Finiteness of Ricci flat supersymmetric non-linear σ-models

Combining the constraints of Kähler differential geometry with the universality of the normal coordinate expansion in the background field method, we study the ultraviolet behavior of 2-dimensional supersymmetric non-linear -models with target space an arbitrary riemannian manifoldM. We show that the constraint ofN=2 supersymmetry requires that all counterterms to the metric beyond one-loop order be cohomologically trivial. It follows that such supersymmetric non-linear -models defined on locally symmetric spaces are super-renormalizable and thatN=4 models are on-shell ultraviolet finite to all orders of perturbation theory.     

Renormalization properties of Bosonic non-linear σ-models built on compact homogeneous Kähler manifolds

The non-linear bosonic σ-models built on compact Kähler homogeneous manifolds are parametrized in such a way that multiplicative renormalizability holds, to all orders of perturbation theory. Moreover, the fields are not renormalized. The essential ingredients of the proof are the homogeneity of the space and the existence of a charge Y that separates the fields in φ and φ̄.     

Critical behaviour of SU(n) quantum chains and topological non-linear σ-models

The critical behaviour of SU(n) quantum “spin” chains, Wess-Zumino-Witten σ-models and grassmanian σ-models at topological angle θ = π (of possible relevance to the quantum Hall effect) is reexamined. It is argued that an additional Z_n symmetry is generally necessary to stabilize the massless phase. This symmetry is not present for the σ-models for n > 2 and is only present for certain representations of “spin” chains.     

A relation between instantons of grassmann σ-models and Toda equations: II

We construct special solutions of Toda equations and show that these are deeply related with irreducible representations of sl(2;). We also show that after taking a continuum limit of Toda equations, these become the well-known solution of the continuum Toda equation.Partially supported by the Grant-in-Aid for Scientific Research, No. 03640085.     

The geometry of the quantum correction for topological σ-models

The ring (Frobenius algebra) of local observables for topological -models on ¹ with values in the grassmannianG(s, n) is known to be the same as the quotient of the homology ring of the target space by the (inhomogeneous) ideal generated by the so-called quantum correction. While the need for a quantum correction comes from algebraic motivations in field theory, the aim of this paper is to understand its geometric meaning. The simple examples of ^{1 n} models tell us that the quantum correction comes by restriction on the boundary of the moduli spaces which allows to compute intersections on moduli spaces of lower degrees. We will check this point of view for the case of ¹ G(s,n) models, yielding a proof of the algebraic result from physics in terms of the geometry of the -model itself.Work partially supported by National Project 40% Probabilistic and geometrical methods in Mathematical Physics and by CNR-Gruppo Nazionale di Fisica Matematica.     

Nonlinear σ-models and their gauging in and out of superspace

We analyze and generalize bosonic nonlinear σ-models and their N = 1,2 supersymmetric extensions in (4 spacetime-dimensional) N = 1 superspace. We give a general construction of nonminimal kinetic terms for gauge fields and of N = 1,2 gauging of isometries on Kähler and hyper-Kähler manifolds. In particular, we study the gauging of noncompact groups. We derive the complete component action and supertrace formula. For N = 2 models, the supertrace always vanishes.     

Exact critical exponents for quantum spin chains,non-linear σ-models at θ=π and the quantum hall effect

We use non-abelian bosonization to predict critical exponents for quantum chains of arbitrary spin and arbitrary symmetry SU(n). Passing to the large representation limit gives non-linear σ-models on the manifolds U(2n)/U(n)×U(n) at topological angle θ=π. For n=1 this is the familiar “O(3)” model; taking the replica limit n→0 given critical exponents for the localization transition in the quantum Hall effect. Given certain assumptions, these exponents should be exact.     

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.     

Universality of the Bethe-ansatz solution for the chiral non-linear σ-model

A euclidean lattice action is constructed to test the idea of universality of the Bethe-ansatz solution for the two-dimensional principal chiral model. The response of the system to uniform external fields is studied using the Monte Carlo simulation. A transition to the gapless phase is observed at the critical external field predicted by the Bethe-ansatz method.     

Multi-grid Monte Carlo via XY embedding. General theory and two-dimensional O(N)-symmetric non-linear σ-models

We introduce a variant of the multi-grid Monte Carlo (MGMC) method, based on the embedding of an XY model into the target model, and we study its mathematical properties for a variety of non-linear σ-models. We then apply the method to the two-dimensional O(N)-symmetric nonlinear σ-models (also called N-vector models) with N = 3,4,8 and study its dynamic critical behavior. Using lattices up to 256 × 256, we find dynamic critical exponentsZ_int, M² 0.70 ± 0.08, 0.60 ± 0.07, 0.52 ± 0.10 for N = 3, 4, 8, respectively (subjective 68% confidence intervals). Thus, for these asymptotically free models, critical slowing down is greatly reduced compared to local algorithms, but not completely eliminated; and the dynamic critical exponent does apparently vary with N. We also analyze the static data for N = 8 using a finite-size scaling extrapolation method. The correlation length ξ agrees with the four-loop asymptotic-freedom prediction to within 1 % over the interval 12 ⪅ ξ ⪅ 650.     

Painlevé analysis and integrability of two-coupled non-linear oscillators

Integrability of a linearly damped two-coupled non-linear oscillators equation is investigated by employing the Painlevé analysis. The following two integrable cases are identified: (i)d = 0, α =β, δ_1 and δ_2 are arbitrary, (ii) d^2= 25α/6, α =β, δ_1 and δ_2 are arbitrary. Exact analytical solution is constructed for the integrable choices.     

