Taichiro Kugo

Local Covariant Operator Formalism of Non-Abelian Gauge Theories and Quark Confinement Problem

A manifestly covariant and local canonical operator formalism of non-Abelian gauge theories is presented in its full detail. This formalism, applicable to Yang-Mills theories as well as to gravity, not only provides us a transparent understanding in the scattering theoretical aspects, but also makes it possible to discuss other important problems directly related to the (Heisenberg) operators and the state vectors: As for the former, the physical S-matrix unitarity is proved quite generally on the basis of the representation of the algebra of the BRS charge, and asymptotic field analysis is explicitly performed for some examples. As for the latter, the problems of observables and the well-definedness of charge operators are discussed and clear results are obtained, where the locality and covariance of the formalism are indispensable. Observables are shown to be invariant under the BRS transformation as well as the unbroken global gauge groups. By analyzing the structure of “Maxwell” equations in YM theories, the converse of the Higgs theorem is found to hold. This turns out to lead to a remarkably simple criterion of quark confinement in QCD. The present formalism is found useful also for the U(1) problem and the charge universality proof in the Weinberg-Salam model. General theory of indefinite metric quantum fields is developed to some extent.

Nonlinear Realization and Hidden Local Symmetries

Abstract The idea of dynamical gauge bosons of hidden local symmetries in nonlinear sigma models is reviewed. Starting with a fresh look at the Goldstone theorem and low energy theorems, we present a modern review of the general theory of nonlinear realization both in nonsupersymmetric and supersymmetric cases. We then show that any nonlinear sigma model based on the manifold G / H is gauge equivalent to a “linear” model possessing a G global × H local symmetry, H local being a hidden local symmetry. The corresponding supersymmetric formulation is also presented. The above gauge equivalence can be extended to a model having a larger symmetry G global × G local . Also reviewed are dynamical calculatio ns showing that in some two-, three- and four-dimensional models, the gauge bosons of the hidden local symmetries acquire the kinetic terms via quantum effects, thus becoming “dynamical”. We suggest that such a dynamical gauge boson may be a rather common phenomenon realized in Nature. As a realistic example, we examine the QCD case where we identify the vector mesons (ϱ,ω,ф,K ∗ ) with the dynamical gauge bosons of the hidden U(3) v local symmetry in the U(3) L × U(3) R /U(3) V nonlinear sigma model. The totality of the vector meson phenomenology seems to support our basic idea. The axial-vector mesons are also incorporated into our framework. Also given is a brief sketch of some applications of this formalism to unified models beyond the standard model, such as technicolor, composite W/Z boson and supergravity models.

Manifestly covariant canonical formulation of Yang-Mills theories physical state subsidiary conditions and physical S-matrix unitarity

Abstract A satisfactory canonical formulation of Yang-Mills theories is presented in a manifestly covariant manner. The subsidiary conditions for physical states are given as Q B |phys> = Q C |phys> = 0 in terms of the two conserved charges Q B and Q C . These conditions assure the physical S -matrix unitarity.

Non-Abelian Anomaly and Vector Mesons as Dynamical Gauge Bosons of Hidden Local Symmetries

We present general solutions to the Wess-Zumino anomaly equation which incorporate vector mesons as dynamical gauge bosons of the hidden local symmetry in the nonlinear chiral Lagrangian. In contrast to the previous attempts to introduce the vector mesons, our formalism enables one to treat consistently and systematically various processes associated with pseudoscalar mesons (Nambu-Goldsone bosons) and vector mesons (dynamical gauge bosons); it is automatic in this framework that the on-shell amplitudes of photons and pseudoscalar mesons such as π^0 →2γ and γ→3 π which are fixed by the low energy theorems, are not affected no matter how the vector mesons participate in those processes. We further show that the “complete vector meson dominance” hypothesis of photon couplings is invalid in either π^0 →2γ or γ→3π process.

Non-polynomial closed string field theory

Abstract A non-polynomial closed string field theory is presented in a complete form, in the framework recently proposed by Saadi and Zwiebach. All the string interaction vertices possessing string overlapping patterns of polyhedra are specified by very simple conditions. It is shown that the Feynman diagrams with these vertices correctly cover the whole moduli space at the tree level. The connection of this fact to the gauge invariance of the tree level action is also discussed.

Schwinger-Dyson equation for massless vector theory and the absence of a fermion pole

Abstract The Schwinger-Dyson equation of the fermion propagator in the massless vector theory is discussed. It is found that the Baker-Johnson-Willey solution in lowest approximation is in fact a confining solution: the Fermion propagator has no pole or cut in the time-like region. Discussions of homogeneous and inhomogeneous equations with momentum integration cut-off are also given in some detail.

Conformal and poincaré tensor calculi in N=1 supergravity

Abstract We present the superconformal tensor calculus for N=1 supergravity in a complete form; irreducible multiplets, their multiplication and embedding formulae and invariant action formulae. It is further clarified in detail how the various versions of N=1 Poincare supergravity (i.e. with different sets of auxiliary fields) are reproduced from the unique superconformal theory. The tensor calculi for all the known versions of Poincare supergravity are derived explicitly.

Off-Shell d=5 Supergravity Coupled to a Matter-Yang-Mills System.

We present an off-shell formulation of matter-Yang-Mills system coupled to supergravity in five dimensional space-time. We give an invariant action for the general system of vector multiplets and hypermultiplets coupled to supergravity as well as the supersymmetry transformation rules. All the auxiliary fields are kept un-eliminated so that the supersymmetry transformation rules remain unchanged even when the action is changed.

Manifestly covariant field theory of interacting string I

Abstract A manifestly covariant field theory is constructed for the interacting bosonic open string. A very simple string action is presented which is invariant under an inhomogeneous nilpotent BRS transformation. The on-shell scattering amplitudes in this theory reproduce the Koba-Nielsen amplitudes at the tree level, aside from a contributions from a necessary quartic interaction term.

Supergravity Tensor Calculus in 5D from 6D

Supergravity tensor calculus in five spacetime dimensions is derived by dimensional reduction from the d = 6 superconformal tensor calculus. In particular, we obtain an off-shell hypermultiplet in 5D from the on-shell hypermultiplet in 6D. Our tensor calculus retains the dilatation gauge symmetry, so that it is a trivial gauge fixing to make the Einstein term canonical in a general matter-Yang-Mills-supergravity coupled system.