Gauge Theory of the Generalized Symmetry on the Torus Membrane

The SDIFF(T2)local-generalized Kac-Moody G(T2) symmetry is an infinite-dimensional group on the torus membrane, whose Lie algebra is the semi-direct sum of the SDIFF(T2)local algebra and the generalized KacMoody algebra g(T2). In this paper, we construct the linearly realized gauge theory of the SDIFF(T2)loc1al-generalized Kac-Moody G(T2) symmetry.``     

DIRECT COMPACTIFICATION OF HETEROTIC STRINGS FROM 26 TO 4 DIMENSIONS VIA T22/G

We discuss compactificstion of the heterotic string in a U=T²²/G manifold, where G acts on the 22-dimensional torus T²² without fixed points. This non-trivial mixture of the internal 16-dimensional space enables chiral theories to exist in U. In a11 the three examples which we discuss in detail,the symmetry groups after compactification are all equal to E₆×SU(3)×E₈', though the imbeddings of these groups in E₆×E₈' are different for different cases. The resulting numbers of massless chiral fermion multiplets are a1so different.     

Projection Operator on Rational Noncommutative OrbifoldT2/Z4

In this paper, we introduce the reduced matrix in kq representation and provide the reduced matrix elements of a projection operator \hat{P} on the rational noncommutative orbifold T²/Z₄. we give the closed form for the projector by Jacobi elliptical functions. Since projectors correspond to soliton solutions of the field theory on the noncommutative orbifold, we thus present a corresponding soliton solution.     

P-Twisted Affine Lie Algebras and Their Associated Vertex Algebras

For any finite-dimensional semisimple Lie algebra g, a Z₊-graded vertex algebra is construsted on the vacuum representation V_k(\hat{g}[ θ]) of \hat{g}[θ], which is a one-dimentional central extension of θ-invariant subspace on the loop algebra Lg=g\otimes C((t^1/p)).     

The first eigenvalue of the Dirac operator on Kähler manifolds

If M^2m is a closed Kähler spin manifold of positive scalar curvature R, then each eigenvalue λ of type r (r {1, …, [(m + 1)/2]}) of the Dirac operator D satisfies the inequality λ² ≥ rR₀/4r − 2, where R₀ is the minimum of R on M^2m. Hence, if the complex dimension m is odd (even) we have the estimation

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for the first eigenvalue of D. In the paper is also considered the limiting case of the given inequalities. In the limiting case with m = 2r − 1 the manifold M^2m must be Einstein. The manifolds S², S² × S², S² × T², P³( ), F( ), P³( ) × T² and F( ³) × T², where F( ³) denotes the flag manifold and T² the 2-dimensional flat torus, are examples for which the first eigenvalue of the Dirac operator realizes the limiting case of the corresponding inequality. In general, if M^2m is an example of odd complex dimension m, then M^2m × T² is an example of even complex dimension m + 1. The limiting case is characterized by the fact that here appear eigenspinors of D² which are Kählerian twistor-spinors.     

On gl（2｜2）（2）k Current Superalgebra and Twisted Conformal Field Theory

Motivated by the recently discovered hidden symmetry of the type IIB Green-Schwarz superstring on certain background, the non-semisimple Kac-Moody twisted superalgebra gl（2｜2）（2）k is investigated by means of the vector coherent state method and boson-fermion realization. The free field realization of the twisted current superalgebra at general level k is constructed. The corresponding Conformai Field Theory （CFT） has zero central charge. According to the classification theory, this CFT is a nonunitary field theory. After projecting out a U（1） factor and an outer automorphism operator, we get the free field representation of psl（2｜2）（2）k, which is the a/gebra of gl（2｜2）（2）k modulo the Z4-outer automorphism, the CFT has central charge -2.     

ELECTRONIC STRUCTURE OF THE T*-TYPE SUPERCONDUCTORS (Bi0.5Sr1.5)(Y,Ce)2Cu2Oy STUDIED BY PHOTOELECTRON SPECTROSCOPY

The electronic structure of T^*-type compounds (Bi_0.5Sr_1.5)(Y_2-xCe_x)Cu₂O_y has been studied by X-ray photoelectron spectroscopy. From analysis of the results, it was found that cation deficiency in Ce⁴⁺ introduced holes to conduction planes in the T^* phase as in the p-type infinite layer compounds. Some Cu ions in the sample without cation-deficiency contained two-oxygen coordination, which resulted in the incompleteness of the CuO₂ sheets. Bi ions in the T^* phase cuprates take exact valence of 3_{+, Pb ions cannot replace them due to the too large an ionic radius of Pb²⁺/Pb⁴⁺.}     

STRING THEORY WITH THREE FAMILIES OF CHIRAL FERMIONS

A heterotic string theory is constructed by compactifying directly from 26 to 4 dimensions via a smooth manifold T²²/G. In the low energy limit, there are three families of chiral fermions with exactly the same quantum numbers as thatin the standard supersymmetric SU(3)×SU(2)×XU(1) model. They couple to supergravity and supergauge fields with the gauge symmetry SU(3)_F×SU(3)_c×SU(3)_L×U(1)_YR×U(1)_I3R.     