A classical solution of the non-linear complex Grassmann σ-model with higher derivatives

We construct a soliton solution of the non-linear complex Grassmann-model with higher derivatives, and show that this solution, as a continuous map, represents a generator of theK-group of a sphere.     

Wave operators and analytic solutions for systems of non-linear Klein-Gordon equations and of non-linear Schrödinger equations

We consider, in a 1+3 space time, arbitrary (finite) systems of nonlinear Klein-Gordon equations (respectively Schrödinger equations) with an arbitrary local and analytic non-linearity in the unknown and its first and second order space-time (respectively first order space) derivatives, having no constant or linear terms. No restriction is given on the frequency sign of the initial data. In the case of non-linear Klein-Gordon equations all masses are supposed to be different from zero.We prove, for such systems, that the wave operator (fromt= tot=0) exists on a domain of small entire test functions of exponential type and that the analytic Cauchy problem, in ⁺׳, has a unique solution for each initial condition (att=0) being in the image of the wave operator. The decay properties of such solutions are discussed in detail.Partially supported by the Swiss National Science FoundationOn leave from Institut de Physique Théorique, 32 Bd d'Ivoy, CH-1211 Geneve 4 Switzerland.     

Effective actions from the conformal invariance conditions of bosonic σ-models with graviton and dilaton backgrounds

We discuss generalised functional relations between the β-functions of bosonic σ-models propagating in graviton and dilaton backgrounds and field variations of the associated effective actions based on these backgrounds. We analyse the constraints on the possible form of the proportionality (non-degenerate) tensors, imposed by classical symmetries of the associated point-like action. As an application we derive the second order [O(α′)] effective action and we find that it is consistent with a ghost free combination for both fields. Moreover we show explicitly that this action is related to the one computed within the framework of string tree-amplitudes by field redefinitions.     

Fusion of visible and infrared imagery for face recognition

In recent years face recognition has received substantial attention, but still remained very challenging in real applications. Despite the variety of approaches and tools studied, face recognition is not accurate or robust enough to be used in uncontrolled environments. Infrared (IR) imagery of human faces offers a promising alternative to visible imagery, however, IR has its own limitations. In this paper, a scheme to fuse information from the two modalities is proposed. The scheme is based on eigenfaces and probabilistic neural network (PNN), using fuzzy integral to fuse the objective evidence supplied by each modality. Recognition rate is used to evaluate the fusion scheme. Experimental results show that the scheme improves recognition performance substantially.     

‘In’ and ‘out’ vertex operators in a class of UV-finite nonlinear σ-models

In and out scalar vertex operators are constructed perturbatively in a class of recently discovered UV finite nonlinear -models describing the string evolution in gravitational plane wave backgrounds. They exhibit peculiar singularities in the target space related to the focusing phenomena in such backgrounds well known from the classical and quantum gravity theories. The computation is performed up to three loops of the usual perturbation expansion and to all loops of the weak field limit. An argument is given that the vertex operator singularities should persist, even when summing up the all perturbation expansions.     

Pathologies of the large-N limit for RPN−1, CPN−1, QPN−1 and mixed isovector/isotensor σ-models

We compute the phase diagram in the N→∞ limit for lattice RP^N−1, CP^N−1 and QP^N−1 σ-models with the quartic action, and more generally for mixed isovector/isotensor models. We show that the N=∞ limit exhibits phase transitions that are forbidden for any finite N. We clarify the origin of these pathologies by examining the exact solution of the one-dimensional model: we find that there are complex zeros of the partition function that tend to the real axis as N→∞. We conjecture the correct phase diagram for finite N as a function of the spatial dimension d. Along the way, we prove some new correlation inequalities for a class of N-component σ-models, and we obtain some new results concerning the complex zeros of confluent hypergeometric functions.     

A study of fringe pattern trace and analysis

In this paper,the gometric center and centroid method are suggested to tracecenter location of a close fringe pattern.The fringe pattern of the interferogram is analysed byusing the general Fourier method.The analytic accuracy is controlled by using P-test methodof statistics.The analytic accuracy and sampling speed of the fringe pattern depend on thequality of the interferogram and the numbers of the sampling points.     

Thermal analysis and infrared study of Nb2O5–TeO2 glasses

Tellurite glasses of the xNb₂O₅–(100–x) TeO₂, (3 ≤ x ≤ 20 mol%) system have been prepared and studied by IR spectroscopy and differential thermal analysis to explore the role of Nb₂O₅ on their structure. IR analysis indicates that NbO₆ transforms TeO₄ units into tellurite structural TeO₃ units, with a shift of lattice vibrations towards higher wavenumbers. The stretching force constant of the tellurite structural units increases with Nb₂O₅ content, a feature that is attributed to the higher bond strength and higher coordination number of Nb₂O₅ relative to TeO₂. The crystallization kinetics has been studied under non-isothermal conditions using the formal theory of transformations for heterogeneous nucleation. The crystallization results are analyzed, and both the activation energy of the crystallization process and the crystallization mechanism are characterized. The thermal stability of these glasses are characterized in terms of characteristic temperatures, such as the glass-transition temperature, T _g, the temperature of onset of crystallization, T _in, the temperature corresponding to the maximum crystallization rate, T _p, and two kinetic parameters, K(T _g) and K(T _p). The results reveal that thermal stability increases with increasing Nb₂O₅ content. XRD diffraction of the studied glasses indicates the presence of microcrystallites of α-tellurite, γ-telluride, Nb₂Te₄O₁₃ and an amorphous matrix.