OSp(1,1|4) BRST-symmetry for string field with the world-sheet metric

The Sp(2) symmetry of the ghost coordinates in the harmonic gauge for the world-sheet metric is extended to the OSp(1,1|4) group. A new set of BRST charges which form a multiplet under this OSp(1,1|4) group is found. Gauge transformations are constructed by using the Sp(4) subgroup and a gauge invariant action is proposed for the OSp(1,1|4) singlet string field.     

New quantum deformation of OSp(1;2)

The complete set of formulas describing the new quantum deformation of the OSp(1;2) supergroup is provided. A general Ansatz is solved for the deformation of the Borel subalgebra of its dual quantum deformation of osp(1;2).     

Lattice models in statistical mechanics for N = 2 superconformal field theory

We study exactly solvable cyclic solid-on-solid models extended to arbitrary higher degrees of the fusion construction. A detailed calculation of their local state probabilities via the corner transfer matrix method is presented. The order parameters thus obtained include new characters of the conformal field theories. We discuss a series of lattice analogues of the N = 2 superconformal minimal models included in this family of the cyclic solid-on-solid models.     

The solution of the N = (0|2) superconformal f-Toda lattice

The general solution of the two-dimensional integrable generalization of the f-Toda chain with fixed ends is explicitly presented in terms of matrix elements of various fundamental representations of the SL(n|n − 1) supergroup. The dominant role of the representation theory of graded Lie algebras in the problem of constructing integrable mappings and lattices is demonstrated.     

AdS2 supergravity and superconformal quantum mechanics

We investigate the asymptotic dynamics of topological anti-de Sitter supergravity in two dimensions. Starting from the formulation as a BF theory, it is shown that the AdS₂ boundary conditions imply that the asymptotic symmetries form a super-Virasoro algebra. Using the central charge of this algebra in Cardy’s formula, we exactly reproduce the thermodynamical entropy of AdS₂ black holes. Furthermore, we show that the dynamics of the dilaton and its superpartner reduces to that of superconformal transformations that leave invariant one chiral component of the stress tensor supercurrent of a two-dimensional conformal field theory. This dynamics is governed by a supersymmetric extension of the de Alfaro-Fubini-Furlan model of conformal quantum mechanics. Finally, two-dimensional de Sitter gravity is also considered, and the dS₂ entropy is computed by counting CFT states.     

Analytic interpolation and Borel summability of the (λ/N|Φ N |:4)2 models

Analytic interpolation in the variable 1/N of (λ/N|Φ _N |^:4)₂ models is constructed at finite volume approximation. We prove Borel summability of the Taylor series at 1/N=0 of their Schwinger functions. We also give an extension of the domain of analyticity in the coupling constant.     

OSp[D+1,3 | 2] unifies the conformal symmetry and BRST

We show that the conformal transformations on the invariant metric of OSp[D,2 | 2], which is the group unifying Lorentz and BRST symmetries, are generated by OSp[D+1, 3 | 2], which thus unifies the conformal and BRST symmetries. We explicitly construct the generators for the scalar and for the spinning particle. We express the generators in terms of the energy-momentum tensor and study their action on the fields. We also study the linear realization of OSp[D+1, 3 | 2] on a space of D+4 bosonic and 2 fermionic variables. Field quantization is also examined.     

The unitary constructions of the N=4 SU (2) extended superconformal algebras

Unitary conditions for the N=4 SU (2) extended superconformal algebras (SUCAs) are derived. All highest weight unitary representations are identified and explicitly realized by free fermion and (twisted) boson constructions, which are essentially free theories.     

