相关论文: Seven Sphere and the Exceptional Nonlinear Superco…

The article is a tribute to my old mentor, collaborator and friend Murray Gell-Mann. In it I describe work by Pierre Ramond, Sung-Soo Kim and myself where we describe the N = 8 Supergravity in the light-cone formalism. We show how the…

We consider resolutions of codimension-two enhanced singularities from $SO(12)$ to $E_7$ and from $E_7$ to $E_8$ in six-dimensional F-theory, where a half-hypermultiplet arises for generic complex structures achieving them. The exceptional…

We show that superconformal ${\cal N}=4,2$ algebras are well-suited to represent some invariant constructions characterizing exotic $\mathbb{R}^4$ relative to a given radial family. We examine the case of ${\cal N}=4, \hat{c}=4$ (at $r=1$…

In the coset model $(D_N^{(1)} \oplus D_N^{(1)},D_N^{(1)})$ at levels $(k_1,k_2)$, the higher spin $4$ current that contains the quartic WZW currents contracted with completely symmetric $SO(2N)$ invariant $d$ tensor of rank $4$ is…

A unified treatment of both superconformal and quasisuperconformal algebras with quadratic non-linearity is given. General formulas describing their structure are found by solving the Jacobi identities. A complete classification of…

The present paper is revised copy of hep-th/9303087 in which higher spin extensions of the nonabelian gauge symmetries for the classical WZNW model are considered. Both linear and nonlinear realizations of the extended affine Kac-Moody…

We present the supersymmetric extension of the recently constructed E$_{8(8)}$ exceptional field theory -- the manifestly U-duality covariant formulation of the untruncated ten- and eleven-dimensional supergravities. This theory is…

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…

In this paper we construct a non-perturbative action of the higher spin symmetry algebra on the gravitational phase space. We introduce a symmetry algebroid $\mathcal{T}$ which allows us to include radiation in an algebraic framework. We…

We present the complete structure of the nonlinear $N=2$ super extension of Polyakov-Bershadsky, $W_3^{(2)}$, algebra with the generic central charge, $c$, at the {\it quantum} level. It contains extra two pairs of fermionic currents with…

We discuss higher-dimensional gravitational instantons by studying appropriate self-duality equations for the spin connection. In seven and in eight dimensions, the corresponding spaces admit a covariantly constant spinor and have…

We review the recently constructed non-trivial fermionic representations of the infinite-dimensional subalgebra K(E10) of the hyperbolic Kac--Moody algebra E10. These representations are all unfaithful (and more specifically, of finite…

We present a consistency condition for 8d ${\cal N} = 1$ supergravity theories with non-trivial global structure $G/Z$ for the non-Abelian gauge group, based on an anomaly involving the $Z$ 1-form center symmetry. The interplay with other…

In this paper we prove classification results to elliptic fully nonlinear conformal equations on certain subdomains of the sphere with prescribed constant mean curvature on its boundary. Such subdomains are the hemisphere (or a geodesic…

We shall first present an explicit realization of the simple $N=4$ superconformal vertex algebra $L_{c} ^{N=4}$ with central charge $c=-9$. This vertex superalgebra is realized inside of the $ b c \beta \gamma $ system and contains a…

Superspace is considered as space of parameters of the supercoherent states defining the basis for oscillator-like unitary irreducible representations of the generalized superconformal group SU(2m,2n/2N) in the field of quaternions H. The…

Higher spin extensions of nonabelian gauge symmetries for both free fermionic model and WZNW model are considered on a classical level. It is characteristic property of the WZNW model that the higher spin currents which correspond to linear…

We construct ten-dimensional supergravity solutions corresponding to the near horizon limit of IIB fivebranes wrapping special Lagrangian three-cycles of constant curvature. The case of branes wrapping a three-sphere provides a gravity dual…

We construct a (1+1)-dimension continuum model of 4-component fermions incorporating the exceptional Lie group symmetry $G_2$. Four gapped and five gapless phases are identified via the one-loop renormalization group analysis. The gapped…

We recall some basic aspects of line and line Complex representations, of symplectic symmetry emerging in bilinear point transformations as well as of Lie transfer of lines to spheres. Here, we identify SU(2) spin in terms of (classical)…