Wen-Li Yang, Yao-Zhong Zhang
The $osp(2n|2n)$ current algebra for a {\it generic} positive integer $n$ at general level $k$ is investigated. Its free field representation and corresponding energy-momentum tensor are constructed. The associated screening currents of the first kind are also presented.
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The free field representation of the osp(1|2) current algebra is analyzed. The four point conformal blocks of the theory are studied. The structure constants for the product of an arbitrary primary operator and a primary field that transforms according to the fundamental representation of osp(1|2) are explicitly calculated.
The free field realization of irreducible representations of $\os$ is constructed, by a unified and systematic scheme. The $q$-analog of this unified scheme is used to construct $q$-free field realization of irreducible representations of $\uos$. By using these realization, the two point function of $N=1$ superconformal (q-superconformal) model based on $\os$ ($\uos$) symmetry have been calculated.
We exhibit surprising relations between higher spin theory and nonlinear realizations of the supergroup $OSp(1|8)$, a minimal superconformal extension of N=1, 4D supersymmetry with tensorial charges. We construct a realization of $OSp(1|8)$ on the coset supermanifold $OSp(1|8)/SL(4,R)$ which involves the tensorial superspace $R^{(10|4)}$ and Goldstone superfields given on it. The covariant superfield equation encompassing the component ones for all integer and half-integer massless higher spins amounts to the vanishing of covariant spinor derivatives of the suitable Goldstone superfields, and,…
Based on the particular orderings introduced for the positive roots of finite dimensional basic Lie superalgebras, we construct the explicit differential operator representations of the $osp(2r|2n)$ and $osp(2r+1|2n)$ superalgebras and the explicit free field realizations of the corresponding current superalgebras $osp(2r|2n)_k$ and $osp(2r+1|2n)_k$ at an arbitrary level $k$. The free field representations of the corresponding energy-momentum tensors and screening currents of the first kind are also presented.
Topological Twist of osp(2|2)\oplus osp(2|2) Conformal Super Algebra in Two Dimensions
在扭曲Osp（2）中找到了拓扑场论的拉格朗日量|2）\oplus osp（2| 2）共形超代数。然后通过消失的Noether流详细阐述了模空间上的约化。
Using a unified and systematic scheme, the free field realization of irreducible representations of osp(2|2) is constructed. By using these realization, the correlation functions of N=2 super-conformal model based on osp(2|2) symmetry and free field representation of ${\hat{osp(2|2)}}$ generators are calculated. Free field representation of currents are used to determine the stress-energy tensor and the central charge of the model.
We construct explicitly the grade star Hermitian adjoint representation of osp(2/1; C) graded Lie algebra. Its proper Lie subalgebra, the even part of the graded Lie algebra osp(2/1; C), is given by su(2) compact Lie algebra. The Baker-Campbell-Hausdorff formula is considered and reality conditions for the Grassman-odd transformation parameters, which multiply the pair of odd generators of the graded Lie algebra, are clarified.
Super coherent states are useful in the explicit construction of representations of superalgebras and quantum superalgebras. In this contribution, we describe how they are used to construct (quantum) boson-fermion realizations and representations of (quantum) superalgebras. We work through a few examples: $osp(1|2)$ and its quantum version $U_t[osp(1|2)]$, $osp(2|2)$ in the non-standard and standard bases and $gl(2|2)$ in the non-standard basis. We obtain free boson-fermion realizations of these superalgebras. Applying the boson-fermion realizations, we explicitly construct their finite-dimens…
On Integrable Models Related to the $osp(1,2)$ Gaudin Algebra
本文定义了$osp(1,2)$ Gaudin代数，并考虑了由它描述的可积模型，包括$osp(1,2)$ Gaudin磁体和与之相关的Dicke模型，对这些模型的最简单情况进行了详细的讨论。费米子的存在下的变量分离的效果表示。
We use the expansion of superalgebras procedure (summarized in the text) to derive Chern-Simons (CS) actions for the (p,q)-Poincare supergravities in three-dimensional spacetime. After deriving the action for the (p,0)-Poincare supergravity as a CS theory for the expansion osp(p|2;R)(2,1) of osp(p|2;R), we find the general (p,q)-Poincare superalgebras and their associated D=3 supergravity actions as CS gauge theories from an expansion of the simple osp(p+q|2,R) superalgebras, namely osp(p+q|2,R)(2,1,2).
