Semi-infinite cohomology in conformal field theory and 2D gravity

We discuss various techniques for computing the semi-infinite cohomology of highest weight modules which arise in the BRST quantization of two dimensional field theories. In particular, we concentrate on two such theories - the G/H coset models and 2D gravity coupled to c ≤ 1 conformal matter.     

T-duality in Affine NA Toda Models

The construction of non-Abelian affine Toda models is discussed in terms of its underlying Lie algebraic structure. It is shown that a subclass of such non-conformal two-dimensional integrable models naturally leads to the construction of a pair of actions, which share the same spectra and are related by canonical transformations.     

Quasinormal spectrum and the black hole membrane paradigm

The membrane paradigm approach to black hole physics introduces the notion of a stretched horizon as a fictitious time-like surface endowed with physical characteristics such as entropy, viscosity and electrical conductivity. We show that certain properties of the stretched horizons are encoded in the quasinormal spectrum of black holes. We compute analytically the lowest quasinormal frequency of a vector-type perturbation for a generic black hole with a translationally invariant horizon (black brane) in terms of the background metric components. The resulting dispersion relation is identical to the one obtained in the membrane paradigm treatment of the diffusion on stretched horizons. Combined with the Buchel–Liu universality theorem for the membrane's diffusion coefficient, our result means that in the long wavelength limit the black brane spectrum of gravitational perturbations exhibits a universal, purely imaginary quasinormal frequency. In the context of gauge–gravity duality, this provides yet another (third) proof of the universality of shear viscosity to entropy density ratio in theories with gravity duals.     

在类比系统中研究引力和黑洞的性质

引力和量子力学的融合是理解时空起源和引力本质的重要问题,也是一个长期悬而未决的基础物理学根本问题。理论物理学家们对此提出了诸多理论猜想,也做出了许多预言。然而一些相关的预言涉及的效应极其微弱,因此难以通过实验观测加以证实。通过类比引力系统,人们可以将这些引力效应转化为实验室可测可控系统的一些效应。对这些类比系统的研究一方面可以帮助人们更深入地理解引力的性质本身,另一方面也可以为其他相关领域的研究提供启发和新的思路。文章将以几个具体的类比系统为例简要介绍类比引力研究的历史和最近的一些研究进展。     

Boson-Fermion Duality in A2 Toda Field Theory

In this paper, we consider a two-dimensional integrable and conformal invariant field theory with two Diracspinors and two scalar fields. This model has chiral symmetry and CP-like symmetry. Moreover, this model also has aNeother current depending only on the matter field. At last, we bosonize the spinor fields.     

On Conformal Field Theory of SLE(κ,ρ)

SLE(κ ρ), a generalization of chordal Schramm-Löwner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = $\alpha_j = \frac{\rho_j}{2 \sqrt{\kappa}}SLE(κ ρ), a generalization of chordal Schramm-Löwner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = $\alpha_j = \frac{\rho_j}{2 \sqrt{\kappa}}SLE(κ ρ), a generalization of chordal Schramm-L?wner evolution (SLE), is discussed from the point of view of statistical mechanics and conformal field theory (CFT). Certain ratios of CFT correlation functions are shown to be martingales. The interpretation is that SLE(κ ρ) describes an interface in a statistical mechanics model whose boundary conditions are created in the Coulomb gas formalism by vertex operators with charges α _j = . The total charge vanishes and therefore the partition function has a simple product form. We also suggest a generalization of SLE(κ ρ)     

A Comment on the Dual Field in the AdS–CFT Correspondence

In the perturbative AdS–CFT correspondence, the dual field whose source are the prescribed boundary values of a bulk field in the functional integral, and the boundary limit of the quantized bulk field are the same thing. This statement is due to the fact that Witten graphs are boundary limits of the corresponding Feynman graphs for the bulk fields, and hence the dual conformal correlation functions are limits of bulk correlation functions. This manifestation of duality is analyzed in terms of the underlying functional integrals of different structure.     

Harrison Metrics for the Schwarzschild Black Hole

Based on the hidden conformed symmetry, some authors have proposed a Harrison metric for the Schwarzschild black hole. We give a procedure which can generate a family of Harrison metrics starting from a general set of SL（2, R） vector fields. By analogy with the subtracted geometry of the Kerr black hole, we find a new Harrison metric for the Schwaxzschild case. its conformal generators axe also investigated using the Killing equations in the near-horizon limit.     

General Rotating Black Hole with Four Charges and Liouville Theory

By considering the dual Liouville theory emerging in the near-horizon limit, we study the thermodynamics of general rotating black hole with four charges in four dimensions. Both the black hole entropy and temperature are found to agree with the gravitational expectations. The relations between the new Liouville formalism and the anomaly approach are also discussed.     

Topological representations of quantum groups and conformal field theory

These are three introductory lectures on the relation between representations of affine Kac-Moody algebras, homology of configuration spaces with local coefficient systems, and quantum groups. The first lecture contains background on highest weight representations of affine Kac-Moody algebras. In the second lecture, conformal blocks, the Friedan-Shenker connection and the Knizhnik-Zamolodchikov (KZ) equation are reviewed. In the third lecture, the case of sl_z is studied in more detail. Integral representations of solutions of the KZ equation are derived, and recent results, obtained in collaboration with C. Wieczerkowski, on the relation between integration cycles and representations of U_q (sl₂) are explained.     

Simple Current Actions of Cyclic Groups

Permutation actions of simple currents on the primaries of a Rational Conformal Field Theory are considered in the framework of admissible weighted permutation actions. The solution of admissibility conditions is presented for cyclic quadratic groups: an irreducible WPA corresponds to each subgroup of the quadratic group. As a consequence, the primaries of a RCFT with an order n integral or half-integral spin simple current may be arranged into multiplets of length k² (where k is a divisor of n) or 3k² if the spin of the simple current is half-integral and k is odd.Mathematical Subject Classifications (2000). 81T40.Work supported by grant OTKA TS044839.     

Conjectured Z2-Orbifold Constructions of Self-Dual Conformal Field Theories at Central Charge 24 – the Neighborhood Graph

By considering constraints on the dimensions of the Lie algebra corresponding to the weight 1-states of Z₂ and Z₃ orbifold models arising from imposing the appropriate modular properties on the graded characters of the automorphisms on the underlying conformal field theory, we propose a set of constructions of all but one of the 71 self-dual meromorphic bosonic conformal field theories at central charge 24. In the Z₂ case, this leads to an extension of the neighborhood graph of the even self-dual lattices in 24 dimensions to conformal field theories, and we demonstrate that the graph becomes disconnected.     

Logarithmic Conformal Field Theories Near a Boundary

We consider logarithmic conformal field theories near a boundary and derive the general form of one and two point functions. We obtain results for arbitrary and two dimensions. Application to two-dimensional magnetohydrodynamics is discussed.     

Current Algebra Associated with Logarithmic Conformal Field Theories

We propose a general framework for deriving the OPEs within a logarithmic conformal field theory (LCFT). This naturally leads to the emergence of a logarithmetic partner of the energy momentum tensor within an LCFT and implies that the current algebra associated with an LCFT is expanded. We derive this algebra for a generic LCFT and discuss some of its implications. We observe that two constants arise in the OPE of the energy-momentum tensor with itself. One of these is the usual central charge.