A Note on ADE-Spectra in Conformal Field Theory

We demonstrate that certain Virasoro characters (and their linear combinations) in minimal and non-minimal conformal models which admit factorized forms are manifestly related to the ADE series. This permits to extract quasi-particle spectra of a Lie algebraic nature which resembles the features of Toda field theory. These spectra possibly admit a construction in terms of the $W_n$-generators. In the course of our analysis we establish interrelations between the factorized characters related to the parafermionic models, the compactified boson and the minimal models.Comment: 7 pages Late

Entropic C-theorems in free and interacting two-dimensional field theories

The relative entropy in two-dimensional field theory is studied on a cylinder geometry, interpreted as finite-temperature field theory. The width of the cylinder provides an infrared scale that allows us to define a dimensionless relative entropy analogous to Zamolodchikov's $c$ function. The one-dimensional quantum thermodynamic entropy gives rise to another monotonic dimensionless quantity. I illustrate these monotonicity theorems with examples ranging from free field theories to interacting models soluble with the thermodynamic Bethe ansatz. Both dimensionless entropies are explicitly shown to be monotonic in the examples that we analyze.Comment: 34 pages, 3 figures (8 EPS files), Latex2e file, continuation of hep-th/9710241; rigorous analysis of sufficient conditions for universality of the dimensionless relative entropy, more detailed discussion of the relation with Zamolodchikov's theorem, references added; to appear in Phys. Rev.

Spin chains with dynamical lattice supersymmetry

Spin chains with exact supersymmetry on finite one-dimensional lattices are considered. The supercharges are nilpotent operators on the lattice of dynamical nature: they change the number of sites. A local criterion for the nilpotency on periodic lattices is formulated. Any of its solutions leads to a supersymmetric spin chain. It is shown that a class of special solutions at arbitrary spin gives the lattice equivalents of the N=(2,2) superconformal minimal models. The case of spin one is investigated in detail: in particular, it is shown that the Fateev-Zamolodchikov chain and its off-critical extension admits a lattice supersymmetry for all its coupling constants. Its supersymmetry singlets are thoroughly analysed, and a relation between their components and the weighted enumeration of alternating sign matrices is conjectured.Comment: Revised version, 52 pages, 2 figure

Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices

We consider Seiberg electric-magnetic dualities for 4d $\mathcal{N}=1$ SYM theories with SO(N) gauge group. For all such known theories we construct superconformal indices (SCIs) in terms of elliptic hypergeometric integrals. Equalities of these indices for dual theories lead both to proven earlier special function identities and new conjectural relations for integrals. In particular, we describe a number of new elliptic beta integrals associated with the s-confining theories with the spinor matter fields. Reductions of some dualities from SP(2N) to SO(2N) or SO(2N+1) gauge groups are described. Interrelation of SCIs and the Witten anomaly is briefly discussed. Possible applications of the elliptic hypergeometric integrals to a two-parameter deformation of 2d conformal field theory and related matrix models are indicated. Connections of the reduced SCIs with the state integrals of the knot theory, generalized AGT duality for (3+3)d theories, and a 2d vortex partition function are described.Comment: Latex, 58 pages; paper shortened, to appear in Commun. Math. Phy

Two-term dilogarithm identities related to conformal field theory

We study 2x2 matrices A such that the corresponding TBA equations yield c[A] in the form of the effective central charge of a minimal Virasoro model. Certain properties of such matrices and the corresponding solutions of the TBA equations are established. Several continuous families and a discrete set of admissible matrices A are found. The corresponding two-term dilogarithm identities (some of which appear to be new) are obtained. Most of them are proven or shown to be equivalent to previously known identities. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(423) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Tensor operators in R-matrix approach

The definitions and some properties (e.g. the Wigner-Eckart theorem, the fusion procedure) of covariant and contravariant q-tensor operators for quasitriangular quantum Lie algebras are formulated in the R-matrix language. The case of U_q(sl(n)) (in particular, for n=2) is discussed in more detail. (orig.)19 refs.Available from TIB Hannover: RA 2999(95-254) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

A note on ADE-spectra in conformal field theory

We demonstrate that certain Virasoro characters (and their linear combinations) in minimal and non-minimal conformal models which admit factorized forms are manifestly related to the ADE series. This permits to extract quasiparticle spectra of a Lie algebraic nature which resembles the features of Toda field theory. These spectra possibly admit a construction in terms of the W_n-generators. In the course of our analysis we establish interrelations between the factorized characters related to the parafermionic models, the compactified boson and the minimal models. (orig.)SIGLEAvailable from TIB Hannover: RR 1596(371) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Fusion of q-tensor operators: quasi-Hopf-algebraic point of view

We discuss fusion of tensor operators for U_q(J) using R-matrix approach. The problem is reduced to construction of the twisting element F which appears in Drinfeld's description of quasi-Hopf algebras. The discussion is illustrated by explicit calculations for the case of U_q(sl(2)). (orig.)Available from TIB Hannover: RR 1596(215) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Factorized combinations of Virasoro characters

We investigate linear combinations of characters for minimal Virasoro models which are representable as a product of several basic blocks. Our analysis is based on consideration of asymptotic behaviour of the characters in the quasi-classical limit. In particular, we introduce a notion of the secondary effective central charge. We find all possible cases for which factorization occurs on the base of the Gauss-Jacobi or the Watson identities. Exploiting these results, we establish various types of identities between different characters. In particular, we present several identities generalizing the Rogers-Ramanujan identities. Applications to quasi-particle representations, modular invariant partition functions, super-conformal theories and conformal models with boundaries are briefly discussed. (orig.)Available from TIB Hannover: RR 1596(343) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman