Llert syncline is located in the South-central Pyrenees, between the eastern termination of the EW-trending Cotiella Basin and the north-western limb of the NS-trending Turbón-Serrado fold system. The Cotiella Basin is an inverted upper Coniacian-lower Santonian salt-floored post-rift extensional basin developed along the northern Iberian rift system. The Turbón-Serrado fold system consists of upper Santonian - Maastrichtian contractional salt-cored anticlines developed along an inverted transfer zone of the Pyrenean rift system. Based on field research, this paper presents a 3D reconstruction of the Llert syncline in order to further constrain the transition between these oblique salt-related structures. Our results suggest that the evolution of the Llert syncline was mainly controlled by tectonic shortening related to the tectonic inversion of the Cotiella Basin synchronously to the growth of the Turbón-Serrado detachment anticline, and by the pre-compressional structural framework of the Pyrenean rift system. Our contribution provides new insight into the geometric and kinematic relationships of structures developed during the inversion of passive margins involving salt

Detection of OH absorption against PSR B1849+00

We have searched for OH absorption against seven pulsars using the Arecibo telescope. In both OH mainlines (at 1665 and 1667 MHz), deep and narrow absorption features were detected toward PSR B1849+00. In addition, we have detected several absorption and emission features against B33.6+0.1, a nearby supernova remnant (SNR). The most interesting result of this study is that a pencil-sharp absorption sample against the PSR differs greatly from the large-angle absorption sample observed against the SNR. If both the PSR and the SNR probe the same molecular cloud then this finding has important implications for absorption studies of the molecular medium, as it shows that the statistics of absorbing OH depends on the size of the background source. We also show that the OH absorption against the PSR most likely originates from a small (<30 arcsec) and dense (>10^5 cm^-3) molecular clump.Comment: 12 pages, 8 figures. Accepted for publication in Ap

Coarse-grained entropy decrease and phase-space focusing in Hamiltonian dynamics

We analyze the behavior of the coarse-grained entropy for classical probabilities in nonlinear Hamiltonians. We focus on the result that if the trajectory dynamics are integrable, the probability ensemble shows transient increases in the coherence, corresponding to an increase in localization of the ensemble and hence the phasespace density of the ensemble. We discuss the connection of these dynamics to the problem of cooling in atomic ensembles. We show how these dynamics can be understood in terms of the behavior of individual trajectories, allowing us to manipulate ensembles to create “cold” dense final ensembles. We illustrate these results with an analysis of the behavior of particular nonlinear integrable systems, including discussions of the spin-echo effect and the seeming violation of Liouville’s theore

Uso de recursos materiales y actividades de experimentación para la enseñanza de matemáticas en bachillerato

El uso de recursos materiales y actividades de experimentación en clase de matemáticas se está normalizando en educación primaria y, quizás en menor medida, en educación secundaria obligatoria. Así podemos encontrar muchos ejemplos de uso de materiales manipulativos y TAC, en las aportaciones que se han ido presentando en diferentes ediciones de las JAEM. En cambio, para la etapa de Bachillerato este tipo de recursos didácticos no parece que sean tan populares. Parece que en Bachillerato el formalismo toma un protagonismo que deja de lado otras opciones. Llevar al aula buenos recursos materiales inmersos en actividades adecuadas puede ser el método de transporte más eficaz para llegar a las ideas de fondo que subyacen en los contenidos propios de bachillerato. Las actividades de experimentación con recursos materiales nos permiten poner en juego el ciclo: experimentación, descubrimiento, conceptuación y formalización de una forma natural. Durante su desarrollo mostraremos y discutiremos con los asistentes la diferente utilización de éstos y cómo pueden gestionarse para que este tipo de actividades puedan ser aportaciones relevantes en los niveles más avanzados de la educación secundaria y que son un buen camino para llegar a comprender y a formalizar ideas abstractas