WdW-patches in AdS3 and complexity change under conformal transformations II

AdS3 Gravity and Conformal Field Theories

We present a detailed analysis of AdS3 gravity, the BTZ black hole and the associated conformal field theories (CFTs). In particular we focus on the non-extreme six-dimensional string solution with background metric AdS3×S near the horizon. In addition we introduce momentum modes along the string, corresponding to a BTZ black hole, and a Taub-NUT soliton in the transverse Euclidean space. We sh...

AdS3 Gravitational Instantons from Conformal Field Theory

A conformal field theory on the boundary of three-dimensional asymptotic anti-de Sitter spaces which appear as near horizon geometry of D-brane bound states is discussed. It is shown that partition functions of gravitational instantons appear as high and low temperature limits of the partition function of the conformal field theory. The result reproduces phase transition between the anti-de Sit...

A Characterization of the Infinitesimal Conformal Transformations on Tangent Bundles

Curvature Structures and Conformal Transformations

1. The notion of a "curvature structure" was introduced in §8, Chapter 1 of [ l ] . In this note we shall consider some of its applications. The details will be presented elsewhere. Let (M, g) be a Riemann manifold. Whenever convenient, we shall denote the inner product defined by g, by ( ). DEFINITION. A curvature structure on (M, g) is a (1, 3) tensor field T such that, for any vector fields ...

Conformal Gauge Transformations in Thermodynamics

In this work, we show that the thermodynamic phase space is naturally endowed with a non-integrable connection, defined by all of those processes that annihilate the Gibbs one-form, i.e., reversible processes. We argue that such a connection is invariant under re-scalings of the connection one-form, whilst, as a consequence of the non-integrability of the connection, its curvature is not and, t...