We determine the Clebsch-Gordan and Racah-Wigner coefficients for continuous series of representations of the quantum deformed algebras U_q(sl(2)) and U_q(osp(1|2)). While our results for the former algebra reproduce formulas by Ponsot and Teschner, the expressions for the orthosymplectic algebra are new. Up to some normalization factors, the associated Racah-Wigner coefficients are shown to agree with the fusing matrix in the Neveu-Schwarz sector of N=1 supersymmetric Liouville field theory.
Hamiltonian Reduction of Super Osp(1,2)} and Sl(2,1) Kac-Moody Algebras
给出了超OSp（1，2）和SL（2，1）卡茨-穆迪代数的Wakimoto构造以及相应的WZW模型的自由场表示.在适当的约束条件下，导出了维拉索罗代数的Feigin-Fuchs表示和N=1和N=2共形对称的余伴随作用.这个公式对应于德林费尔德和索科洛夫哈密顿约化的超协变扩展。
We study the free field realization of the two-dimensional osp(1|2) current algebra. We consider the case in which the level of the affine osp(1|2) symmetry is a positive integer. Using the Coulomb gas technique we obtain integral representations for the conformal blocks of the model. In particular, from the behaviour of the four-point function, we extract the structure constants for the product of two arbitrary primary operators of the theory. From this result we derive the fusion rules of the osp(1|2) conformal field theory and we explore the connections between the osp(1|2) affine symmetry …
On a possible algebra morphism of U$_q$[OSP(1/2N)] onto the deformed oscillator algebra W$_q$(N)
提出了一个猜想，即变形玻色产生和湮灭算符的$n$对的代数是$U_q[osp(1/2n)]$的一个因子-代数，并在$n=2$情形下证明了这个猜想.为此，我们表明，对于任何值的$q$ $U_q[osp(1/4)]$可以被看作是一个超代数，自由产生的两对$B_1^\pm$，$B_2^\pm$变形的para-Bose运营商。我们写下所有的Hopf代数关系，Cartan-Weyl基的模拟，生成元和$U_q[osp(1/2n)]$中的基之间的“对易”关系完全根据$B_1^\pm$，$B_2^\pm$。
Based on the quantum superspace construction of $q$-deformed algebra, we discuss a supersymmetric extension of the deformed Virasoro algebra, which is a subset of the $q$-$W_{\infty}$ algebra recently appeared in the context of two-dimensional string theory. We analyze two types of deformed super-Virasoro algebra as well as their $osp(1,2)$ subalgebras. Applying our quantum superspace structure to conformal field theory, we find the same type of deformation of affine $sl(2)$ algebra.
The fusion of Verma modules of the osp(1|2) current algebra is studied. In the framework of an isotopic formalism, the singular vector decoupling conditions are analyzed. The fusion rules corresponding to the admissible representations of the osp(1|2) algebra are determined. A relation between the characters of these last representations and those corresponding to the minimal superconformal models is found. A series of equations that relate the descendants of the highest weight vectors resulting from a fusion of Verma modules are obtained. Solving these equations the singular vectors of the th…
We study Yang-Baxter equations with orthosymplectic supersymmetry. We extend a new approach of the construction of the spinor and metaplectic $\hat{\cal R}$-operators with orthogonal and symplectic symmetries to the supersymmetric case of orthosymplectic symmetry. In this approach the orthosymplectic $\hat{\cal R}$-operator is given by the ratio of two operator valued Euler Gamma-functions. We illustrate this approach by calculating such $\hat{\cal R}$ operators in explicit form for special cases of the $osp(n|2m)$ algebra, in particular for a few low-rank cases. We also propose a novel, simpl…
The super-AdS_5 X S^5 and the four-dimensional N=4 superconformal algebras play important roles in superstring theories. It is often discussed the roles of the osp(1|32) algebra as a maximal extension of the superalgebras in flat background. In this paper we show that the su(2,2|4), the super-AdS_5 X S^5 algebra or the superconformal algebra, is not a restriction of the osp(1|32) though the bosonic part of the former is a subgroup of the latter. There exist only two types of u(1) extension of the super-AdS_5 X S^5 algebra if the bosonic AdS_5 X S^5 covariance is imposed. Possible significance …
As a step to understand general patterns of integrability in 1+1 quantum field theories with supergroup symmetry, we study in details the case of $OSP(1/2)$. Our results include the solutions of natural generalizations of models with ordinary group symmetry: the $UOSP(1/2)_{k}$ WZW model with a current current perturbation, the $UOSP(1/2)$ principal chiral model, and the $UOSP(1/2)\otimes UOSP(1/2)/UOSP(1/2)$ coset models perturbed by the adjoint. Graded parafermions are also discussed. A pattern peculiar to supergroups is the emergence of another class of models, whose simplest representative…
A Superalgebra Morphism of Uq[OSP(1/2N)] onto the Deformed Oscillator Superalgebra Wq(N)
证明了变形振子超代数$W_q(n)$（在Fock表象中，它本质上是由$q$玻色子的$n$对生成的）是量子化泛包络代数$U_q[osp(1/2n)]$的因子代数.我们为变形的$osp(1/2n)$写出了Cartan-Weyl基的$q$ -模拟，并给出了所有Cartan-Weyl生成元的振荡器实现.
