Spacetime Geometry as Statistic Ensemble of Strings

Jacobson theorem (Ref. \cite{jacobson}) shows that Einstein gravity may be understood as a thermodynamical equation of state; a microscopic realization of this result is however lacking. In this paper, we propose that this may be achieved by assuming the spacetime geometry as a macroscopic system, whose thermodynamical behavior is described by a statistical ensemble, whose microscopic components are low-dimensional geometries. We show that this picture is consistent with string theory by proposing a particular model for the microscopic geometry, where the spacetime metric plays the role of an ordinary thermodynamical potential in a special ensemble. In this scenario, Einstein equation is indeed recovered as an equation of state, and the black hole thermodynamics is reproduced in a thermodynamic limit (large length scales). The model presented here is background-independent and, in particular, it provides an alternative formulation of string theory.Comment: 14 pages, no figure

Lorentz Symmetry Breaking and Planar Effects from Non-Linear Electrodynamics

We propose a modification of standard linear electrodynamics in four dimensions, where effective non-trivial interactions of the electromagnetic field with itself and with matter fields induce Lorentz violating Chern-Simons terms. This yields two consequences: it provides a more realistic and general scenario for the breakdown of Lorentz symmetry in electromagnetism and it may explain the effective behavior of the electromagnetic field in certain planar phenomena (for instance, Hall effect). A number of proposals for non-linear electrodynamics is discussed along the paper. Important physical implications of the breaking of Lorentz symmetry, such as optical birefringence and the possibility of having conductance in the vacuum are commented on

Einstein-Cartan formulation of Chern-Simons Lorentz-violating Gravity

We consider a modification of the standard Einstein theory in four dimensions, alternative to R. Jackiw and S.-Y. Pi, Phys. Rev. D 68, 104012 (2003), since it is based on the first-order (Einstein-Cartan) approach to General Relativity, whose gauge structure is manifest. This is done by introducing an additional topological term in the action which becomes a Lorentz-violating term by virtue of the dependence of the coupling on the space-time point. We obtain a condition on the solutions of the Einstein equations, such that they persist in the deformed theory, and show that the solutions remarkably correspond to the classical solutions of a collection of independent 2+1-d (topological) Chern-Simons gravities. Finally, we study the relation with the standard second-order approach and argue that they both coincide to leading order in the modulus of the Lorentz-violating vector field.Comment: Final versio

Emergent spacetime, and a model for unitary gravitational collapse in AdS

We propose a CFT unitary description of the gravitational collapse. The starting point is the model of a black hole in AdS proposed by Maldacena in arXiv: 0106112 [hep-th]. We show that by proposing a two-copies version of the AdS/CFT conjecture, the process of formation of black holes so as other spacetimes with horizons may be described as an unitary process in the dual field theory. In doing this, we construct a well defined framework to describe general spacetimes as entangled states, in terms of the spectrum of states on the exact Anti-de-Sitter background. As application, we show how the description of the Hawking-Page transition results simplified in this formalism and some novel aspects may be observed. Finally, a simplified analysis based on weakly coupled bulk fields is discussed.Comment: 19 pages, 1 figur

Area Operators in Holographic Quantum Gravity

We argue that the holographic formula relating entanglement entropy and the area of a minimal surface is the key to define the area of surfaces in the (emergent) spacetime from the dual theory on the boundary. So we promote the entropy/area relation to operators to define the "area" observable in a holographic formulation of quantum gravity, then we find a suitable geometric representation for the states, and show that the Ryu-Takayanagi proposal is recovered in the approximation of semi-classical gravity. Finally, we discuss this picture in the example of a AdS-Black hole.Comment: Essay written for the Gravity Research Foundation 2014 Awards for Essays on Gravitation. Minor corrections. Figure and reference adde

TFD Extension of Open String Field Theory

We study the application of the rules of Thermo Field Dynamics (TFD) to the covariant formulation of Open String Field Theory (OSFT). We extend the states space and fields according to the duplication rules of TFD and construct the corresponding classical action. The result is interpreted as a theory whose fields would encode the statistical information of open strings. The physical spectrum of the free theory is studied through the cohomology of the extended BRST charge, and, as a result, we get new fields in the spectrum emerging by virtue of the quantum entanglement and, noticeably, it presents degrees of freedom that could be identified as those of closed strings. We also show, however, that their appearing in the action is directly related to the choice of the inner product in the extended algebra, so that different sectors of fields could be eliminated from the theory by choosing that product conveniently. Finally, we study the extension of the three-vertex interaction and provide a simple prescription for it whose results at tree-level agree with those of the conventional theory.Comment: 25 pages, no figures. File format, typos, Abstract and references modified. New subsection and concluding comments were added. To appear in Phys. Rev.