Supersymmetric Topological Quantum Field Theories Of Differential Forms I. Gauge p-forms

We consider the topological theory of Witten type for gauge differential p-forms. It is shown that some topological invariants such as linking numbers appear under quantization of this theory. The non-abelian generalization of the model is discussed.Comment: 12 pages, Late

The Geometry of Small Causal Diamonds

The geometry of causal diamonds or Alexandrov open sets whose initial and final events $p$ and $q$ respectively have a proper-time separation $\tau$ small compared with the curvature scale is a universal. The corrections from flat space are given as a power series in $\tau$ whose coefficients involve the curvature at the centre of the diamond. We give formulae for the total 4-volume $V$ of the diamond, the area $A$ of the intersection the future light cone of $p$ with the past light cone of $q$ and the 3-volume of the hyper-surface of largest 3-volume bounded by this intersection valid to ${\cal O} (\tau ^4)$. The formula for the 4-volume agrees with a previous result of Myrheim. Remarkably, the iso-perimetric ratio ${3V_3 \over 4 \pi} / ({A \over 4 \pi}) ^{3 \over 2}$ depends only on the energy density at the centre and is bigger than unity if the energy density is positive. These results are also shown to hold in all spacetime dimensions. Formulae are also given, valid to next non-trivial order, for causal domains in two spacetime dimensions. We suggest a number of applications, for instance, the directional dependence of the volume allows one to regard the volumes of causal diamonds as an observable providing a measurement of the Ricci tensor.Comment: 17 pages, no figures; Misprints in eqs.(62), (65), (66) and (81) corrected; a new note on page 13 (with 2 new equations) adde

Horizon State, Hawking Radiation and Boundary Liouville Model

We demonstrate that the near-horizon physics, the Hawking radiation and the reflection off the radial potential barrier, can be understood entirely within a conformal field theory picture in terms of one- and two-point functions in the boundary Liouville theory. An important element in this demonstration is the notion of {\it horizon state}, the Hawking radiation being interpreted as a result of the transition of horizon state to the ordinary states propagating outside black hole horizon.Comment: Revtex, 5pages; final version to appear in Phys.Rev.Let

Black hole entropy: statistical mechanics agrees thermodynamics

We discuss the connection between different entropies introduced for black hole. It is demonstrated on the two-dimensional example that the (quantum) thermodynamical entropy of a hole coincides (including UV-finite terms) with its statistical-mechanical entropy calculated according to 't Hooft and regularized by Pauli-Villars.Comment: 10 pages, latex. Some new discussion added. Version to appear in Phys Rev.

Quantum entropy of the Kerr black hole arising from gravitational perturbation

The quantum entropy of the Kerr black hole arising from gravitational perturbation is investigated by using Null tetrad and \'t Hooft\'s brick-wall model. It is shown that effect of the graviton\'s spins on the subleading correction is dependent of the square of the spins and the angular momentum per unit mass of the black hole, and contribution of the logarithmic term to the entropy will be positive, zero, and negative for different value of $a/r_+$.Comment: 8 pages, 1 figure, Latex. to appear in Phys. Rev.

Holography with Gravitational Chern-Simons Term

The holographic description in the presence of gravitational Chern-Simons term is studied. The modified gravitational equations are integrated by using the Fefferman-Graham expansion and the holographic stress-energy tensor is identified. The stress-energy tensor has both conformal anomaly and gravitational or, if re-formulated in terms of the zweibein, Lorentz anomaly. We comment on the structure of anomalies in two dimensions and show that the two-dimensional stress-energy tensor can be reproduced by integrating the conformal and gravitational anomalies. We study the black hole entropy in theories with a gravitational Chern-Simons term and find that the usual Bekenstein-Hawking entropy is modified. For the BTZ black hole the modification is determined by area of the inner horizon. We show that the total entropy of the BTZ black hole is precisely reproduced in a boundary CFT calculation using the Cardy formula.Comment: 19 pages, Latex; v3: minor corrections, some clarification

Non-minimal coupling and quantum entropy of black hole

Formulating the statistical mechanics for a scalar field with non-minimal $\xi R \phi^2$ coupling in a black hole background we propose modification of the original 't Hooft ``brick wall'' prescription. Instead of the Dirichlet condition we suggest some scattering ansatz for the field functions at the horizon. This modifies the energy spectrum of the system and allows one to obtain the statistical entropy dependent on the non-minimal coupling. For $\xi<0$ the entropy renormalizes the classical Bekenstein-Hawking entropy in the correct way and agrees with the result previously obtained within the conical singularity approach. For a positive $\xi$, however, the results differ.Comment: 16 pages, latex, no figures; an error in calculation of the entropy corrected, the entropy now is positive for any non-minimal couplin