We define and study a lattice model which we argue is in the universality class of the $OSp(2S+2|2S)$ supercoset sigma model for a large range of values of the coupling constant $g_σ^2$. In this first paper, we analyze in details the symmetries of this lattice model, in particular the decomposition of the space of the quantum spin chain $V^{\otimes L}$ as a bimodule over $OSp(2S+2|2S)$ and its commutant, the Brauer algebra $B_L(2)$. It turns out that $V^{\otimes L}$ is a nonsemisimple module for both $OSp(2S+2|2S)$ and $B_L(2)$. The results are used in the companion paper to elucidate the stru…
Quantization of the Lie Algebra SO(2N+1) and of the Lie Superalgebra Osp(1/2N) with Preoscillator Generators
李代数$so(2n+1)$和李超代数$osp(1/2n)$用$3n$生成元量子化，称为预振荡器生成元。除了$n$“Cartan”元素外，预振子发生器在$so(2n+1)$的情况下是变形的para-Fermi算子，在$osp(1/2n)$的情况下是变形的para-Bose算子。相应的变形泛包络代数$U_q[so(2n+1)]$和$U_q[osp(1/2n)]$与用Chevalley算子定义的等价.“预振子”这个名字是为了表明在某种表示中，这些算符简化为已知的变形费米算符和玻色算符。
We prove that the family of non-linear $W$-algebras $SW(3/2,2)$ which are extensions of the $N=1$ superconformal algebra by a primary supercurrent of conformal weight $2$ can be realized as a quantum Hamiltonian reduction of the Lie superalgebra $osp(3|2)$. In consequence we obtain an explicit free field realization of the algebra in terms of the screening operators. At central charge $c=12$ the $SW(3/2,2)$ superconformal algebra corresponds to the superconformal algebra associated to sigma models based on eight-dimensional manifolds with special holonomy $Spin(7)$, i.e., the Shatashvili-Vafa …
A new Lagrangian realizing the symmetry of the M Algebra in eleven-dimensional space-time is presented. By means of the novel technique of Abelian Semigroup Expansion, a link between the M Algebra and the orthosymplectic algebra osp(32|1) is established, and an M Algebra-invariant symmetric tensor of rank six is computed. This symmetric invariant tensor is a key ingredient in the construction of the new Lagrangian. The gauge-invariant Lagrangian is displayed in an explicitly Lorentz-invariant way by means of a subspace separation method based on the extended Cartan homotopy formula.
Osp(1|2) and Sl(2) Reductions in Generalised Super-Toda Models and Factorization of Spin 1/2 Fields
我表明，经典户田模型建立在超代数，并从减少相对于$Sl(2)$代数，是“线性超对称化”（通过添加自旋1/2字段），当且仅当$Sl(2)$是玻色子的一部分，$OSp(1|2)$代数。在这种情况下，该模型等价于从关于$OSp(1|2)$代数的约化构造的模型，直到自旋1/2场。相应的$W$代数通过自旋1/2场（玻色子和费米子）的因式分解而联系起来。我用一个例子来说明这种因式分解：建立在$Sl(n+1|2)$上的超共形代数。
We study the conformal field theories corresponding to current superalgebras $osp(2|2)^{(1)}_k$ and $osp(2|2)^{(2)}_k$. We construct the free field realizations, screen currents and primary fields of these current superalgebras at general level $k$. All the results for $osp(2|2)^{(2)}_k$ are new, and the results for the primary fields of $osp(2|2)^{(1)}_k$ also seem to be new. Our results are expected to be useful in the supersymmetric approach to Gaussian disordered systems such as random bond Ising model and Dirac model.
