Hawking Radiation in the Dilaton Gravity with a Non-Minimally Coupled Scalar Field

We discuss the two-dimensional dilaton gravity with a scalar field as the source matter where the coupling with the gravity is given, besides the minimal one, through an external field. This coupling generalizes the conformal anomaly in the same way as those found in recent literature, but with a diferent motivation. The modification to the Hawking radiation is calculated explicity and shows an additional term that introduces a dependence on the (effective) mass of the black-hole.Comment: 13 pages, latex file, no figures, to be published in IJM

Domain wall fermion and CP symmetry breaking

We examine the CP properties of chiral gauge theory defined by a formulation of the domain wall fermion, where the light field variables $q$ and $\bar q$ together with Pauli-Villars fields $Q$ and $\bar Q$ are utilized. It is shown that this domain wall representation in the infinite flavor limit $N=\infty$ is valid only in the topologically trivial sector, and that the conflict among lattice chiral symmetry, strict locality and CP symmetry still persists for finite lattice spacing $a$. The CP transformation generally sends one representation of lattice chiral gauge theory into another representation of lattice chiral gauge theory, resulting in the inevitable change of propagators. A modified form of lattice CP transformation motivated by the domain wall fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion invariant, is analyzed in detail; this provides an alternative way to understand the breaking of CP symmetry at least in the topologically trivial sector. We note that the conflict with CP symmetry could be regarded as a topological obstruction. We also discuss the issues related to the definition of Majorana fermions in connection with the supersymmetric Wess-Zumino model on the lattice.Comment: 33 pages. Note added and a new reference were added. Phys. Rev.D (in press

Hawking Radiation, Covariant Boundary Conditions and Vacuum States

The basic characteristics of the covariant chiral current $$and the covariant chiral energy-momentum tensor$$ are obtained from a chiral effective action. These results are used to justify the covariant boundary condition used in recent approaches \cite{Isowilczek,Isoumtwilczek,shailesh,shailesh2,Banerjee} of computing the Hawking flux from chiral gauge and gravitational anomalies. We also discuss a connection of our results with the conventional calculation of nonchiral currents and stress tensors in different (Unruh, Hartle-Hawking and Boulware) states.Comment: 18 pages, no figures, minor changes, to appear in Phys. Rev.

Hawking Radiation and Covariant Anomalies

Generalising the method of Wilczek and collaborators we provide a derivation of Hawking radiation from charged black holes using only covariant gauge and gravitational anomalies. The reliability and universality of the anomaly cancellation approach to Hawking radiation is also discussed.Comment: Minor changes, conforms to published versio

Higher-loop anomalies in chiral gravities

The one-loop anomalies for chiral $W_{3}$ gravity are derived using the Fujikawa regularisation method. The expected two-loop anomalies are then obtained by imposing the Wess-Zumino consistency conditions on the one-loop results. The anomalies found in this way agree with those already known from explicit Feynman diagram calculations. We then directly verify that the order $\hbar^2$ non-local BRST Ward identity anomalies, arising from the ``dressing'' of the one-loop results, satisfy Lam's theorem. It is also shown that in a rigorous calculation of $Q^2$ anomaly for the BRST charge, one recovers both the non-local as well as the local anomalies. We further verify that, in chiral gravities, the non-local anomalies in the BRST Ward identity can be obtained by the application of the anomalous operator $Q^2$, calculated using operator products, to an appropriately defined gauge fermion. Finally, we give arguments to show why this relation should hold generally in reparametrisation-invariant theories.Comment: 21 pages, latex, 12 figures as uuencoded postscript. To appear in Nucl. Phys.

Hawking Radiation via Gravitational Anomalies in Non-spherical Topologies

We study the method of calculating the Hawking radiation via gravitational anomalies in gravitational backgrounds of constant negative curvature. We apply the method to topological black holes and also to topological black holes conformally coupled to a scalar field.Comment: 25 pages, no figures, version to be published in Phys. Rev.

