Conservative Currents of Boundary Charges in AdS2+1 Gravity

The boundary charge which constitutes the Virasoro algebra in (2+1)-dimensional anti-de Sitter gravity is derived by Noether theorem and diffeomorphic invariance. It shows that the boundary charge under discussion recently exhausts all the available independent nontrivial charges. Therefore, for any specific spacetime, the state counting via the central charge of the Virasoro algebra is exact.     

Framed Vertex Operator Algebras, Codes and the Moonshine Module

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge ?, two codes are introduced and studied. It is proved that such vertex operator algebras are rational. For lattice vertex operator algebras and related ones, decompositions into direct sums of irreducible modules for the product of the Virasoro algebras of central charge ? are explicitly described. As an application, the decomposition of the moonshine vertex operator algebra is obtained for a distinguished system of 48 Virasoro algebras. Received: 14 July 1997 / Accepted: 8 September 1997     

Central charges in the canonical realization of asymptotic symmetries: An example from three dimensional gravity

It is shown that the global charges of a gauge theory may yield a nontrivial central extension of the asymptotic symmetry algebra already at the classical level. This is done by studying three dimensional gravity with a negative cosmological constant. The asymptotic symmetry group in that case is eitherR×SO(2) or the pseudo-conformal group in two dimensions, depending on the boundary conditions adopted at spatial infinity. In the latter situation, a nontrivial central charge appears in the algebra of the canonical generators, which turns out to be just the Virasoro central charge.     

Constrained fermionic system and its equivalence with the free parafermionic theory and nonlinear sigma model

We construct the parafermionic (of orderq) representation of the Kac-Moody and Virasoro algebra and compare it with a constrained fermionic system. We find that the central charge of the Virasoro algebra of the constrained fermionic system depends on the regularization scheme. Using the path integral method, we demonstrate this dependence for theq=2 case and find that it can have the same central charge as the free parafermionic theory or the non-linear sigma model depending on the regularization scheme. We point out some ambiguity in the quantization of the constrained system in Hamiltonian formulation.     

Gravitational anomalies and entropy

A derivation of entropy from the expressions for two dimensional gravitation anomalies is given. Starting from the near horizon anomalous energy–momentum tensors corresponding to particular anomalies, the Virasoro algebra with central extension is obtained. The central charge is identified by comparing with the standard form of the algebra. Then the conserved charge in the ground state is computed. Finally, using the Cardy formula the entropy is obtained. Here both the vector and chiral theories are discussed.     

The relationship among canonical quantisation, Polyakov's functional integral and BRST quantisation of the string

We explore the relationship among the three covariant approaches to the first quantisation of the bosonic string by using the descent equations to calculate the central extension of the Virasoro algebra and the square of the BRST charge from the Weyl anomaly.     

The Cohomology Algebra of the Semi-Infinite Weil Complex

In 1993, Lian-Zuckerman constructed two cohomology operations on the BRST complex of a conformal vertex algebra with central charge 26. They gave explicit generators and relations for the cohomology algebra equipped with these operations in the case of the c = 1 model. In this paper, we describe another such example, namely, the semi-infinite Weil complex of the Virasoro algebra. The semi-infinite Weil complex of a tame -graded Lie algebra was defined in 1991 by Feigin-Frenkel, and they computed the linear structure of its cohomology in the case of the Virasoro algebra. We build on this result by giving an explicit generator for each non-zero cohomology class, and describing all algebraic relations in the sense of Lian-Zuckerman, among these generators.     

Anyonic interpretation of Virasoro characters and the thermodynamic Bethe ansatz

Employing factorized versions of characters as products of quantum dilogarithms corresponding to irreducible representations of the Virasoro algebra, we obtain character formulae which admit an anyonic quasi-particle interpretation in the context of minimal models in conformal field theories. We propose anyonic thermodynamic Bethe ansatz equations, together with their corresponding equation for the Virasoro central charge, on the base of an analysis of the classical limit for the characters and the requirement that the scattering matrices are asymptotically phaseless.     

