Extensions Of Virasoro Algebra Research Articles

Warped AdS3 black holes in higher derivative gravity theories

We consider warped AdS_3 black holes in generic higher derivatives gravity theories in 2+1 dimensions. The asymptotic symmetry group of the phase space containing these black holes is the semi-direct product of a centrally extended Virasoro algebra and an affine u(1) Kac-Moody algebra. Previous works have shown that in some specific theories, the entropy of these black holes agrees with a Cardy-like entropy formula derived for warped conformal field theories. In this paper, we show that this entropy matching continues to hold for the most general higher derivative theories of gravity. We also discuss the existence of phase transitions.

Nonlocal dynamics and infinite nonrelativistic conformal symmetries

We study the symmetry of the class of nonlocal models which includes the nonlocal extension of the Pais-Uhlenbeck oscillator. As a consequence, we obtain an infinite-dimensional symmetry algebra, containing the Virasoro algebra, which can be considered as a generalization of the nonrelativistic conformal symmetries to the infinite order. Moreover, this nonlocal extension resembles to some extent the string model, and on the quantum level, it leads to the centrally extended Virasoro algebra.

Classification of simple weight modules for super-Virasoro algebra with a finite-dimensional weight space

There are two extensions of Virasoro algebra with particular importance in superstring theory: the Ramond algebra and the Neveu-Schwarz algebra, which are ℤ2-graded extensions of the Virasoro algebra. In this paper, we show that the support of a simple weight module over the Ramond algebra with an infinite-dimensional weight space coincides with the weight lattice and that all intersections of non-trivial weight spaces and odd part or even part of the module are infinite-dimensional. This result together with the one that we have obtained over the Neveu-Schwarz algebra generalizes the result for the Virasoro algebra to the super-Virasoro algebras.

A NEAR HORIZON CFT DUAL FOR KERR–NEWMAN AdS

We show that the near horizon regime of a Kerr–Newman AdS (KNAdS) black hole, given by its two-dimensional analogue a là Robinson and Wilczek (Phys. Rev. Lett.95, 011303 (2005)), is asymptotically AdS2 and dual to a one-dimensional quantum conformal field theory (CFT). The s-wave contribution of the resulting CFT's energy–momentum tensor together with the asymptotic symmetries, generate a centrally extended Virasoro algebra, whose central charge reproduces the Bekenstein–Hawking entropy via Cardy's formula. Our derived central charge also agrees with the near extremal Kerr/CFT correspondence (Phys. Rev. D80, 124008 (2009)) in the appropriate limits. We also compute the Hawking temperature of the KNAdS black hole by coupling its Robinson and Wilczek two-dimensional analogue (RW2DA) to conformal matter.

Polynomial fusion rings of W-extended logarithmic minimal models

The countably infinite number of Virasoro representations of the logarithmic minimal model LM(p,p′) can be reorganized into a finite number of W-representations with respect to the extended Virasoro algebra symmetry W. Using a lattice implementation of fusion, we recently determined the fusion algebra of these representations and found that it closes, albeit without an identity for p>1. Here, we provide a fusion-matrix realization of this fusion algebra and identify a fusion ring isomorphic to it. We also consider various extensions of it and quotients thereof and introduce and analyze commutative diagrams with morphisms between the involved fusion algebras and the corresponding quotient polynomial fusion rings. One particular extension is reminiscent of the fundamental fusion algebra of LM(p,p′) and offers a natural way of introducing the missing identity for p>1. Working out explicit fusion matrices is facilitated by a further enlargement based on a pair of mutual Moore–Penrose inverses intertwining between the W-fundamental and enlarged fusion algebras.

Extensions of the Virasoro algebra and gauged WZW models

To any non-trivial embedding of sl(2) in a (super) Lie algebra, one can associate an extension of the Virasoro algebra. We realize the extended Virasoro algebra in terms of a WZW model in which a chiral, solvable group is gauged, the gauge group being determined by the sl(2) embedding. The resulting BRST cohomology is computed and the field content of the extended Virasoro algebra is determined. The closure of the extended Virasoro algebra is shown. Applications such as the quantum Miura transformation and the effective action of the associated extended gravity theory are discussed.

Construction of the K = 8 fractional superconformal algebras

We construct the K = 8 fractional superconformal algebras. There are two such extended Virasoro algebras, one of which was constructed earlier, involving a fractional spin (equivalently, conformal dimension) 6 5 current. The new algebra involves two additional fractional spin currents with spin 13 5 . Both algebras are non-local and satisfy non-abelian braiding relations. The construction of the algebras uses the isomorphism between the Z 8 parafermion theory and the tensor product of two tricritical Ising models. For the special value of the central charge c = 52 55 , corresponding to the eighth member of the unitary minimal series, the 13 5 currents of the new algebra decouple, while two spin 23 5 currents (level-2 current algebra descendants of the 13 5 currents) emerge. In addition, it is shown that the K = 8 algebra involving the spin 13 5 currents at central charge c = 12 5 is the appropriate algebra for the construction of the K = 8 (four-dimensional) fractional superstring.

