Noise-driven nonlinear sigma model

We present a noise-driven model for obtaining the gap and line-width as functions of the temperature in the nonlinear sigma model. The method is phenomenological and rests on the following physical idea: a classical external stochastic field is introduced representing the coupling of the sigma field with a noise source. Moreover, we assume that the inelastic scattering length is much longer than the elastic one, justifying the neglect of dissipation for temperatures such that the nonlinear sigma model is a good approximation for antiferromagnetic spin chains. This phenomenological approach is justified by comparison with other theoretical predictions and with experiment.     

General relativity as a soldered nonlinear sigma model

It is shown that the known analogies between general relativity and the nonlinear sigma models are not restricted to kinematics but extend also to the dynamics. Some comments are made on possible consequences of this point of view and on the so-called gauge theories of gravitation.     

Topological massive sigma models

In this paper we construct topological sigma models which include a potential and are related to twisted massive supersymmetric sigma models. Contrary to a previous construction these models have no central charge and do not require the manifold to admit a Killing vector. We use the topological massive sigma model constructed here to simplify the calculation of the observables. Lastly it is noted that this model can be viewed as interpolating between topological massless sigma models and topological Landau-Ginzburg models.     

Multiple soft pion production in nonlinear chiral sigma model

Multiple soft pion production in the baryon scattering reactions is considered in the framework of chiral nonlinear sigma model neglecting the pion mass. Treating baryons in the eikonal approximation as classical sources, a set of analytical solutions for the pion field is found. A tree S-matrix is constructed on the basis of these solutions describing the emission (or absorption) of any number of soft pions. Then the contribution of soft virtual pions is taken into account in a closed form. It is shown that the loop corrections strongly suppress the pion radiation, and for the two limiting cases of nonrelativistic and ultra-relativistic baryon scatterings there is no pion emission from the “ends”. Thus, the mechanism similar to the soft photon bremsstrahlung in the quantum electrodynamics seems to be unable to create a state with a large number of the soft pions.     

Supersymmetric nonlinear sigma model in AdS5

We construct the supersymmetric nonlinear sigma model in a fixed AdS₅ background. We use component fields and find that the complex bosons must be the coordinates of a hyper-Kähler manifold that admits a Killing vector satisfying an inhomogeneous tri-holomorphic condition. We propose boundary conditions that map the on-shell bulk hypermultiplets into off-shell chiral multiplets on 3-branes that foliate the bulk. The supersymmetric AdS₅ isometries reduce to superconformal transformations on the brane fields.     

Calculation of anomalous dimensions for the nonlinear sigma model

The relevant scaling operators without derivatives for the orthogonal, unitary and symplectic nonlinear σ-model are classified and their anomalous dimensions are calculated up to three-loop order. The exponents for the participation ratio and for higher averaged moments of the wave functions for Anderson localization are obtained. For nonmagnetic scattering the two-loop and three-loop term vanishes.     

Quantum nonlinear sigma model for arbitrary spin Heisenberg antiferromagnets

We derive a quantum nonlinear sigma model (QNLSM) for quantum Heisenberg antiferromagnets (QHA) with arbitrary S (spin) values. A upper limit of the low temperature is naturally carried out for the reliability of the QNLSM. The S dependence of the effective coupling constant and the spin-wave velocity in the QNLSM are also obtained explicitly. The resulting spin-wave velocity for 2D spin-1/2 QHA highly concurs with the experimental data of high T(c) compound La(2)CuO(4). The predicted correlation lengths for 2D QHA and spin-gap magnitudes for 1D QHA also agrees with the accurate numerical results.     

Heterotic p-branes from massive sigma models

We explicitly construct massive (0,4) supersymmetric ADHM sigma models which have heterotic p-brane solitons as their conformal fixed points. These yield the familiar gauge 5-brane and a new 1-brane solution which preserve half and a quarter of the space-time supersymmetry, respectively. We also discuss an analogous construction for the type 11 NS-NS p-branes using (4,4) supersymmetric models.