208 research outputs found
Spectrum of Two-Dimensional (Super)Gravity
We review the BRST analysis of the system of a (super)conformal matter
coupled to 2D (super)gravity. The spectrum and its operator realization are
reported. In particular, the operators associated with the states of nonzero
ghost number are given. We also discuss the ground ring structure of the
super-Liouville coupled to matter. In appendices, hermiticities,
states for conformal matter coupled to gravity and the proof for the
spectrum are discussed.Comment: 34 page
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), , 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 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
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 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
Canonical Equivalence between Super D-string and Type IIB Superstring
We show that the super D-string action is canonically equivalent to the type
IIB superstring action with a world-sheet gauge field. Canonical transformation
to the type IIB theory with dynamical tension is also constructed to establish
the SL(2,Z) covariance beyond the semi-classical approximations.Comment: Latex, 11 page
Anomalies in the ERG Approach
The antifield formalism adapted in the exact renormalization group is found
to be useful for describing a system with some symmetry, especially the gauge
symmetry. In the formalism, the vanishing of the quantum master operator
implies the presence of a symmetry. The QM operator satisfies a simple
algebraic relation that will be shown to be related to the Wess-Zumino
condition for anomalies. We also explain how an anomaly contributes to the QM
operator.Comment: 13 page
Towards the Super Yang-Mills Theory on the Lattice
We present an entirely new approach towards a realization of the
supersymmetric Yang-Mills theory on the lattice. The action consists of the
staggered fermion and the plaquette variables distributed in the Euclidean
space with a particular pattern. The system is shown to have fermionic
symmetries relating the fermion and the link variables.Comment: 12 pages, 3 figure
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