Yangian代数在混合介子态的纠缠和衰变中的应用

Yangian代数是超出李代数更大的无穷维代数,是研究非线性量子完全可积系统的新对称特性的有力数学工具.基于介子态中夸克-味su(3)对称性和Yangian代数生成元的跃迁特性,本文研究了Yangian代数Y(su(3))生成元在三种正反介子态(π~±,K~±,K~0和K~0)各自组成的三种混合介子态(π,K和K_i~0)衰变中的作用.将Y(su(3))代数的八个生成元(I~±,U~±,V~±,I~3和I~8)作为跃迁算子,作用在混合介子态上,研究其可能的衰变道,以及衰变前后纠缠度的变化.结果表明:1)在李代数范围内的生成元I~3和I~8作用下,三种混合介子态衰变后组成成分没有发生变化,其中混合介子态π在I~8作用下衰变前后纠缠无变化,其他衰变纠缠度发生了变化;2)在其他的六个(I~±,U~±和V~±)超出李代数的生成元的作用下,三种混合介子态衰变前后组成成分发生了变化,其中两个衰变后变成单态,纠缠度为零;两个衰变不存在;剩余两个衰变后纠缠度发生了变化,此外在带电(K)和中性(K_I~0)两类K型混合介子态的六种可能的衰变中,两种类型的末态的纠缠度两两相同;3)三种混合介子态之间可以通过I~±,U~±和V~±算子循环转化,具有明显的对称性.本文从具有的对称性上提供了一种探索混合介子态可能衰变的方法,并且可以用此方法去预测可能的未知衰变粒子和解释己测得的衰变问题.     

Top-Quark Condensate at Finite Temperature and Electroweak Symmetry Restoration

The gap equation at finite temperature in the top-quark condensate scheme of electroweak symmetry breaking is proven to have the identical form in both the imaginary and real time formalisms of thermal field theory. By means of the gap equation, combined with the basic relation to define the vacuum expectation value v of the effective Higgs field, we analyze the dependence on temperature T and chemical potential p of the dynamical top-quark mass as the order parameter characteristic of symmetry breaking, and obtain the p-T criticality curve for symmetry restoration. We find out that the critical temperature T_c = 2υ for μ = 0 and the critical chemical potential μ_c = 2 π υ / √3 for T = 0. When μ = 0, the top-quark mass near T_c has the leading (T_c² - T²)^1/2 behavior with an extra factor dependent on temperature T and the momentum cutoff Λ. However, it is generally argued that the symmetry restoration at T ≥ T_c is still a second-order phase transition.     

A Method for Obtaining Integrable Couplings

By making use of the vector product in R³, a commuting operation is introduced so that R³ becomes a Lie algebra. The resulting loop algebra \tilde R³ is presented, from which the well-known AKNS hierarchy is produced. Again via applying the superposition of the commuting operations of the Lie algebra, a commuting operation in R⁶ is constructed so that R⁶ becomes a Lie algebra. Thanks to the corresponding loop algebra \tilde R³ of the Lie algebra R³, the integrable coupling of the AKNS system is obtained. The method presented in this paper is rather simple and can be used to work out integrable coupling systems of the other known integrable hierarchies of soliton equations.     

High—Dimensional Integrable Models with Infinitely Dimensional Virasoro—Type Symmetry Algebra

Using every realization of the Virasoro-type symmetry algebra[σ(f1),σ(f2)]=σ(f1f2-f2f1),we can obtain various high-dimensional integrable models under the meaning that they possess infinitely many symmetries,By means of a concrete realization ,many(3 1)-dimensional equations which possess Kac-Moody-Virasoro-type infinite dimensional symmetry algebras are obtained.     

Spontaneous symmetry breaking of affine field theory

It is possible to construct non-Abelian field theories by gauging Kac-Moody algebras. Here we discuss the spontaneous symmetry breaking of such theories via the Higgs mechanism. If the Higgs particle lies in the Cartan subalgebra of the Kac-Moody algebra, the previously massless vectors acquire a mass spectrum that is linear in the Kac-Moody index and has additional fine structure depending on the associated Lie algebra.     

