Exact factorized S-matrix of the chiral field in two dimensions

The exact factorized S-matrix and the spectrum for the two-dimensional SU(N)-principal chiral field are presented.     

(8,0) Locally supersymmetric sigma models with conformal invariance in two dimensions

The (8,0) conformal supergravity, and an action which describes its coupling to an arbitrary number of (8,0) scalar multiplets are constructed. The 64+64 components of the conformal supermultiplet occur as Lagrange multipliers which lead to differential and algebraic constraints on the fields of the scalar multiplets. Solving the algebraic constraints yields an (8,0) locally supersymmetric sigma model based on the manifold SO(8 + n,m)/SO(8)×SO(n,m), where n,m ⩾ 0.     

Conductance fluctuations in disordered superconductors with broken time-reversal symmetry near two dimensions

We extend the analysis of the conductance fluctuations in disordered metals by Altshuler, Kravtsov, and Lerner (AKL) to disordered superconductors with broken time-reversal symmetry in d=(2+?)$d=(2+\mathrm{?})$ dimensions (symmetry classes C and D of Altland and Zirnbauer). Using a perturbative renormalization group analysis of the corresponding non-linear sigma model (NLσM) we compute the anomalous scaling dimensions of the dominant scalar operators with 2s   gradients to one-loop order. We show that, in analogy with the result of AKL for ordinary, metallic systems (Wigner–Dyson classes), an infinite number of high-gradient operators would become relevant (in the renormalization group sense) near two dimensions if contributions beyond one-loop order are ignored. We explore the possibility to compare, in symmetry class D, the ?=(2−d)$\mathrm{?}=(2-d)$ expansion in d<2$d<2$ with exact results in one dimension. The method we use to perform the one-loop renormalization analysis is valid for general symmetric spaces of Kähler type, and suggests that this is a generic property of the perturbative treatment of NLσMs defined on Riemannian symmetric target spaces.     

XIII. Exact S-matrices and form factors in 1 + 1 dimensional field theoretic models with soliton behaviour

A review is given of the derivation of exact S-matrices in field theoretic models with soliton behaviour, that means models obeying infinitely many conservation laws which imply the factorization of the S-matrix. Form factors of various operators are calculated exactly by means of Watson's theorem. The exact value of the finite Sine-Gordon wave function renormalization constant is determined.     

Realizing tri-bimaximal mixing in minimal seesaw model with S4 family symmetry

In this Letter, we realize the tri-bimaximal mixing in the lepton sector in the context of minimal seesaw in which only two right-handed neutrinos are introduced, with the discrete group S4 as the family symmetry. In order to constrain the form of superpotential, a Z3 symmetry is also introduced. In the model, the mass matrices for charged leptons and right-handed neutrinos are diagonal. The unitary matrix that diagonalizes the light Majorana neutrino mass matrix is exact tri-bimaximal at LO, and is corrected by small quantities of O(0.01) at NLO. The mechanism to get the particular scalar VEV alignments used is also presented. Phenomenologically, the mass spectrum is of normal hierarchy with m₁=0, and ∑mi and |mee| are about 0.058 eV and 0.003 eV respectively.     

Evidence for two types of low-energy charge transfer excitations in Sr2CuO3

A comparative analysis of electron energy-loss spectroscopy (EELS) spectra for the 1D insulating cuprate Sr2CuO3 with transferred momentum q--> axially and radially to the chain axis allows one to elucidate the structure of the charge transfer gap in in-chain response. It is determined by the superposition of two types of excitations with different magnitudes of dispersion. The low-energy response with q--> radially to the chain direction, but yet within the plane of CuO4 plaquettes, exhibits also a dispersionless peak near 2 eV. The theoretical simulation of the EELS data using exact diagonalizations of an appropriate extended Hubbard Hamiltonian for relevant clusters requires the explicit consideration of low-lying oxygen 2p pi states within the CuO4 plaquette plane beyond the standard pd sigma extended Hubbard model widely used for cuprates with corner-shared CuO4 plaquettes.     

Zero-mass scalar and electrostatic fields with the central symmetry in the general relativity

All asymptotically flat space solutions of Einstein equations with energy-momentum tensor of electrostatic and zero-mass scalar static central symmetric fields as a source were found. There are five branches of general solution; only two of them are contained in previous Penney's solution. In a limit of pure electrostatic field and pure scalar field our solutions become identical with corresponding solutions known previously.     

