A one-loop finite contorted non-linear σ-model without Wess-Zumino term

An explicit breaking interaction term of (1, 0) supersymmetry, governed by a dimensionless coupling parameter, is added to the σ-model action in such a way as to describe the torsion to which the fermions couple. Using (1, 0) supergraph methods, it is shown that, under certain assumptions on the torsion-like explicit breaking term, one-loop finiteness is achieved without spoiling the Ricci-flatness of the target manifold.     

Geometrical structure and ultraviolet finiteness in the supersymmetric σ-model

A complete geometrical classification of supersymmetric -models is given. Extended supersymmetry requires covariantly constant complex structures, and Kahler and hyperkahler manifolds play a special role. As an application of the classification, it is shown that a particular class of these models is on-shell ultraviolet finite to all orders in perturbation theory.     

Heterotic σ-models and conformal supergravity in two dimensions

The (1, 0) and (2, 0) type heterotic σ-models with Wess-Zumino term are coupled to conformal supergravity in two dimensions. There are no new restrictions on the σ-model manifolds in addition to those which arise in the globally supersymmetric cases. In the (1, 0) case possible isometries of the scalar manifold are gauged. A derivation of d = 2 conformal supergravity based on the super Lie algebra OSp(2, N)⊕OSp(2, N) (N = 1, 2) is given.     

Geometry and duality in supersymmetric σ-models

The Supersymmetric Dual Sigma Model (SDSM) is a local field theory introduced to be nonlocally equivalent to the Supersymmetric Chiral nonlinear σ-Model (SCM), this dual equivalence being proven by explicit canonical transformation in tangent space. This model is here reconstructed in superspace and identified as a chiral-entwined supersymmetrization of the Dual Sigma Model (DSM). This analysis sheds light on the boson fermion symphysis of the dual transition, and on the new geometry of the DSM.     

Four-loop β-function for the N = 1 and N = 2 supersymmetric non-linear sigma model in two dimensions

A superspace calculation of the four-loop β-function is presented for two-dimensional N= 1,2 supersymmetric non-linear σ-models. It is concluded that besides the one-loop contribution which vanishes on Ricci-flat manifolds, the β-function receives four-loop contributions which do not vanish in the Ricci-flat case. Implications for the superstring are discussed.     

Background field method for nonlinear σ-model in stochastic quantization

We formulate the background field method for the nonlinear σ-model in stochastic quantization. We demonstrate a one-loop calculation for a two-dimensional non-linear σ-model on a general riemannian manifold based on our formulation. The formulation is consistent with the known results in ordinary quantization. As a simple application, we also analyse the multiplicative renormalization of the O(N) nonlinear σ-model.     

Spontaneous breaking of chiral symmetry, and eventually of parity, in a σ-model with two Mexican hats

A σ-model with two linked Mexican hats is discussed. This scenario could be realized in low-energy QCD when the ground state and the first excited (pseudo)scalar mesons are included, and where not only in the subspace of the ground states, but also in that of the first excited states, a Mexican hat potential is present. This possibility can change some basic features of a low-energy hadronic theory of QCD. It is also shown that spontaneous breaking of parity can occur in the vacuum for some parameter choice of the model.     

Pion,sigma and nucleon propagators in the linear σ-model

We study the pion, sigma and nucleon propagators of the linear -model in the one-loop approximation. We show that in the renormalized model the meson propagators exhibit imaginary poles. Such nonphysical poles disappear when a cutoff is introduced. The maximum of this cutoff value is shown to be of the order _c1.2 Gev. Once this value is fixed it is possible to find a set of parameters which allow for a selfconsistent interpretation of physical properties associated with the propagators. A 400 MeV wide resonance appears in the sigma propagator, the nucleon is a bound state and in its continuum two Roper resonances can be identified.Work supported in part by CNPq and FAPEMIG (Brasil) and CERN project no. PCERN/C/FAE/74/91     

String solutions in the S2 nonlinear σ-model with a gauge field

A variant of the S² nonlinear -model of Faddeev with an Abelian gauge field is considered. By using a direct variational method we demonstrate the existence of string-like solutions in this model and we establish the regularity of these solutions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, No. 5, pp. 79–83, May, 1986.     

Bosonization and the O(3) σ-model

The rules of vector bosonization with respect to the O(4) σ-model with a Wess—Zumino term, and the O(3) σ-model with an instanton term are derived. The critical points at which the theories become conformally invariant are found.     

The supersymmetric WKB approximation of ring-shaped oscillator potential in r and θ dimensions with spherical polar coordinates

According to calculation of the energy spectrum of ring-shape oscillator potential by using the supersymmetric WKB approximation, it is shown that the energy spectrum of some noncentral separable potentials can be exactly obtained in r and θ dimensions by above method.     

New nonlinear σ-model with N=4 extended supersymmetry

A new nonlinear -model with N=4 supersymmetry in d=2 is constructed in terms of a N=2 tensor multiplet in d=4. Four equivalent formulations of the theory in superspace are obtained. The component structure of the model is considered by means of the Legendre transformation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 70–74, September, 1987.     

Keldysh technique and non-linear σ-model: basic principles and applications

The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of the underlying microscopic models. A large part of the review is devoted to derivation and applications of the non-linear σ-model for disordered metals and superconductors. We discuss topics such as transport properties, mesoscopic effects, counting statistics, interaction corrections, kinetic equations, etc. The section devoted to disordered superconductors includes the Usadel equation, fluctuation corrections, time-dependent Ginzburg–Landau theory, proximity and Josephson effects, etc.     

Effective action and vacuum instability in the chiral σ-model and the standard electroweak model

We develop a partial expansion of the effective action from fermion integration relevant for spatially small configurations of the meson fields in the chiral σ-model. It is shown that this leads (in this semiclassical approximation) to a vacuum instability. For weak Yukawa coupling, when the semiclassical calculation is valid, this would indicate an instability of the Weinberg-Salam model, implying that the latter is only an effective theory. We give an estimate of the approximate length scale at which this occurs.     

The equivalence theorem for the heavy-Higgs Standard Model and the gauged nonlinear σ-model

The equivalence theorem states that the leading part of the amplitude for a process with external longitudinally polarized vector bosons is given by the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons. The validity of this theorem within the standard model with a heavy Higgs boson and within the gauged nonlinear -model (in which the Higgs boson is absent) is shown. Furthermore it is examined to what extent also internal lines other than scalar lines can be neglected. A simple power-counting method is developed which determines the leading diagrams for a given process at an arbitrary loop order. This method is also applied to effective Lagrangians with additional nonstandard interaction terms of higher dimension (chiral Lagrangians).     

Anomalous current algebras in the Skyrme model or chiral G×G with Wess-Zumino term

We deal with chiral G×G field theory with Wess-Zumino term (or the Skyrme model) specified in terms of its Goldstone fields. Working in four dimensions we derive the current of the Noether currents of the theory in the canonical formalism displaying its anomalous structure.