Publications (18)5.83 Total impact
-
Article: Anomalies in the ERG Approach
[show abstract] [hide abstract]
ABSTRACT: 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.04/2011; -
Article: Realization of symmetry in the ERG approach to quantum field theory
[show abstract] [hide abstract]
ABSTRACT: 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 figures09/2009; -
Article: Ward-Takahashi identity for Yang-Mills theory in the Exact Renormalization Group
[show abstract] [hide abstract]
ABSTRACT: We give a functional derivation of the Ward-Takahashi identity for Yang-Mills theory in the framework of the exact renormalization group. The identity realizes non-abelian gauge symmetry nontrivially despite the presence of a momentum cutoff. The cutoff deforms the gauge transformation by introducing composite operators. In our functional method, which is an extension of the method used in our previous work on QED, these composite operators are expressed in terms of the Wilson action that depends on both a UV cutoff and an IR cutoff.08/2008; -
Article: Quantum Master Equation for QED in Exact Renormalization Group
[show abstract] [hide abstract]
ABSTRACT: 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.05/2007; -
Article: Genuine Symmetry of Staggered Fermion
[show abstract] [hide abstract]
ABSTRACT: We present a new formulation of the staggered fermion on the D-dimensional lattice based on the SO(2D) Clifford algebra, which is naturally present in the action. The action of the massless staggered fermion is invariant under the discrete rotation and the SO(2D) chiral and other discrete transformations. From transformation properties of the fermion, we find two local meson operators (one scalar and one pseudoscalar) in addition to two standard meson operators. Comment: 11 pages, 1 figure12/2004; -
Article: Towards the Super Yang-Mills Theory on the Lattice
[show abstract] [hide abstract]
ABSTRACT: 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 figures12/2001; -
Article: Realization of Global Symmetries in the Wilsonian Renormalization Group
[show abstract] [hide abstract]
ABSTRACT: 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 pages11/2001; -
Article: Regularized quantum master equation in the wilsonian
[show abstract] [hide abstract]
ABSTRACT: Using the Pauli-Villars regularization, we make a perturbative analysis of the quantum master equation (QME), Σ = 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 Proeyen jacobian factor for the classical UV action. When the QME cannot be satisfied, the non-vanishing Σ 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.Journal of High Energy Physics 10/2001; 2001(10):032. · 5.83 Impact Factor -
Article: BRS Symmetry, the Quantum Master Equation, and the Wilsonian Renormalization Group
[show abstract] [hide abstract]
ABSTRACT: Recently we made a proposal for realization of an effective BRS symmetry along the Wilsonian renormalization group flow. In this paper we show that the idea can be naturally extended for the most general gauge theories. Extensive use of the antifield formalism is made to reveal some remarkable structure of the effective BRS symmetry. The average action defined with a continuum analog of the block spin transformation obeys the quantum master equation (QME), provided that an UV action does so. We show that the RG flow described by the exact flow equations is generated by canonical transformations in the field-antifield space. Using the relation between the average action and the Legendre effective action, we establish the equivalence between the QME for the average action and the modified Ward-Takahashi identity for the Legendre action. The QME remains intact when the regularization is removed. Comment: 19 pages01/2001; -
Article: Exact BRS Symmetry realized on the Renormalization Group Flow
[show abstract] [hide abstract]
ABSTRACT: Using the average action defined with a continuum analog of the block spin transformation, we show the presence of gauge symmetry along the Wilsonian renormalization group flow. As a reflection of the gauge symmetry, the average action satisfies the quantum master equation(QME). We show that the quantum part of the master equation is naturally understood once the measure contribution under the BRS transformation is taken into account. Furthermore an effective BRS transformation acting on macroscopic fields may be defined from the QME. The average action is explicitly evaluated in terms of the saddle point approximation up to one-loop order. It is confirmed that the action satisfies the QME and the flow equation. Comment: Latex, 15 pages06/2000; -
Article: Exact Symmetries realized on the Renormalized Group Flow
[show abstract] [hide abstract]
ABSTRACT: We show that symmetries are preserved exactly along the (Wilsonian) renormalization group flow, though the IR cutoff deforms concrete forms of the transformations. For a gauge theory the cutoff dependent Ward-Takahashi identity is written as the master equation in the antifield formalism: one may read off the renormalized BRS transformation from the master equation. The Maxwell theory is studied explicitly to see how it works. The renormalized BRS transformation becomes non-local but keeps off-shell nilpotency. Our formalism is applicable for a generic global symmetry. The master equation considered for the chiral symmetry provides us with the continuum analog of the Ginsparg-Wilson relation and the L{\" u}scher's symmetry. Comment: Latex, 10 pages12/1999; -
Article: Bifurcation Phenomena in Optimal Velocity Model for Traffic Flows
[show abstract] [hide abstract]