Polynomial deformations of $osp(1/2)$ and generalized parabosons
我们考虑由三个元素$A,B,H$生成的代数$R$服从三个关系$[H,A]=A$，$[H,B]=-B$和$\{A,B\}=f(H)$ .当$f(H)=H$与李超代数$osp(1/2)$一致时;当$f$是多项式时，我们称之为$osp(1/2)$的多项式变形。不可约表示的$R$的描述，并在情况下$°(f)\leq 2$，我们得到一个完整的分类，显示出一些相似之处，但也有一些有趣的差异与通常的$osp(1/2)$表示。讨论了它与变形振子代数的关系，从而将$R$解释为广义抛物子代数。
With the motivation to develop superconformal field theory on S^3, we introduce a 2n-extended supersphere S^{3|4n}, with n=1,2,..., as a homogeneous space of the three-dimensional Euclidean superconformal group OSp(2n|2,2) such that its bosonic body is S^3. Supertwistor and bi-supertwistor realizations of S^{3|4n} are derived. We study in detail the n=1 case, which is unique in the sense that the R-symmetry subgroup SO^*(2n) of the superconformal group is compact only for n=1. In particular, we show that the OSp(2|2,2) transformations preserve the chiral subspace of S^{3|4}. Several supercoset…
We show that the SU(2)_0 WZNW model has a hidden OSp(2|2)_{-2} symmetry. Both these theories are known to have logarithms in their correlation functions. We also show that, like OSp(2|2)_{-2}, the logarithmic structure present in the SU(2)_0 model is due to the underlying c=-2 sector. We also demonstrate that the quantum Hamiltonian reduction of SU(2)_0 leads very directly to the correlation functions of the c=-2 model. We also discuss some of the novel boundary effects which can take place in this model.
In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_n and D_n Lie algebra and by the superalgebra Osp(n|2m). We present a unified formulation of the quantum inverse scattering method for many of these lattice models. The appropriate fundamental commutation rules are found, allowing us to construct the eigenvectors and the eigenvalues of the transfer matrix associated to the B_n, C_n, D_n, Osp(2n-1|2), Osp(2|2n-2), Osp(2n-2|2) and Osp(1|2n) mode…
Heisenberg and Drinfeld doubles of Uq(gl(1|1)) and Uq(osp(1|2)) super-algebras
本文研究了 Uq(gl(1|1)) 和 Uq(osp(1|2)) 超代数的 Heisenberg 和 Drinfeld 双代数，证明了其与 handle 代数的同构关系，并扩展到加权设置。
Galilean conformal algebra (GCA) is an Inonu-Wigner (IW) contraction of a conformal algebra, while Newton-Hooke string algebra is an IW contraction of an AdS algebra which is the isometry of an AdS space. It is shown that the GCA is a boundary realization of the Newton-Hooke string algebra in the bulk AdS. The string lies along the direction transverse to the boundary, and the worldsheet is AdS_2. The one-dimensional conformal symmetry so(2,1) and rotational symmetry so(d) contained in the GCA are realized as the symmetry on the AdS_2 string worldsheet and rotational symmetry in the space tran…
An orthogonal basis of weight vectors for a class of infinite-dimensional representations of the orthosymplectic Lie superalgebra osp(2m+1|2n) is introduced. These representations are particular lowest weight representations V(p), with a lowest weight of the form [-p/2,...,-p/2|p/2,...,p/2], p being a positive integer. Explicit expressions for the transformation of the basis under the action of algebra generators are found. Since the relations of algebra generators correspond to the defining relations of m pairs of parafermion operators and n pairs of paraboson operators with relative paraferm…
The SuperConformal theory in three space-time dimensions with SO(16) $R$-symmetry, 128 bosons, and 128 fermions, cannot sustain interactions. This result is obtained using both light-cone superspace techniques which rely on algebraic consistency, and covariant methods which rely on SO(16) Fierz identities which fail to produce the desired algebra.
