For an arbitrary Frobenius manifold a system of Virasoro constraints is constructed. In the semisimple case these constraints are proved to hold true in the genus one approximation. Particularly, the genus ≤ 1 Virasoro conjecture of T.Eguchi, K.Hori, M.Jinzenji, and C.-S.Xiong and of S.Katz is proved for smooth projective varieties having semisimple quantum cohomology.

In this paper, we construct the super Witt algebra and Virasoro in framework of [Formula: see text]-deformed quantum algebras. Moreover, perform text]-algebra, text]-algebra discuss text]-Virasoro ([Formula: text] even). Besides, define another study a toy model for constraints. Relevant particular cases induced from algebras known literature are deduced formalism developed.

A realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and its suitable representation. The embedding into algebras of in analogue to the classical Jordan—Schwinger map. number examples such computed. In particular, we obtain twisted Heisenberg-Virasoro Schrödinger-Virasoro among others. More generally, construct an arbitrary locally convex t...

We give expressions for the singular vectors in the highest weight representations of the Virasoro algebra. We verify that the expressions — which take the form of a product of operators applied to the highest weight vector — do indeed define singular vectors. These results explain the patterns of embeddings amongst Virasoro algebra highest weight representations. Conformal field theory relies ...

For every p ≥ 2, we obtained an explicit construction of a family of W(2, 2p − 1)-modules, which decompose as direct sum of simple Virasoro algebra modules. Furthermore, we classified all irreducible self-dual W(2, 2p − 1)-modules, we described their internal structure, and computed their graded dimensions. In addition, we constructed certain hidden logarithmic intertwining operators among two ...

We compute the short distance expansion of fields or operators that live in the coadjoint representation of an infinite dimensional Lie algebra by using only properties of the adjoint representation and its dual. We explicitly compute the short distance expansion for the duals of the Virasoro algebra, affine Lie Algebras and the geometrically realized N -extended supersymmetric GR Virasoro alge...

The fractional supersymmetry chiral algebras, A(K), in two-dimensional conformal field theory are extended Virasoro algebras with fractional spin currents J (K). We show that associativity and closure of A(K) determines its structure constants in the case that the Virasoro algebra is extended by precisely one current. We compute the structure constants of the A(K) algebras explicitly and we sho...

We study a bosonic string with one end free and the other confined to a D0−brane. Only the odd oscillator modes are allowed, which leads to a Virasoro algebra of even Virasoro modes only. The theory is quantized in a gauge where world-sheet time and ordinary time are identified. There are no negative or null norm states, and no tachyon. The Regge slope is twice that of the open string; this can...