Weyl Invariance and Spurious Black Hole in Two-Dimensional Dilaton Gravity

In two-dimensional dilaton gravity theories, there may exist a global Weyl invariance which makes black hole spurious. If the global invariance and the local Weyl invariance of the matter coupling are intact at the quantum level, there is no Hawking radiation. We explicitly verify the absence of anomalies in these symmetries for the model proposed by Callan, Giddings, Harvey and Strominger. The crucial observation is that the conformal anomaly can be cohomologically trivial and so not truly anomalous in such dilaton gravity models.Comment: 28 pages, KANAZAWA-93-0

Regularized Quantum Master Equation in the Wilsonian Renormalization Group

Using the Pauli-Villars regularization, we make a perturbative analysis of the quantum master equation (QME), $\Sigma =0$, for the Wilsonian effective action. It is found that the QME for the UV action determines whether exact gauge symmetry is realized along the renormalization group (RG) flow. The basic task of solving the QME can be reduced to compute the Troost-van Niuwenhuizen-Van Proyen jacobian factor for the classical UV action. When the QME cannot be satisfied, the non-vanishing $\Sigma$ is proportional to a BRS anomaly, which is shown to be preserved along the RG flow. To see how the UV action fulfills the QME in anomaly free theory, we calculate the jacobian factor for a pure Yang-Mills theory in four dimensions.Comment: 18 page

Realization of symmetry in the ERG approach to quantum field theory

We review the use of the exact renormalization group for realization of symmetry in renormalizable field theories. The review consists of three parts. In part I (sects. 2,3,4), we start with the perturbative construction of a renormalizable field theory as a solution of the exact renormalization group (ERG) differential equation. We show how to characterize renormalizability by an appropriate asymptotic behavior of the solution for a large momentum cutoff. Renormalized parameters are introduced to control the asymptotic behavior. In part II (sects. 5--9), we introduce two formalisms to incorporate symmetry: one by imposing the Ward-Takahashi identity, and another by imposing the generalized Ward-Takahashi identity via sources that generate symmetry transformations. We apply the two formalisms to concrete models such as QED, YM theories, and the Wess-Zumino model in four dimensions, and the O(N) non-linear sigma model in two dimensions. We end this part with calculations of the abelian axial and chiral anomalies. In part III (sects. 10,11), we overview the Batalin-Vilkovisky formalism adapted to the Wilson action of a bare theory with a UV cutoff. We provide a few appendices to give details and extensions that can be omitted for the understanding of the main text. The last appendix is a quick summary for the reader's convenience.Comment: 166 pages, 27 figure

Quantum Master Equation for QED in Exact Renormalization Group

Recently, one of us (H.S.) gave an explicit form of the Ward-Takahashi identity for the Wilson action of QED. We first rederive the identity using a functional method. The identity makes it possible to realize the gauge symmetry even in the presence of a momentum cutoff. In the cutoff dependent realization, the abelian nature of the gauge symmetry is lost, breaking the nilpotency of the BRS transformation. Using the Batalin-Vilkovisky formalism, we extend the Wilson action by including the antifield contributions. Then, the Ward-Takahashi identity for the Wilson action is lifted to a quantum master equation, and the modified BRS transformation regains nilpotency. We also obtain a flow equation for the extended Wilson action.Comment: 15 pages, no figur

Realization of Global Symmetries in the Wilsonian Renormalization Group

We present a method to solve the master equation for the Wilsonian action in the antifield formalism. This is based on a representation theory for cutoff dependent global symmetries along the Wilsonian renormalization group (RG) flow. For the chiral symmetry, the master equation for the free theory yields a continuum version of the Ginsparg-Wilson relation. We construct chiral invariant operators describing fermionic self-interactions. The use of canonically transformed variables is shown to simplify the underlying algebraic structure of the symmetry. We also give another non-trivial example, a realization of SU(2) vector symmetry. Our formalism may be used for a non-perturbative truncation of the Wilsonian action preserving global symmetries.Comment: 11 page