Projectivised representations of $U_q osp(2,2)$
我们用有限差分算子构造了包络代数$U_q osp(2,2)$的表示，并在准精确可解方程的框架下讨论了这一结果。
We study some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra, a graded extension of the four-dimensional Poincare' algebra with two odd generators, a vector and a scalar, and two central charges. The anticommutator between the two odd generators gives the four-momentum operator, from which the name vector supersymmetry. We construct the Casimir operators for this algebra and we show how both algebra and Casimirs can be derived by contraction from the simple orthosymplectic algebra OSp(3,2|2). In particular, we construct the analogue of superspin for vector supersymmetry and…
Algebra of the constraints of twistor-like p-branes restoring 3/4 fraction of the spontaneously broken D=4 N=1 supersymmetry is studied using the conversion method. Classical and quantum realizations of the BRST charge, unified superalgebra of the global generalized superconformal OSp(1|8) and Virasoro and Weyl symmetries are constructed. It is shown that the quantum Hermitian BRST charge is nilpotent and the quantized OSp(1|8) superalgebra is closed.
The goal of this paper is to give an explicit construction of the Fock spaces of the parafermion and the paraboson algebra, for an infinite set of generators. This is equivalent to constructing certain unitary irreducible lowest weight representations of the (infinite rank) Lie algebra so(\infty) and of the Lie superalgebra osp(1|\infty). A complete solution to the problem is presented, in which the Fock spaces have basis vectors labelled by certain infinite but stable Gelfand-Zetlin patterns, and the transformation of the basis is given explicitly. We also present expressions for the characte…
We study the crossing symmetry of the conformal blocks of the conformal field theory based on the affine Lie superalgebra osp(1|2). Within the framework of a free field realization of the osp(1|2) current algebra, the fusion and braiding matrices of the model are determined. These results are related in a simple way to those corresponding to the su(2) algebra by means of a suitable identification of parameters. In order to obtain the link invariants corresponding to the osp(1|2) conformal field theory, we analyze the corresponding topological Chern-Simons theory. In a first approach we quantiz…
Geometrical Aspect of Topologically Twisted 2-Dimensional Conformal Superalgebra
我们研究了拓扑扭曲的OSP（2| 2）+osp（2）|2）共形超代数。该代数包括拉格朗日量，它是拓扑场论的固有量，由费米子生成元组成。用osp（2）规范系统研究拉格朗日量|2）+osp（2）|2）揭示了代数的几何特征：导出了与代数相联系的模空间，阐明了费米子生成元在模空间中的重要作用，并从代数的几何方面论证了拓扑扭曲与模问题之间的特殊关系。
Taking seriously the hypothesis that the full symmetry algebra of M-theory is osp(1|32,R), we derive the supersymmetry transformations for all fields that appear in 11- and 12-dimensional realizations and give the associated SUSY algebras. We study the background-independent osp(1|32,R) cubic matrix model action expressed in terms of representations of the Lorentz groups SO(10,2) and SO(10,1). We explore further the 11-dimensional case and compute an effective action for the BFSS-like degrees of freedom. We find the usual BFSS action with additional terms incorporating couplings to transverse …
We show how OSp(1|32) gives a unifying framework to describe d=10 type II string theories, d=11 M-theory and d=12 F-theory. The theories are related by different identifications of their symmetry operators as generators of OSp(1|32). T- and S-dualities are recognized as redefinitions of generators. Some (s,t) signatures of spacetime allow reality conditions on the generators. All those that allow a real structure are related again by redefinitions within the algebra, due to the fact that the algebra OSp(1|32) has only one real realization. The redefinitions include space/space, time/time and s…
Induced (N,0) supergravity as a constrained Osp(N,2) WZWN model and its effective action
通过对Osp（N $|$ 2）WZWN模型的电流进行约束，得到了d=2维任意$N$及其诱导作用量的手征$(N,0) $超引力理论.基础对称代数是Knizhnik和Bershadsky的非线性SO（N）超共形代数。并对实例$N=3$进行了详细的计算。通过对经典变换规则的量子修正，我们证明了规范场和电流的规范代数是封闭的。导出了沃德恒等式的可积性条件。在一个循环中计算有效动作。它是有限的，并且可以通过用有限的Z因子重新标度中心荷和场从感生作用获得。
We prove explicitly that the general D=3, N=4 Chern-Simons-matter (CSM) theory has a complete OSp(4|4) superconformal symmetry, and construct the corresponding conserved currents. We re-derive the OSp(5|4) superconformal currents in the general N=5 theory as special cases of the OSp(4|4) currents by enhancing the supersymmetry from N=4 to N=5. The closure of the full OSp(4|4) superconformal algebra is verified explicitly.