Geometric phases, gauge symmetries and ray representation

The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is based on the equivalence class $\{e^{i\alpha(t)}\psi(t,\vec{x})\}$ which is not a symmetry of the Schr\"{o}dinger equation. This equivalence class when understood as defining generalized rays in the Hilbert space is not generally consistent with the superposition principle in interference and polarization phenomena. The hidden local gauge symmetry, which arises from the arbitrariness of the choice of coordinates in the functional space, is then proposed as a basic gauge symmetry in the non-adiabatic phase. This re-formulation reproduces all the successful aspects of the non-adiabatic phase in a manner manifestly consistent with the conventional notion of rays and the superposition principle. The hidden local symmetry is thus identified as the natural origin of the gauge symmetry in both of the adiabatic and non-adiabatic phases in the absence of gauge fields, and it allows a unified treatment of all the geometric phases. The non-adiabatic phase may well be regarded as a special case of the adiabatic phase in this re-formulation, contrary to the customary understanding of the adiabatic phase as a special case of the non-adiabatic phase. Some explicit examples of geometric phases are discussed to illustrate this re-formulation.Comment: 30 pages. Some clarifying sentences have been added in abstract and in the body of the paper. A new additional reference and some typos have been corrected. To appear in Int. J. Mod. Phys.

A Perturbative Study of a General Class of Lattice Dirac Operators

A perturbative study of a general class of lattice Dirac operators is reported, which is based on an algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer. The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. We study one-loop fermion contributions to the self-energy of the gauge field, which are related to the fermion contributions to the one-loop $\beta$ function and to the Weyl anomaly. We first explicitly demonstrate that the Ward identity is satisfied by the self-energy tensor. By performing careful analyses, we then obtain the correct self-energy tensor free of infra-red divergences, as a general consideration of the Weyl anomaly indicates. This demonstrates that our general operators give correct chiral and Weyl anomalies. In general, however, the Wilsonian effective action, which is supposed to be free of infra-red complications, is expected to be essential in the analyses of our general class of Dirac operators for dynamical gauge field.Comment: 30 pages. Some of the misprints were corrected. Phys. Rev. D (in press

Generalized Ginsparg-Wilson algebra and index theorem on the lattice

Recent studies of the topological properties of a general class of lattice Dirac operators are reported. This is based on a specific algebraic realization of the Ginsparg-Wilson relation in the form $\gamma_{5}(\gamma_{5}D)+(\gamma_{5}D)\gamma_{5} = 2a^{2k+1}(\gamma_{5}D)^{2k+2}$ where $k$ stands for a non-negative integer. The choice $k=0$ corresponds to the commonly discussed Ginsparg-Wilson relation and thus to the overlap operator. It is shown that local chiral anomaly and the instanton-related index of all these operators are identical. The locality of all these Dirac operators for vanishing gauge fields is proved on the basis of explicit construction, but the locality with dynamical gauge fields has not been established yet. We suggest that the Wilsonian effective action is essential to avoid infrared singularities encountered in general perturbative analyses.Comment: 11 pages. Talk given at APCTP-Nankai Joint Symposium on Lattice Statistics and Mathematical Physics, Tianjin, China, 8-11 October, 2001. To be published in the Proceedings and in Int. Jour. Mod. Phys.

Temperature in Fermion Systems and the Chiral Fermion Determinant

We give an interpretation to the issue of the chiral determinant in the heat-kernel approach. The extra dimension (5-th dimension) is interpreted as (inverse) temperature. The 1+4 dim Dirac equation is naturally derived by the Wick rotation for the temperature. In order to define a ``good'' temperature, we choose those solutions of the Dirac equation which propagate in a fixed direction in the extra coordinate. This choice fixes the regularization of the fermion determinant. The 1+4 dimensional Dirac mass ($M$) is naturally introduced and the relation: $|$4 dim electron momentum$|$ $\ll$ $|M|$ $\ll$ ultraviolet cut-off, naturally appears. The chiral anomaly is explicitly derived for the 2 dim Abelian model. Typically two different regularizations appear depending on the choice of propagators. One corresponds to the chiral theory, the other to the non-chiral (hermitian) theory.Comment: 24 pages, some figures, to be published in Phys.Rev.