Gauge fixing of Chern-Simons <Emphasis Type="Italic">N</Emphasis>-extended supergravity

We treat N-extended supergravity in 2 + 1 space-time dimensions as a Yang-Mills gauge field with Chern-Simons action associated to the N-extended Poincaré supergroup. We fix the gauge of this theory within the Batalin-Vilkovisky scheme.Received: 26 January 2004, Published online: 25 June 2004W. Spalenza: Supported in part by the Conselho Nacional de Desenvolvimento Científico e Tecnológico CNPq, Brazil     

ISO(3, 1) gauge theory of gravity

We establish a Poincaré affine frame bundle, give the operation of gauge groupISO(3, 1) on the fiber bundle, obtain the action of the Poincaré gauge theory of gravity, and advance two sets of gravitational gauge field equations of the theory. We discuss some special cases of the theory.     

SL(2,C)-gauge theory andN=1 supergravity

It is shown that as Riemannian space may be taken to give rise to a Poincaré gauge theory of gravitation, the superspace where the coordinates are given by (X, ), being a spinorial variable gives rise to anSL(2, C)-gauge theory and corresponds toN= 1 supergravity. It leads to a conserved current and the conserved quantity here corresponds to isospin, where the latter is taken to be generated from conformal reflection. Thus, supergravity plays a predominant role in the microlocal space-time.     

ISO(3,1¦N) andOSp(N¦4) supergravities

We advance anISO(3,1¦N) extended Poincaré supergravity and anOSp(N¦4) de Sitter supergravity by using the supergauge action mechanisms of supergroups on the superspaces and by treating the gravitational parts of these two supergravities as the gauge theories of gravity, give a new matrix representation ofISO(3,1¦N) generators and a new one ofOSp(N¦4) ones, obtain the commutation and anticommutation relations ofiso(3, 1¦N) andosp(N¦4) superalgebras, construct the actions of these Supergravities and discuss some other problems. A particle multiplets method based on the supersymmetry transformation is used and the probable numbers of particles of different helicities in the two supergravities are given.     

Gauge Invariance of det (iD)2+1 and the Influence

The gauge invariance of det (iD) in (2+l)-dimensional spacetime is argued in two approaches.Unlike the (3 + 1)-dimensional case, det (iD) does not carry any topological information.Some brief discussions are presented.     

A SOLVABLE 1+1-DIMENSIONAL U(1) GAUGE THEORY

A 1+1-dimensional U(1+1) gauge theory is proposed and the exact solution of its spectrum and corresponding energy eigenstates is found.     

Some remarks on the geometry of superspace supergravity

In this note, we first give a quick presentation of the supergeometry underlying supergravity theories, using an intrinsic differential geometric language. For this, we adopt the point of view of Cartan geometries, and rely as well on the work of John Lott, who has found a unified geometrical interpretation of the torsion constraints for many supergravity theories, based on the use of H-structures. In this framework, the constraints amount to requiring first-order integrability of H-structures, for a specific supergroup H.The supergroup H used by Lott is not the usual diagonal representation of the Lorentz group on superspace, but an extension of the latter. This extension appears to be natural and it can be related to the super-Poincaré group. We also observe that the constraints arising from the requirement of first-order integrability have basically the same form, in any spacetime dimension.Looking at supergravity from an affine viewpoint (i.e. as a gauge theory for the super-Poincaré group), we show that requiring first-order integrability amounts to requiring the equivalence, up to gauge transformations, between infinitesimal gauge supertranslations acting on the supervielbein and infinitesimal superdiffeomorphisms acting on the supervielbein.The latter action is performed through a covariant Lie derivative, whose expression involves naturally the supertorsion tensor. We use this expression to show that the term added to the spin connection, in the supercovariant derivative of d=11 supergravity, has a natural superspace origin. In particular, the 4-form field strength is related to a specific component of the supertorsion tensor.We conclude by some general remarks concerning Killing spinors in geometry and supergravity, discussing their possible interpretations, as Killing vector fields on a specific supermanifold on one hand, and as parallel spinors for an appropriate connection on the other hand. We show that this last interpretation is very natural from the point of view of Klein and Cartan geometries.     

Linearized N=2 Poincaré supergravity in terms of SU(2)-extended superfields

Linearized Poincaré N=2 supergravity is presented in terms of SU(2)-extended superfields. Thus, the connection of SU(2)-extended superfields with the structure of auxiliary fields in N=2 supergravity is established.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 31–34, October, 1986.     

Gauge semi-simple extension of the Poincaré group

An approach to the cosmological term problem is proposed, using the gauge semi-simple tensor extension of the D-dimensional Poincaré group as a basis.     

Strong coupling effects in noncommutative spaces from OM theory and supergravity

We show that a four-parameter class of (3+1)-dimensional NCOS theories can be obtained by dimensional reduction on a general 2-torus from OM theory. Compactifying two spatial directions of NCOS theory on a 2-torus, we study the transformation properties under the SO(2,2;Z) T-duality group. We then discuss non-perturbative configurations of non-commutative super Yang–Mills theory. In particular, we calculate the tension for magnetic monopoles and (p,q) dyons and exhibit their six-dimensional origin, and construct a supergravity solution representing an instanton in the gauge theory. We also compute the potential for a monopole–antimonopole in the supergravity approximation.     

Darboux Transformation and New Soliton-like Solutions for (1+1)-Dimensional Higher-Order Broer-Kaup System

In this letter, we construct a kind of new Darboux transformation for the (1+1)-dimensional higher-order Broer-Kaup (HBK) system with the help of a gauge transformation of a spectral problem. By applying this new Darboux transformation, some new soliton-like solutions of the (1+1)-dimensional HBK system are obtained.     