We show that the complete superalgebra of symmetries, including central charges, that underlies F-theories, M-theories and type II string theories in dimensions 12, 11 and 10 of various signatures correspond to rewriting of the same OSp(1|32) algebra in different covariant ways. One only has to distinguish the complex and the unique real algebra. We develop a common framework to discuss all signatures theories by starting from the complex form of OSp(1|32). Theories are distinguished by the choice of basis for this algebra. We formulate dimensional reductions and dualities as changes of basis …
Admissible level $\mathfrak{osp}(1|2)$ minimal models and their relaxed highest weight modules
本文结合两类自由场实现、屏蔽算子与 Jack 基对称函数理论，计算 Zhu 代数表示，并分类 Neveu-Schwarz 与 Ramond 扇区中的 $\mathfrak{osp}(1|2)$ 极小模型单松弛最高权模。
Topological gravity with exchange algebra
通过扭曲有效的$(2,0)$超引力得到拓扑引力.我们证明了这种拓扑引力具有无穷多个带共形权$0$的BRST不变量。它们是OSp $(2,2)$多重态的一个塔，满足OSp $(2,2)$的经典交换代数.我们认为，这些BRST不变量成为量子理论中的物理算子，它们的关联函数根据量子OSp $(2,2)$群编织。拓扑有效引力的这些性质是标准拓扑引力所不具备的。
In this paper we briefly review the main results obtained in arXiv:0812.1982, where some algebraic properties of the 'vector supersymmetry' (VSUSY) algebra have been studied. VSUSY is a graded extension of the Poincare' algebra in 4 dimensions with two central charges. We derive all independent Casimir operators of VSUSY and we find two distinct spin-related operators in the case of nonvanishing central charges. One is the analogue of superspin for VSUSY and the other is a new spin, called C-spin, whose value is fixed to 1/2. We also show that the VSUSY algebra and its Casimir operators can be…
We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model introduced possesses hidden invariance under N=2 Poincaré supergroup with a central charge saturating the BPS bound. At the classical level the model admits a Hamiltonian formulation with two first class constraints on the phase space $T^*(R^{1,2})\times {\cal L}^{1|1}$, where the Kähler supermanifold ${\cal L}^{1|1}\cong OSp(2|2)/U(1|1)$ is a minimal superextens…
We demonstrate that the general D=3, N=5 Chern-Simons matter theory possesses a full OSp(5|4) superconformal symmetry, and construct the corresponding superconformal currents. The closure of the superconformal algebra is verified in detail. We also show that the conserved OSp(6|4) superconformal currents in the general N=6 theory can be obtained as special cases of the OSp(5|4) currents by enhancing the R-symmetry of the N=5 theory from USp(4) to SU(4).
We review some results recently obtained for the conformal field theories based on the affine Lie superalgebra osp(1|2). In particular, we study the representation theory of the osp(1|2) current algebras and their character formulas. By means of a free field representation of the conformal blocks, we obtain the structure constants and the fusion rules of the model. (Lecture delivered at the CERN-Santiago de Compostela-La Plata Meeting, "Trends in Theoretical Physics", La Plata, Argentina, April-May 1997).