An Analytical APproach to the Turbulence—Relaxed State in Tokamak Plasmas

Starting from the continuity, temperature, and motion equations of the trapped electron fluid in general tokamak magnetic field with positive or reversed shear and the definition of Lagrangian invariant, dL/dt≡(\partial_t+ u•▽)L=0, where u is convective velocity, the trapped electron dynamics is considered in the following two assumptions: (i) the turbulence is low frequency electrostatic, and (ii) L is a functional only of the density n, temperature T, and magnetic field B, and the effect of perturbation potential φ is included in the convective velocity u, i.e., u is a functional of n, T, B, and φ. The Lagrangian invariant hidden in the trapped electron dynamics is strictly found: L=ln[(n/B)^c₁(T/B^2/3)^c₂], where c₁ and c₂ are dimensionless changeable parameters and c₁∝c₂. From this Lagrangian invariant the turbulent particle and electron thermal transport scaling laws are derived: 〈n>_ψq(ψ)=const. and 〈T^3/2>_ψq(ψ)=const., which, in the limit of large aspect ratio, reduce to n(r)q(r)=const. and T^3/2(r)q(r)=const., respectively. The latter two scaling laws are compared with existent experimental results, being in good agreement.     

Anomalous low-temperature heat capacity in antiperovskite compounds

The low-temperature heat capacities are studied for antiperovskite compounds AX M_3(A = Al, Ga, Cu, Ag, Sn, X = C,N, M = Mn, Fe, Co). A large peak in(C- γ T)/T~3 versus T is observed for each of a total of 18 compounds investigated,indicating an existence of low-energy phonon mode unexpected by Debye T~3 law. Such a peak is insensitive to the external magnetic field up to 80 k Oe(1 Oe = 79.5775 A·m-1). For compounds with smaller lattice constant, the peak shifts towards higher temperatures with a reduction of peak height. This abnormal peak in(C- γ T)/T~3 versus T of antiperovskite compound may result from the strongly dispersive acoustic branch due to the heavier A atoms and the optical-like mode from the dynamic rotation of X M_6 octahedron. Such a low-energy phonon mode may not contribute negatively to the normal thermal expansion in AX M_3 compounds, while it is usually concomitant with negative thermal expansion in open-structure material(e.g., ZrW_2O_8, Sc F_3).     

Additional symmetries for integrable equations and conformal algebra representation

We present a regular procedure for constructing an infinite set of additional (spacetime variables explicitly dependent) symmetries of integrable nonlinear evolution equations (INEEs). In our method, additional symmetry equations arise together with their L-A pairs, so that they are integrable themselves. This procedure is based on a modified dressing method. For INEEs in 1+1 dimensions, some appropriate symmetry equations are shown to form the vector fields on a circle S ¹ algebra representation. In contrast to the so-called isospectral deformations, these symmetries result from conformal transformations of the associated linear problem spectrum. For INEEs in 2+1 dimensions, the commutation relations for symmetry equations are shown to coincide with operators , with integer m, p. Some additional results about Kac-Moody algebra applications are presented.     

On the fundamental representation of borcherds algebras with one imaginary simple root

Borcherds algebras represent a new class of Lie algebras which have almost all the properties that ordinary Kac-Moody algebras have, but the only major difference is that these generalized Kac-Moody algebras are allowed to have imaginary simple roots. The simplest nontrivial examples one can think of are those where one adds by hand one imaginary simple root to an ordinary Kac-Moody algebra. We study the fundamental representation of this class of examples and prove that an irreducible module is given by the full tensor algebra over some integrable highest weight module of the underlying Kac-Moody algebra. We also comment on possible realizations of these Lie algebras in physics as symmetry algebras in quantum field theory.Supported by Konrad-Adenauer-Stiftung e.V.Supported by Deutsche Forschungsgemeinschaft.     

T in a model of a nonlinear optical resonator

Oscillations characterized by three incommensurate frequencies (three-dimensional torus of T³) appear in a model of a nonlinear optical resonator driven by a laser beam with transversally inhomogeneous identity distribution. Destruction of T³ leading to chaos occurs when a combination harmonic of two frequencies grows suddenly in the vicinity of the third frequency (and vice versa).     

High-Order Binary Symmetry Constraints of a Liouville Integrable Hierarchy and Its Integrable Couplings

A 3 × 3 matrix spectral problem and a Liouville integrable hierarchy are constructed by designing a new subalgebra of loop algebra A^-2. Furthermore, high-order binary symmetry constraints of the corresponding hierarchy are obtained by using the binary nonlinearization method. Finally, according to another new subalgebra of loop algebra A^-2, its integrable couplings are established.     

Temperature Dependence of Decuplet Baryon Masses from Thermal QCD Sum Rules

In the present work, the masses of the decuplet baryons at finite temperature are investigated using thermal QCD sum rules. Making use of the quark propagator at finite temperature, we calculate the spectral functions to T8 order, and find that there are no contributions to the spectral functions at T8 order and the temperature corrections mainly come from that containing T4 ones. The calculations show very little temperature dependence of the masses below T = 0.11 Ge V. While above that value, the masses decrease with increasing temperature. The results indicate that the hadron-quark phase transition temperature may be Tc≥ 0.11 Ge V for the decuplet bayons.