The deformed Virasoro algebra plays a similar role for deformed conformal fields as the Virasoro algebra in the usual string and conformal field theories. We show that there exists a physical theory, the discrete-time QFT, in which framework the deformations of (super)Virasoro algebra constructed earlier on an abstract mathematical background emerge. Specifically, the deformed Virasoro and supe...

It was shown by Brown and Henneaux that the classical theory of gravity on AdS3 has an infinite-dimensional symmetry group forming a Virasoro algebra. More recently, Giveon, Kutasov and Seiberg (GKS) constructed the corresponding Virasoro generators in the first-quantized string theory onAdS3. In this paper, we explore various aspects of string theory on AdS3 and study the relation between thes...

It was shown by Brown and Henneaux that the classical theory of gravity on AdS3 has an infinite-dimensional symmetry group forming a Virasoro algebra. More recently, Giveon, Kutasov and Seiberg (GKS) constructed the corresponding Virasoro generators in the first-quantized string theory on AdS3. In this paper, we explore various aspects of string theory on AdS3 and study the relation between the...

Quantum cohomology is a family of new ring structures on the space of cohomology classes of a compact symplectic manifold (or a smooth projective variety) V . The quantum products are defined by third order partial derivatives of the generating function of primary Gromov-Witten invariants of V (cf. [RT1]). In a similar way, using the generating function of all descendant Gromov-Witten invariant...

We prove that for simple complex finite dimensional Lie algebras, affine Kac-Moody Lie algebras, the Virasoro algebra and the Heisenberg-Virasoro algebra, simple highest weight modules are characterized by the property that all positive root elements act on these modules locally nilpotently. We also show that this is not the case for higher rank Virasoro and for Heisenberg algebras.

We classify the Harish-Chandra modules over the higher rank Virasoro and super-Virasoro algebras: It is proved that a Harish-Chandra module, i.e., an irreducible weight module with finite weight multiplicities, over a higher rank Virasoro or super-Virasoro algebra is a module of the intermediate series. As an application, it is also proved that an indecomposable weight module with finite weight...

We construct new realizations of the Virasoro algebra inspired by the Calogero model. The Virasoro algebra we find acts as a kind of spectrum-generating algebra of the Calogero model. We furthermore present the su-perextension of these results and introduce a class of higher-spin extensions of the Virasoro algebra which are of the W ∞-type.

For a simple vertex operator algebra whose Virasoro element is a sum of commutative Virasoro elements of central charge 1 2 , 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 1 ...

Virasoro algebra possesses a representation in the tangent space to the space of normalized univalent functions defined in the unit disk and smooth on its boundary. We discuss connections between representations of the Virasoro algebra and the Löwner-Kufarev equations in partial and ordinary derivatives. Virasoro generators turn to be conservative quantites for the Löwner-Kufarev ODE, and the L...

We obtain the orbifold Virasoro master equation (OVME) at integer order λ, which summarizes the general Virasoro construction on orbifold affine algebra. The OVME includes the Virasoro master equation when λ = 1 and contains large classes of stress tensors of twisted sectors of conventional orbifolds at higher λ. The generic construction is like a twisted sector of an orbifold (with non-zero gr...