Geometric sigma model of the Universe

The purpose of this work is to demonstrate how an arbitrarily chosen background of the Universe can be made a solution of a simple geometric sigma model.Geometric sigma models are purely geometric theories in which spacetime coordinates are seen as scalar fields coupled to gravity.Although they look like ordinary sigma models,they have the peculiarity that their complete matter content can be gauged away.The remaining geometric theory possesses a background solution that is predefined in the process of constructing the theory.The fact that background configuration is specified in advance is another peculiarity of geometric sigma models.In this paper,I construct geometric sigma models based on different background geometries of the Universe.Whatever background geometry is chosen,the dynamics of its small perturbations is shown to have a generic classical stability.This way,any freely chosen background metric is made a stable solution of a simple model.Three particular models of the Universe are considered as examples of how this is done in practice.     

The yang-yang anomaly in fluid criticality: experiment and scaling theory

Yang and Yang proved that the divergence of C(V)(T) at a gas-liquid critical point implies that either d(2)p/dT(2) identical withp(")(sigma) or d(2)&mgr;/dT(2) identical with&mgr;(")(sigma) or both diverge when T-->T(c)- on the phase boundary sigma. They queried the lattice-gas prediction that &mgr;(")(sigma) remains finite. Analysis of two-phase heat-capacity data provides, for the first time, evidence for such a Yang-Yang anomaly (&mgr;(")(sigma)-->+/-infinity) in propane and suggests an anomaly of opposite sign in CO (2). A revision of standard scaling theory for fluid criticality is demanded: specifically, p-p(c) must appear in the ordering field. The coexistence diameter hence gains a |T-T(c)|(2beta) term.     

Classical integrability of two-dimensional non-linear sigma models

The conditions under which a general two-dimensional non-linear sigma model is classically integrable are given. These requirements are found by demanding that the equations of motion of the theory are expressible as a zero curvature relation. Some new integrable two-dimensional sigma models are then presented.     

Gauge-invariant sigma models in N=2 superspace

We construct a new broad class of gauge-invariant nonlinear sigma models in N=2 superspace. The dimensional reduction of the theories obtained to d=2 leads to N=4 nonlinear sigma models which are devoid of ultraviolet divergence in all orders of perturbation theory.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 49–53, February, 1989.     

Interacting physical states of the bosonic string. II

The Diff anomaly for the standard sigma model lagrangian is considered, and some puzzling aspects of the dilation coupling are clarified. It is shown how the central charge is related to the Diff anomaly and some of its properties are illustrated. The consistency of the BRST invariance requirement with the existence of different vacua for the string is discussed.     

Anomaly constraints on nonlinear sigma models

Anomalies in nonlinear sigma models can sometimes be cancelled by local counterterms. We show that these counterterms have a simple topological interpretation, and that the requirements for anomaly cancellation can be easily understood in terms of 't Hooft's anomaly matching conditions. We exhibit the anomaly cancellation on homogeneous spaces $\text{G}\text{H}$ and on general riemannian manifolds $\text{M}$. We include external gauge fields on the manifolds and derive the generalized anomaly-cancellation conditions. Finally, we discuss the implications of this work for superstring theories.     

Ultra-violet finiteness of supersymmetric non-linear sigma models

It is shown that N = 4 supersymmetric non-linear sigma models in two spacetime dimensions are ultra-violet finite to all orders in perturbation theory.     

Superbosonization Formula and its Application to Random Matrix Theory

Starting from Gaussian random matrix models we derive a new supermatrix field theory model. In contrast to the conventional non-linear sigma models, the new model is applicable for any range of correlations of the elements of the random matrices. We clarify the domain of integration for the supermatrices, and give a demonstration of how the model works by calculating the density of states for an ensemble of almost diagonal matrices. It is also shown how one can reduce the supermatrix model to the conventional sigma model.     

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.     

Massive nonlinear sigma models and BPS domain walls in harmonic superspace

Four-dimensional massive nonlinear sigma models and BPS wall solutions are studied in the off-shell harmonic superspace approach in which supersymmetry is manifest. The general nonlinear sigma model can be described by an analytic harmonic potential which is the hyper-Kähler analog of the Kähler potential in theory. We examine the massive nonlinear sigma model with multi-center four-dimensional target hyper-Kähler metrics and derive the corresponding BPS equation. We study in some detail two particular cases with the Taub-NUT and double Taub-NUT metrics. The latter embodies, as its two separate limits, both Taub-NUT and Eguchi–Hanson metrics. We find that domain wall solutions exist only in the double Taub-NUT case including its Eguchi–Hanson limit.     

Pion production by neutral currents in neutrino-nucleon collisions

It is argued that the apparent arbitrariness of the “anomaly” in Fujikawa's approach should be placed into the context of the regularization of the theory not just the regularization of the anomaly. When the theory is regularized at the level of the action the consistent anomaly arises. The converse also holds, namely that if the anomaly is not consistent then the regulator employed does not, by itself, regulate the theory at the level of the action. The criterion that the regularization presription be given at the outset is advocated, and a discussion of results of various two-dimensional models given.     