Irreducible representations of Virasoro-toroidal Lie algebras

Toroidal Lie algebras and their vertex operator representations were introduced in [MEY] and a class of indecomposable modules were investigated. In this work, we extend the toroidal algebra by the Virasoro algebra thus constructing a semi-direct product algebra containing the toroidal algebra as an ideal and the Virasoro algebra as a subalgebra. With the use of vertex operators and certain oscillator representations of the Virasoro algebra it is proved that the corresponding Fock space gives rise to a class of irreducible modules for the Virasoro-toroidal algebra.To A. John Coleman on the occasion of his 75th birthday     

W∞ Algebra and High-Order Virasoro Algebra

We give the relation between W_∞ algebra and high-order Virasoro algebra (HOVA), i.e., W_∞ algebra is the limit of HOVA. Then we give the super high-order Virasoro algebra from super W_∞ algebra.     

Asymptotic symmetry of geometries with Schrödinger isometry

We show that the asymptotic symmetry algebra of geometries with Schrödinger isometry in any dimension is an infinite-dimensional algebra containing one copy of Virasoro algebra. It is compatible with the fact that the corresponding geometries are dual to non-relativistic CFTs whose symmetry algebra is the Schrödinger algebra which admits an extension to an infinite-dimensional symmetry algebra containing a Virasoro subalgebra.     

New quantum treatment of Liouville field theory

We exhibit a new treatment of the quantum Liouville theory in a box. In this treatment, the central charge of the Virasoro algebra is finite at the critical dimension of the associated string model, and we show how to reconstruct conformally covariant quantum field operators, in terms of a set of equally spaced harmonic oscillators.     

Statistical entropies of extremal Kaluza-Klein AdS black holes in arbitrary dimensions

We have investigated the microscopic interpretations of the entropies for the four-dimensional extremal Kaluza-Klein AdS black hole and its higher-dimensional generalizations by using the Kerr/CFT correspondence. These newly-found Kaluza-Klein AdS black holes are charged rotating asymptotically AdS black hole solutions of gauged supergravity in four and higher dimensions. With suitable boundary conditions on the perturbations of the near-horizon geometry, it is shown that the asymptotic symmetry generators form a two-dimensional Virasoro algebra with a central term. By utilizing the central charge and the temperature of the dual conformal field theory, Cardy formula reproduces the expected Bekenstein-Hawking entropy. Directly working on the ordinary metrics of the extremal Kaluza-klein AdS black holes without taking the near-horizon limit, we also re-derive their microscopic entropies.     

Holography at an extremal De Sitter horizon

Rotating maximal black holes in four-dimensional de Sitter space, for which the outer event horizon coincides with the cosmological horizon, have an infinite near-horizon region described by the rotating Nariai metric. We show that the asymptotic symmetry group at the spacelike future boundary of the near-horizon region contains a Virasoro algebra with a real, positive central charge. This is evidence that quantum gravity in a rotating Nariai background is dual to a two-dimensional Euclidean conformal field theory. These results are related to the Kerr/CFT correspondence for extremal black holes, but have two key differences: one of the black hole event horizons has been traded for the cosmological horizon, and the near-horizon geometry is a fiber over dS₂ rather than AdS₂.     

The Virasoro algebra

Three theroems are proved. With suitable hypotheses in each case, characterizations are found for the Virasoro algebra, for some of its representations, and for the Ramond-Neveu-Schwarz superalgebra built around the Virasoro algebra.     

VIRASORO ALGEBRA FOR THE THEORY OF THE REDUCED GRAVITY

In the paper we give a new transformation in the reduced gravity, which is associated with the Virasoro algebra without the center term. To compare with the Geroch group it is easy to establish the relationship between the Virasoro algebra and the Kac-Moody algebra in the theory of the reduced gravity. Then we point out that the transformation can be adopted to generated the new solutions of the Ernst equation from the old ones.     

A quantum deformation of the Virasoro algebra and the Macdonald symmetric functions

A quantum deformation of the Virasoro algebra is defined. The Kac determinants at arbitrary levels are conjectured. We construct a bosonic realization of the quantum deformed Virasoro algebra. Singular vectors are expressed by the Macdonald symmetric functions. This is proved by constructing screening currents acting on the bosonic Fock space.     

The Virasoro vertex algebra and factorization algebras on Riemann surfaces

This paper focuses on the connection of holomorphic two-dimensional factorization algebras and vertex algebras which has been made precise in the forthcoming book of Costello–Gwilliam. We provide a construction of the Virasoro vertex algebra starting from a local Lie algebra on the complex plane. Moreover, we discuss an extension of this factorization algebra to a factorization algebra on the category of Riemann surfaces. The factorization homology of this factorization algebra is computed as the correlation functions. We provide an example of how the Virasoro factorization algebra implements conformal symmetry of the beta–gamma system using the method of effective BV quantization.     

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