We introduce a natural set of asymptotic conditions in the spacelike stretched AdS sector of topologically massive gravity. The Poisson bracket algebra of the canonical generators is shown to have the form of the semi-direct sum of a u(1) Kac-Moody and a Virasoro algebra, with central charges. Using the Sugawara construction, we prove that the asymptotic symmetry coincides with the conformal sy...

The relation between super-Virasoro anomaly and super-Weyl anomaly in N = 1 NSR superstring coupled with 2D supergravity is investigated from canonical theoretical view point. The WZW action canceling the super-Virasoro anomaly is explicitly constructed. It is super-Weyl invariant but nonlocal functional of 2D supergravity. The nonlocality can be remedied by the super-Liouvlle action, which in ...

An N2 dimensional representation of the periodic Temperley-Lieb algebra TLL(x) is presented. It is also a representation of the cyclic group ZN . We choose x = 1 and define a Hamiltonian as a sum of the generators of the algebra acting in this representation. This Hamiltonian gives the time evolution operator of a stochastic process. In the finite-size scaling limit, the spectrum of the Hamilto...

The near-horizon properties of a black hole are studied within an algebraic framework, using a scalar field as a simple probe to analyze the geometry. The operator H governing the near-horizon dynamics of the scalar field contains an inverse square interaction term. It is shown that the operators appearing in the corresponding algebraic description belong to the representation space of the Vira...

We study non-linear integrable partial differential equations naturally arising as bi-Hamiltonian Euler equations related to the looped cotangent Virasoro algebra. This infinite-dimensional Lie algebra (constructed in [16]) is a generalization of the classical Virasoro algebra to the case of two space variables. Two main examples of integrable equations we obtain are quite well known. We show t...

Exploiting Virasoro constraints on the effective finite-volume partition function, we derive generalized Leutwyler-Smilga spectral sum rules of the Dirac operator to high order. By introducing N v fermion species of equal masses, we next use the Virasoro constraints to compute two (low-mass and large-mass) expansions of the partially quenched chiral condensate through the replica method of lett...

We describe a simple way of obtaining horizon entropy using the approach based on the Virasoro algebra and central charge. We show that the Virasoro algebra defined by the Noether currents corresponding to the surface term of gravitational action, for the diffeomorphisms which leave the horizon structure unaltered, has a central extension that directly leads to the horizon entropy. In this appr...

In this article we develop an approach to deformations of the Witt and Virasoro algebras based on σ-derivations. We show that σ-twisted Jacobi type identity holds for generators of such deformations. For the σ-twisted generalization of Lie algebras modeled by this construction, we develop a theory of central extensions. We show that our approach can be used to construct new deformations of Lie ...

We analyze the asymptotic symmetries of near extremal Kerr black holes in four dimensions using the AdS2/CFT1 correspondence. We find a Virasoro algebra with central charge cR = 12J that is independent from the Virasoro algebra (with the same central charge) that acts on the degenerate ground state. The energy of the excitations is computed as well, and we can use Cardy’s formula to determine t...

Some identities between unitary minimal Virasoro characters at levels m = 3, 4, 5 are shown to arise as a consequence of relations between Artin L-functions of different quadratic fields. The definitions and concepts of number theory necessary to present the theta function identities which can be derived from these relations are introduced. A new infinite family of identities between Virasoro c...