The Kazhdan-Lusztig category of $\mathfrak{osp}_{1|2n}$ at irrational levels
本文证明了 $\mathfrak{osp}_{1|2n}$ 在无理水平下的 Kazhdan-Lusztig 对应，建立了其仿射顶点算子超代数范畴与量子群范畴及 $\mathfrak{so}_{2n+1}$ 对应范畴的辫子张量等价，并构造了新的简单共形顶点（超）代数族。
Supersymmetric Construction of W-Algebras from Super Toda and Wznw Theories
利用基于超李代数的WZNW模型，系统地构造了超W-代数。这是超Toda模型的对称结构，它可以从WZNW理论通过Hamilton约化得到。本文根据改进的能量动量张量定义的共形自旋，对单根为费米子根的超李代数进行了一般性的分类。利用Dirac括号结构和W-代数的显式构造，对$OSP(1,2)$，$OSP(2,2)$，$OSP(3,2)$和$D(2,1 \mid α)$的情形进行了详细的讨论.在相关情况下讨论了$N=1$和$N=2$超共形代数。
We consider partial spontaneous breaking of N=1 AdS4 supersymmetry OSp(1|4) down to N=1, d=3 Poincare supersymmetry in the nonlinear realizations framework. We construct the corresponding worldvolume Goldstone superfield action and show that it describes the N=1 AdS4 supermembrane. It enjoys OSp(1|4) supersymmetry realized as a field-dependent modification of N=1, d=3 superconformal symmetry and goes into the superfield action of ordinary N=1, D=4 supermembrane in the flat limit. Its bosonic core is the Maldacena-type conformally invariant action of the AdS4 membrane. We show how to reproduce …
Realization of the conformal higher spin symmetry on the 4d massless field supermultiplets is given. The self-conjugated supermultiplets, including the linearized ${\cal N}=4$ SYM theory, are considered in some detail. Duality between non-unitary field-theoretical representations and the unitary doubleton--type representations of the 4d conformal algebra $su(2,2)$ is formulated in terms of a Bogolyubov transform. The set of 4d massless fields of all spins is shown to form a representation of $sp(8)$. The obtained results are extended to the generalized superspace invariant under $osp(L, 2M)$ s…
We study a longstanding problem of identification of the fermion-monopole symmetries. We show that the integrals of motion of the system generate a nonlinear classical Z_2-graded Poisson, or quantum super- algebra, which may be treated as a nonlinear generalization of the $osp(2|2)\oplus su(2)$. In the nonlinear superalgebra, the shifted square of the full angular momentum plays the role of the central charge. Its square root is the even osp(2|2) spin generating the u(1) rotations of the supercharges. Classically, the central charge's square root has an odd counterpart whose quantum analog is,…
We study the unitary supermultiplets of the N=4 d=7 anti-de Sitter (AdS_7) superalgebra OSp(8^*|4), with the even subalgebra SO(6,2) X USp(4), which is the symmetry superalgebra of M-theory on AdS_7 X S^4. We give a complete classification of the positive energy doubleton and massless supermultiplets of OSp(8^*|4) . The ultra-short doubleton supermultiplets do not have a Poincaré limit in AdS_7 and correspond to superconformal field theories on the boundary of AdS_7 which can be identified with d=6 Minkowski space. We show that the six dimensional Poincare mass operator vanishes identically fo…
Identical Particles and Permutation Group
二次量子化被重新审视，并且产生和湮灭算符似乎与代数h（1）和超代数osp（1）有着同样的联系|2），这表明是兼容的玻色和费米统计。这两个代数在单模扇区中是完全等价的，但是由于OSP（1| 2），在多粒子情况下不同。同样的方案被直接推广到量子情形h_q（1）和osp_q（1| 2）。
We discuss the issue of how to include magnetic charges in the AdS(4) superalgebra osp(4|2). It is shown that the usual way of introducing a pseudoscalar central charge on the right hand side of the basic anticommutator does not work, because this breaks SO(2,3) covariance. We propose a way out by promoting the magnetic charge to a vector charge, which amounts to enlarge osp(4|2) to the superconformal algebra su(2,2|1). The conditions for 1/4, 1/2 and 3/4 BPS states are then analyzed. These states form the boundary of the convex cone associated with the Jordan algebra of 4x4 complex hermitian …
We study the positive energy unitary representations of 2N extended superconformal algebras OSp(8*|2N) in six dimensions. These representations can be formulated in a particle basis or a supercoherent state basis, which are labeled by the superspace coordinates in d=6. We show that the supercoherent states that form the bases of positive energy representations of OSp(8*|2N) can be identified with conformal superfields in six dimensions. The massless conformal superfields correspond precisely to the ultra short doubleton supermultiplets of OSp(8*|2N). The other positive energy unitary represent…
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