We use the Regge-Teitelboim method to treat surface integrals in gauge theories to find global charges in Chern-Simons theory. We derive the affine and Virasoro generators as global charges associated with symmetries of the boundary. The role of boundary conditions is clarified. We prove that for diffeomorphisms that do not preserve the boundary there is a classical contribution to the central ...

This is a brief summary of our works [arXiv:1112.4063, arXiv:1201.4501] on constructing higher genus B-model from perturbative quantization of BCOV theory. We analyze Givental’s symplectic loop space formalism in the context of B-model geometry on Calabi–Yau manifolds, and explain the Fock space construction via the renormalization techniques of gauge theory. We also give a physics interpretati...

We derive properties of N-extended G R super Virasoro algebras. These include adding central extensions, identification of all primary fields and the action of the adjoint representation on its dual. The final result suggest identification with the spectrum of fields in supergravity theories and superstringrM-theory constructed from NSR N-extended supersymmetric G R Virasoro algebras. q 2000 El...

By starting from known graded Lie algebras, including Virasoro algebras, new kinds of time-dependent evolution equations are found possessing graded symmetry algebras. The modified KP equations are taken as an illustrative example: new modified KP equations with m arbitrary time-dependent coefficients are obtained possessing symmetries involving m arbitrary functions of time. A particular grade...

We give a simple derivation of the Virasoro constraints in the Kontsevich model, first derived by Witten. We generalize the method to a model of unitary matrices, for which we find a new set of Virasoro constraints. Finally we discuss the solution for symmetric matrices in an external field. ⋆ Research supported in part by NSF grant PHY90-21984 † E-mail: [email protected]; newman@puhep...

We consider the M(2, 3) Minimal Liouville gravity, whose states in the gravity sector are represented by irreducible modules of the Virasoro algebra. We present a recursive construction for BRST cohomology classes. This construction is based on using an explicit form of singular vectors in irreducible modules of the Virasoro algebra. We construct an algebra of operators acting on the BRST cohom...

We study the nonunitary representations of N = 2 Super Virasoro algebra for the rational central charges ĉ < 1. The resolutions for the irreducible representations of N = 2 SV ir in terms of the ”2-d gravity modules” are obtained and their characters are computed. The correspondence between N = 2 nonunitary ”minimal” models and the Virasoro minimal models + 2-d gravity is shown at the level of ...

A new set of realizations of the Virasoro algebra on a bosonic Fock space are found by explicitly computing the Virasoro representations associated with coadjoint orbits of the form DiffS 1 /S 1. Some progress is made in understanding the unitary structure of these representations. The characters of these representations are exactly the bosonic partition functions calculated previously by Witte...

The projective action of the Lie algebra of the diieomorphisms of the circle on the algebraic Fock space CZ 1 ; Z 2 ; : : :] of holomorphic polynomials in innnitely many variables leads to the well-known Virasoro anomaly of string theory. In this article we rst derive the formulas for the Virasoro generators acting on CZ 1 ; Z 2 ; : : :] by means of the reprojection procedure of geometric quant...