Inversion relations,phase transitions and transfer matrix excitations for special spin models in two dimensions

The infrared and Raman active phonons (k=0) of orthorhombic TbF₃ and of isomorphous HoF₃ have been observed and attributed to the different irreducible representations of the factor groupD _2h. Moreover we investigated crystal-field excitations of the 4f-configuration of the Rare-Earth-ions and effects of their interaction with optical phonons, especially as a function of an external magnetic field. The infrared reflection spectra of these materials not only display reststrahlen bands of electric dipolar but also of magnetic dipolar type with a characteristic shape of the latter bands.On entering the ferromagnetic ordered state pertinent symmetry reductions (D _{2hC 2h}) become evident in the system of electronic transitions and optical phonons in TbF₃ by a change of selection rules and a magnetization-induced transfer of transition intensities to new components of the transition dipole or of the Raman polarizability tensor. These observations are in accordance with general symmetry considerations.The delocalization of the crystal-field excitations results in a Davydov splitting of the single-ion transitions.     

1/N Expansion for a supersymmetric o(n) model in four dimensions

An application is considered of the stationary phase method to computation of the generating functional of Green's functions [1, 2] for a four-dimensional supersymmetric -model [3, 4]. In the leading order in 1/V, a renormalized potential is obtained, which is unbound from below, unlike in a similar two-dimensional case [5].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 7–10, January, 1984.     

On the absence of spontaneous breakdown of continuous symmetry for equilibrium states in two dimensions

Using the Bogoliubov inequality, we extend previously known results concerning the absence of continuous symmetry breakdown for equilibrium states of certain quantum and classical lattice, and continuum systems in two space dimensions.Partially supported by the N.S.F. under grant MCS 7801433.Partially supported by the N.S.F. under grant MCS 7906633.     

Conformal symmetry in two dimensions: An explicit recurrence formula for the conformal partial wave amplitude

An explicit recurrence relation for the conformal block functions is presented. This relation permits one to evaluate theX-expansion of these functions order-by-order and appropriate for numerical calculations.     

Synchronisation and general dynamic symmetry of a vibrating system with two exciters rotating in opposite directions

We derive the non-dimensional coupling equation of two exciters, including inertia coupling, stiffness coupling and load coupling. The concept of general dynamic symmetry is proposed to physically explain the synchronisation of the two exciters, which stems from the load coupling that produces the torque of general dynamic symmetry to force the phase difference between the two exciters close to the angle of general dynamic symmetry. The condition of implementing synchronisation is that the torque of general dynamic symmetry is greater than the asymmetric torque of the two motors. A general Lyapunov function is constructed to derive the stability condition of synchronisation that the non-dimensional inertia coupling matrix is positive definite and all its elements are positive. Numeric results show that the structure of the vibrating system can guarantee the stability of synchronisation of the two exciters, and that the greater the distances between the installation positions of the two exciters and the mass centre of the vibrating system are, the stronger the ability of general dynamic symmetry is.     

Generalizations of CPn−1 with non-abelian gauge symmetry in 2 + ϵ dimensions

This paper considers non-linear σ models having global U(n) and local U(k) symmetries (1 ? k < n) in space-time dimensions d > 2. The special case k = 1 is the CP^n?1 model. The renormalizability to all orders of these models (in the presence of gauge invariant sources) is demonstrated in 2 + ? dimensions. A second order phase transition is shown to occur at a coupling strength of order ?, analogous to that in the O(n) model. Certain critical exponents associated with this transition are evaluated at two loop order. We are able to compare the two phases only in the limit n → ∞, k fixed.     

Schwinger functions for the Yukawa model in two dimensions with space-time cutoff

It is shown that a Euclidean version of the formulae of Matthews and Salam for the Green's functions of a two-dimensional Yukawa model with interaction in a finite space-time volume makes sense, if renormalized correctly.     

Conditions for static balance for the post-Newtonian two-body problem with electric charge in general relativity

The usual condition for static balance, for two bodies with masses and charges m_i and e_i (i = 1, 2), is $\text{e}{}_{\mathrm{i}}\text{=±G}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{m}{}_{\mathrm{i}}$. From a post-Newtonian analysis of the two-body problem, an alternate condition for static balance $\text{e}{}_{\mathrm{i}}\text{=±(Gm}{}_1\text{m}{}_2\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ has been found. We do not know if this condition is exact beyond the post-Newtonian approximation.