Geometric quantization of an OSp(1/2) coadjoint orbit

In this Letter, we show how the complete geometric quantization extends to specific supersymplectic supermanifolds. More precisely, we extend this procedure to OSp(1/2)-coadjoint orbits, which are graded extensions of elliptic Sp(2, )-coadjoint orbits. Our approach exploits results obtained in a previous work, where the notion of a super-Kähler supermanifold was defined, and the former orbits were shown to be nontrivial examples of such a notion. As their underlying Kähler manifolds, these supermanifolds carry a natural (super-Kähler) polarization, a crucial notion that was so far lacking. Geometric quantization leads here to a nontrivial representation of osp(1/2), which is realized in a space of square integrable holomorphic sections of a super-Hermitian complex line bundle sheaf-with-connection over the homogenous space OSp(1/2)/U(1).     

Local BRS transformations and OSp(3,1¦2) symmetry of Yang-Mills theories

We consider a certain local generalization of BRS transformations of Yang-Mills theory in which the anti-commuting parameter is space time dependent. While these are not exact symmetries, they do lead to a new nontrivial WT identity. We make a precise connection between the “local BRS” and the broken orthosymplectic symmetry recently found in superspace formulation of Yang-Mills theory by showing that the local BRS WT identity is precisely the WT identity obtained in the superspace formulation via a superrotation. This “local BRS” WT identity could lead to new consequences not contained in the usual BRS WT identity.     

Fermionic flows and tau function of the N = (1|1) superconformal Toda lattice hierarchy

An infinite class of fermionic flows of the N = (1|1) superconformal Toda lattice hierarchy is constructed and their algebraic structure is studied. We completely solve the semi-infinite N = (1|1) Toda lattice and chain hierarchies and derive their tau functions, which may be relevant for building supersymmetric matrix models. Their bosonic limit is also discussed.     

Spin models and superconformal Yang–Mills theory

We apply novel techniques in planar superconformal Yang–Mills theory which stress the role of the Yangian algebra. We compute the first two Casimirs of the Yangian, which are identified with the first two local Abelian Hamiltonians with periodic boundary conditions, and show that they annihilate the chiral primary states. We streamline the derivation of the R-matrix in a conventional spin model, and extend this computation to the gauge theory. We comment on higher-loop corrections and higher-loop integrability.     

Polynomial identities,indices, and duality for theN=1 superconformal modelSM(2, 4v)

We prove polynomial identities for theN=1 superconformal modelSM(2, 4v) which generalize and extend the known Fermi/Bose character identities. Our proof uses theq-trinomial coefficients of Andrews and Baxter on the bosonic side and a recently introduced very general method of producing recursion relations forq-series on the fermionic side. We use these polynomials to demonstrate a dual relation underqq ^–1 betweenSM(2, 4v) andM(2v–1, 4v). We also introduce a genralization of the Witten index which is expressible in terms of the Rogers false theta functions.Dedicated to the memory of Claude Itzykson.     

SO q (4) quantum mechanics

In this paper we extend our previously discovered exact solution for an SU(2) Yang-Mills-Higgs theory, to the general group SU(N+1). Using the first-order formalism of Bogomolny, an exact, spherically symmetric solution for the gauge and scalar fields is found. This solution is similar to the Schwarzschild solution of general relativity, in that the gauge and scalar fields become infinite on a spherical shell of radiusr ₀=K. However in the Schwarzschild case the singularity at the event horizon is a coordinate singularity while for the present solution the singularity is a true singularity. It is speculated that this solution may give a confinement mechanism for non-Abelian gauge theories, since any particle which carries the SU(N+1) charge would become permanently trapped inside the regionr<r ₀.     

The refined elliptic genus and Coulomb gas formulations of N = 2 superconformal coset models

We describe, in some detail, a number of different Coulomb gas formulations of N = 2 superconformal coset models. We also give the mappings between these formulations. The ultimate purpose of this is to show how the Landau-Ginzburg structure of these models can be used to extract the W-generators, and to show how the computation of the elliptic genus can be refined so as to extract very detailed information about the characters of component parts of the model.     

Study of N = 2 superconformal field theories in 4 dimensions

Making use of the exact solutions of the N = 2 supersymmetric gauge theories, we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have constructed represent universality classes of the 4-dimensional N = 2 SCFTs.