ℵ0-extended supergravity and Chern-Simons theories

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in three dimensions by gauging its intrinsic global SO(N) symmetry. We call these ℵ₀ (Aleph-null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ℵ₀ supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ℵ₀ globally and locally supersymmetric theories in three dimensions. As an interesting application, we present ℵ₀ supergravity Liouville theory in two dimensions after appropriate dimensional reduction from three dimensions.     

Upon Generating (2+1)-dimensional Dynamical Systems

Under the framework of the Adler-Gel’fand-Dikii(AGD) scheme, we first propose two Hamiltonian operator pairs over a noncommutative ring so that we construct a new dynamical system in 2+1 dimensions, then we get a generalized special Novikov-Veselov (NV) equation via the Manakov triple. Then with the aid of a special symmetric Lie algebra of a reductive homogeneous group G, we adopt the Tu-Andrushkiw-Huang (TAH) scheme to generate a new integrable (2+1)-dimensional dynamical system and its Hamiltonian structure, which can reduce to the well-known (2+1)-dimensional Davey-Stewartson (DS) hierarchy. Finally, we extend the binormial residue representation (briefly BRR) scheme to the super higher dimensional integrable hierarchies with the help of a super subalgebra of the super Lie algebra sl(2/1), which is also a kind of symmetric Lie algebra of the reductive homogeneous group G. As applications, we obtain a super 2+1 dimensional MKdV hierarchy which can be reduced to a super 2+1 dimensional generalized AKNS equation. Finally, we compare the advantages and the shortcomings for the three schemes to generate integrable dynamical systems.     

具有广义Virasoro对称代数的(3+1)维Painlevé可积模型

寻找高维可积模型(特别是3+1维可积模型)是非线性物理中的一个非常重要的问题.建立了一种利用广义Virasoro对称性的高维实现首先找到了一些(3+1)维Virasoro可积模型,并证明(3+1)维Virasoro可积模型均具有KacMoodyVirasoro对称代数.更进一步,利用WeissTaborCarnevale的奇性分析方法,证明了其中一个Virasoro可积模型也是Painlev啨可积的. 关键词： 广义Virasoro代数 Painlevé性质 (3+1)维可积模型     

The (2+1)-dimensional supersymmetric CPN−1 model and the central charge

The supersymmetry algebra is examined for the (2+1)-dimensional supersymmetric CP^N?1 model, on the basis of the observation of Witten and Olive in (1+1) and (3+1) dimensions. We then demonstrate that also in this (2+1)-dimensional model the usual supersymmetry algebra is modified by the appearance of the topological numbers of the solitons, which are nothing but the instantons in (1+1) dimensions, as central charges. To obtain the model, we begin by constructing the supersymmetric model in (3+1) dimensions. Then it is reduced to (2+1) dimensions by means of the dimensional reduction technique. We observe that the (2+1)-dimensional supersymmetric CP^N?1 model thus obtained admits an O(2) extended supersymmetry.     

New Multi-soliton Solutions for the （2＋1）-Dimensional Kadomtsev-Petviashvili Equation

In this paper, an explicit N-fold Darboux transformation with multi-parameters for both a （1＋1）- dimensional Broer-Kaup （BK） equation and a （1＋1）-dimensional high-order Broer-Kaup equation is constructed with the help of a gauge transformation of their spectral problems. By using the Darboux transformation and new basic solutions of the spectral problems, 2N-soliton solutions of the BK equation, the high-order BK equation, and the Kadomtsev-Petviashvili （KP） equation are obtained.     

A New Class of Stable (2+1) Dimensional Thin Shell Wormhole

Few years ago, Bañados, Teitelboim and Zanelli (BTZ) (in Phys. Rev. Lett. 69:1849 (1992)) has discovered an explicit vacuum solution of (2+1)-dimensional gravity with negative cosmological constant. It has been argued that the existence of such physical systems with an event horizon and thermodynamic properties similar to (3+1) dimensional black holes. These vacuum solutions of (2+1)-dimensional gravity are asymptotically anti-de Sitter and are known as BTZ black holes. We provide a new type of thin-shell stable wormhole from the BTZ black holes. This is the first example of stable thin shell wormhole in (2+1)-dimension. Several characteristics of this thin-shell wormhole have been discussed.     

A(1+1)-DIMENSIONAL LATTICE U(1) GAUGE MODEL AND THE FERMION SPECIES DOUBLING

A(1+1)-dimensional lattice U91) gauge model with fermion species doubling is solved exactly.The results show that doubling exists for meson states composed of fermions and antifermions.Furthermore we prove that Susskind fermions can beat the doubling of meson states.     

2+1维U(1)格点规范场论中真空态的研究

对2+1维U(1)格点规范场论真空态进行研究,仔细推导出连续极限下真空谈函数中参数μ₀和μ₂的普适表达式,并用截断本征方程法进行数值计算.     

Discretized light cone quantization in a 3+1 dimensional valence model for quarkonium

Led by successes of the nonperturbative method of discretized light cone quantization (DLCQ) in 1+1-dimensional toy models, we study the feasibility of extending it to 3+1 dimensional theories. Within aSU(N _c ) nonabelian gauge theory, DLCQ is applied to a quarkonium system, where the Fock space has been truncated to the valence quark and antiquark only. In the light cone gauge the valenceq \(\bar q\) -model Hamiltonian matrix has an interesting structure which enables us to reduce the problem of diagonalization of some extremely large matrices to an amount of numerical labor already coped with in 1+1 dimensions. The model spectrum and the eigenfunctions are calculated independent of the order of the nonabelian gauge group, in special cases even analytically. The type of spectrum which appears after the calculation has been regularized covariantly may be interpreted as a sign that the quarks are confined in this model.