FRACTIONAL SUPERSYMMETRY AND MINIMAL COSET MODELS IN CONFORMAL FIELD THEORY

Starting from fractional supersymmetry as an extended Virasoro algebra, we generalize Felder's BRST cohomology method to construct the characters and branching functions — in terms of string functions — of the SU(2) and SU(3) coset models, for both the unitary and nonunitary cases.

Structure constants of the fractional supersymmetry chiral algebras

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 show that correlators of J ( K) 's satisfy non-abelian braiding relations.

The quantum group structure associated with non-linearly extended Virasoro algebras

Recently, an infinite family of chiral Virasoro vertex operators, whose exchange algebra is given by the universalR-matrix ofSL(2) q , has been constructed. In the present paper, the case of non-linearly (W-) extended Virasoro symmetries, related to the algebrasA N,N>1, is considered along the same line. Contrary to the previous case (A 1) the standardR-matrix ofSL(N+1)q does not come out, and a different solution of Yang and Baxter's equations is derived. The associated quantum group structure is displayed.

Quantum conformal algebra with central extension

The only admissible q-deformed centrally extended Virasoro algebra is obtained. The deformed central term is reduced in the nondeformed limit only to a part of the usual one.

TWISTED CHARACTERS AND PARTITION FUNCTIONS IN EXTENDED VIRASORO ALGEBRAS

The characters of the degenerate representations of the extended Virasoro algebras associated with the 2-twisted Lie algebras [Formula: see text], [Formula: see text] and [Formula: see text] are derived and their modular transformation properties examined. Modular invariant partition functions for [Formula: see text] and [Formula: see text][Formula: see text] are presented.

Connection between infinite conservation laws in a coupled Ziber-Shabat-Mikhailov equation and a coupled Kaup-Kupershmidt equation

A simple connection between an infinite sequence of conserved quantities inboth a coupled Ziber-Shabat-Mikhailov equation and a coupled Kaup-Kupershmidt equation is presented. It is shown that both sequences may be transformed into a single sequence of classically commuting operators expressed in terms of the generators of an extended Virasoro algebra associated to the Hirota-Satsuma equation.

Non-linearly extended virasoro algebras: New prospects for building string theories

Converging facts are presented as evidence showing that there exist string theories of a novel type where the recently discovered non-linearly extended Virasoro algebras appear as world-sheet symmetries. These new theories are shown to exhibit rather novel properties, in particular, at the Planck mass, they may involve fundamental interactions mediated by massless particles with spins higher than two. The generalized ghost systems lead to string-field topological actions characterized by new cohomologies. For A N = SU N + 1 , as an example, the structure is similar to the cohomology of v-dimensional manifolds, with v = 2 + N( N + 1)/2.

Twisted structures of extended virasoro algebras

We study the twisted conformal algebras generated by the outer automorphisms of simple Lie algebras. For each of the A n−1 (2), D n (2), E 6 (2), and D 4 (3) algebras, we derive the spectrum of the conformal dimensions of its primary fields making use of a generalized Feigin-Fuks representation.

The extended Virasoro algebras from Z N symmetric spectral equations

The KdV-type spectral equations, which are equivalent to Z N symmetric matrix spectral equations under the Miura transformation and have the A N−1 (1) Kac-Moody algebra as a hidden symmetry, are considered. Thus the Poisson bracket, which corresponds to the adjoint of the recursion operator should be shown giving the realization of the classical extended Virasoro algebras that involve the generators of higher spins as KdV-type potentials. The Z 3 and Z 4 cases are displayed explicitly.

The KP hierarchy and extended Virasoro algebras

The extended Virasoro algebra with spin-3 current is derived in the framework of the KP hierarchy. A speculative form of a further extension of the Virasoro algebra with spin-4 current is given.

Systematic approach to conformal systems with extended Virasoro symmetries

The Toda field theories, which exist for every simple Lie group, are shown to give realizations of extended Virasoro algebras that involve generators of spins higher than or equal to two. They are uniquely determined from the canonical lagrangian formalism. The quantization of the Toda field theories gives a systematic treatment of generalized conformal bosonic models. The well-known pattern of conformal field theories with non-extended Virasoro algebra, appears to be repeated for any simple group, leading to a “periodic table”, parallel to the mathematical classification of simple Lie groups.

AN INFINITE CLASS OF NEW CONFORMAL FIELD THEORIES WITH EXTENDED ALGEBRAS

A large class of 2D conformal field theories with extended Virasoro algebras related to the GKO construction on the coset SU(2)⊗SU(2)/SU(2) is introduced. Through a Feigin-Fuchs construction the Kac formula is deduced. Characters of the highest-weight irreducible representations are given in terms of the GKO decomposition branching functions. Modular invariant partition functions are constructed and an A-D-E classification based on a triple of simply-laced Lie algebras is analyzed in detail.