On the QCD phase structure from effective models

Some recent theoretical developments of the QCD phase diagram are summarized. Chiral symmetry restoration and the confinement/deconfinement transition at nonzero temperature and quark densities are analyzed in the framework of an effective linear sigma model with three light quark flavors. The sensitivity of the chiral transition as well as the existence of a critical end point in the phase diagram on the value of the sigma mass is explored. The influence of the axial anomaly on the chiral critical surface is addressed. Finally, the modifications by the inclusion of the Polyakov loop on the phase structure are investigated.     

Unconventional integer quantum Hall effect in graphene

Monolayer graphite films, or graphene, have quasiparticle excitations that can be described by (2+1)-dimensional Dirac theory. We demonstrate that this produces an unconventional form of the quantized Hall conductivity sigma(xy) = -(2e2/h)(2n+1) with n = 0, 1, ..., which notably distinguishes graphene from other materials where the integer quantum Hall effect was observed. This unconventional quantization is caused by the quantum anomaly of the n=0 Landau level and was discovered in recent experiments on ultrathin graphite films.     

Non-perturbative effects in supersymmetric sigma models

A scheme for taking account of crucial non-perturbative effects in a quantum field theory ahead of developing perturbation series for it is extended here from bosonic to supersymmetric sigma models in two dimensions. The scheme writes field products in the lagrangian in terms of suitably defined normal ordered products and VEVs of field products. The exact values of the latter can be inferred directly from the symmetry and supersymmetry Ward identities of the theory, so that a lagrangian with scale breaking effects explicitly treated, is available for use in perturbation theory. The supersymmetric sigma model on the manifold S^N is used to illustrate many aspects of the scheme.     

Non-Birational Twisted Derived Equivalences in Abelian GLSMs

In this paper we discuss some examples of abelian gauged linear sigma models realizing twisted derived equivalences between non-birational spaces, and realizing geometries in novel fashions. Examples of gauged linear sigma models with non-birational Kähler phases are a relatively new phenomenon. Most of our examples involve gauged linear sigma models for complete intersections of quadric hypersurfaces, though we also discuss some more general cases and their interpretation. We also propose a more general understanding of the relationship between Kähler phases of gauged linear sigma models, namely that they are related by (and realize) Kuznetsov’s ‘homological projective duality.’ Along the way, we shall see how ‘noncommutative spaces’ (in Kontsevich’s sense) are realized physically in gauged linear sigma models, providing examples of new types of conformal field theories. Throughout, the physical realization of stacks plays a key role in interpreting physical structures appearing in GLSMs, and we find that stacks are implicitly much more common in GLSMs than previously realized.     

GLSMs for partial flag manifolds

In this paper we outline some aspects of nonabelian gauged linear sigma models. First, we review how partial flag manifolds (generalizing Grassmannians) are described physically by nonabelian gauged linear sigma models, paying attention to realizations of tangent bundles and other aspects pertinent to (0, 2) models. Second, we review constructions of Calabi–Yau complete intersections within such flag manifolds, and properties of the gauged linear sigma models. We discuss a number of examples of nonabelian GLSMs in which the Kähler phases are not birational, and in which at least one phase is realized in some fashion other than as a complete intersection, extending previous work of Hori–Tong. We also review an example of an abelian GLSM exhibiting the same phenomenon. We tentatively identify the mathematical relationship between such non-birational phases, as examples of Kuznetsov’s homological projective duality. Finally, we discuss linear sigma model moduli spaces in these gauged linear sigma models. We argue that the moduli spaces being realized physically by these GLSMs are precisely Quot and hyperquot schemes, as one would expect mathematically.     

Magnetic hyperfine anomalies

This study is concerned with the measurement and interpretation of magnetic hyperfine anomalies in electronic and muonic atoms. i.e. effects of the distribution of nuclear magnetization on the magnetic dipole hyperfine interaction. After a summary of the relevant theory and a review of experimental techniques, hyperfine anomaly results are discussed in terms of various nuclear models. The use of the anomaly for yielding information about the origin of magnetic hyperfine interactions is outlined. Experimental and theoretical hyperfine anomalies are tabulated.     

Vacuum Stability in Kaluza-Klein Geometric Sigma Models

In Kaluza-Klein geometric sigma models, the scalar fields coupled to higher-dimensional gravity are pure gauge. The gauge fixed theory contains no matter fields, and can consistently be reduced to 4 dimensions, provided the internal space is chosen in the form of a group manifold. The effective 4-dimensional theory includes standard Einstein and Yang-Mills sectors, and is free of the classical cosmological constant problem. In this paper, the stability of the internal excitations is analyzed. It is shown that the initial Lagrangian can be modified to lead to a classically stable effective 4-dimensional theory, independently of the particular group used, and retaining all the basic features of the unmodified theory.