ABSTRACT: In the optimal velocity model with a time lag, we show that there appear multiple exact solutions in some ranges of car density, describing a uniform flow, a stable and an unstable congested flows. This establishes the presence of subcritical Hopf bifurcations. Our analytic results have far-reaching implications for traffic flows such as hysteresis phenomena associated with discontinuous transitions between uniform and congested flows.09/1999; -
Article: Toda Lattice Solutions of Differential-Difference Equations for Dissipative Systems
[show abstract] [hide abstract]
ABSTRACT: In a certain class of differential-difference equations for dissipative systems, we show that hyperbolic tangent model is the only the nonlinear system of equations which can admit some particular solutions of the Toda lattice. We give one parameter family of exact solutions, which include as special cases the Toda lattice solutions as well as the Whitham's solutions in the Newell's model. Our solutions can be used to describe temporal-spatial density patterns observed in the optimal velocity model for traffic flow. Comment: Latex, 13 pages, 1 figure10/1998; -
Article: Electric-Magnetic Duality Rotations and Invariance of Actions
[show abstract] [hide abstract]
ABSTRACT: For D=4 theories of a single U(1) gauge field strength coupled to gravity and matters, we show that the electric-magnetic duality can be formulated as an invariance of the actions. The symmetry is associated with duality rotation acting directly on the gauge field. The rotation is constructed in flat space, and an extension to curved spaces is also given. It is non-local and non-covariant, yet generates off-shell extended transformation of the field strength. The algebraic condition of Gaillard and Zumino turns out to be a necessary and sufficient condition for the invariance of actions. It may be used as a guiding principle in constructing self-dual actions in string and field theories. Comment: Latex, 15 pages06/1998; -
Article: Canonical Equivalence between Super D-string and Type IIB Superstring
[show abstract] [hide abstract]
ABSTRACT: 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 pages01/1998; -
Article: Solvable optimal velocity models and asymptotic trajectory
[show abstract] [hide abstract]
ABSTRACT: In the optimal velocity model proposed as a version of car following model, it has been found that a congested flow is generated spontaneously from a homogeneous flow for a certain range of the traffic density. A well-established congested flow obtained in a numerical simulation shows a remarkable repetitive property, such that the velocity of a vehicle evolves exactly in the same way as that of its preceding one except with a time delay T. This leads to a global pattern formation in time development of the vehicle's motion, and gives rise to a closed trajectory on Δx-v (headway-velocity) plane connecting congested and free flow points. To obtain the closed trajectory analytically, we propose an approach to the pattern formation, which makes it possible to reduce the coupled car following equations to a single difference-differential equation (Rondo equation). To demonstrate our approach, we employ a class of linear models which are exactly solvable. We also introduce the concept of ``asymptotic trajectory'' to determine T and vB (the backward velocity of the pattern), the global parameters associated with the vehicle's collective motion in a congested flow, in terms of parameters, such as the sensitivity a, which appeared in the original coupled equations.Phys. Rev. E. 55(6). -
Article: Exact symmetries realized on the renormalization group flow
[show abstract] [hide abstract]
ABSTRACT: We show that symmetries are preserved exactly along the (Wilsonian) renormalization group flow, though the IR cutoff deforms concrete forms of the transformations. For a gauge theory the cutoff dependent Ward–Takahashi identity is written as the master equation in the antifield formalism: one may read off the renormalized BRS transformation from the master equation. The Maxwell theory is studied explicitly to see how it works. The renormalized BRS transformation becomes non-local but keeps off-shell nilpotency. Our formalism is applicable for a generic global symmetry. The master equation considered for the chiral symmetry provides us with the continuum analog of the Ginsparg–Wilson relation and the Lüscher's symmetry.Physics Letters B. -
Article: Self-duality in super D3-brane action
[show abstract] [hide abstract]
ABSTRACT: We establish self-duality of super D3-brane theory as an exact symmetry of the action both in the Lagrangian and Hamiltonian formalisms. In the Lagrangian formalism, the action is shown to satisfy the Gaillard-Zumino condition. This algebraic relation is recognized in our previous paper to be a necessary and sufficient condition for generic action of U(1) gauge field strength coupled with gravity and matters to be self-dual. For the super D3-brane action, SO(22) duality transformation of a world-volume gauge field should be associated with SO(2) rotation of fermionic brane coordinates in the N = 2 SUSY multiplet. This SO(2) duality symmetry is lifted to SL(2, ) symmetry in the presence of a dilaton and axion background fields. In the canonical formalism, we show that the duality rotation is described by a canonical transformation, and the Hamiltonian of the D3-brane action is invariant under the transformation.Nuclear Physics B.
Top co-authors
Top Journals
Institutions
-
2001
-
Niigata University
- Faculty of Education
Niigata-shi, Niigata-ken, Japan
-
