Poincare Polynomials and Level Rank Dualities in the N=2N=2 Coset Construction

We review the coset construction of conformal field theories; the emphasis is on the construction of the Hilbert spaces for these models, especially if fixed points occur. This is applied to the $N=2$ superconformal cosets constructed by Kazama and Suzuki. To calculate heterotic string spectra we reformulate the Gepner con- struction in terms of simple currents and introduce the so-called extended Poincar\'e polynomial. We finally comment on the various equivalences arising between models of this class, which can be expressed as level rank dualities. (Invited talk given at the III. International Conference on Mathematical Physics, String Theory and Quantum Gravity, Alushta, Ukraine, June 1993. To appear in Theor. Math. Phys.)Comment: 14 pages in LaTeX, HD-THEP-93-4

Current-Current Deformations of Conformal Field Theories, and WZW Models

Moduli spaces of conformal field theories corresponding to current-current deformations are discussed. For WZW models, CFT and sigma model considerations are compared. It is shown that current-current deformed WZW models have WZW-like sigma model descriptions with non-bi-invariant metrics, additional B-fields and a non-trivial dilaton.Comment: 30 pages, latex, v2: remarks and references adde

The spectrum of states with one current acting on the adjoint vacuum of massless QCD2

We consider a ``one current'' state, which is obtained by the application of a color current on the ``adjoint'' vacuum. This is done in $QCD_2$, with the underlying quarks in the fundamental representation. The quarks are taken to be massless, in which case the theory on the light-front can be ``currentized'', namely, formulated in terms of currents only. The adjoint vacuum is shown to be the application of a current derivative, at zero momentum, on the singlet vacuum. We apply the operator $M^2=2P^+P^-$ on these states and find that in general they are not eigenstates of $M^2$ apart from the large $N_f$ limit. Problems with infra-red regularizations are pointed out. We discuss the fermionic structure of these states.Comment: 18 pages, no figures. v2: minor corrections. v3: added some clarifications and remarks, mainly on the contribution of zero modes. Typos corrected, references added. To appear in Nuclear Physics

Symmetries between Untwisted and Twisted Strings on Asymmetric Orbifolds

We study symmetries between untwisted and twisted strings on asymmetric orbifolds. We present a list of asymmetric orbifold models to possess intertwining currents which convert untwisted string states to twisted ones, and vice versa. We also present a list of heterotic strings on asymmetric orbifolds with supersymmetry between untwisted and twisted string states. Some of properties inherent in asymmetric orbifolds, which are not shared by symmetric orbifolds, are pointed out.Comment: Plain Tex, 35 pages, NBI-HE-92-34, KOBE-92-0

Boundary states, matrix factorisations and correlation functions for the E-models

The open string spectra of the B-type D-branes of the N=2 E-models are calculated. Using these results we match the boundary states to the matrix factorisations of the corresponding Landau-Ginzburg models. The identification allows us to calculate specific terms in the effective brane superpotential of E_6 using conformal field theory methods, thereby enabling us to test results recently obtained in this context.Comment: 20 pages, no figure

On the complete classification of the unitary N=2 minimal superconformal field theories

Aiming at a complete classification of unitary N=2 minimal models (where the assumption of space-time supersymmetry has been dropped), it is shown that each modular invariant candidate of a partition function for such a theory is indeed the partition function of a minimal model. A family of models constructed via orbifoldings of either the diagonal model or of the space-time supersymmetric exceptional models demonstrates that there exists a unitary N=2 minimal model for every one of the allowed partition functions in the list obtained from Gannon's work. Kreuzer and Schellekens' conjecture that all simple current invariants can be obtained as orbifolds of the diagonal model, even when the extra assumption of higher-genus modular invariance is dropped, is confirmed in the case of the unitary N=2 minimal models by simple counting arguments.Comment: 53 pages; Latex; minor changes in v2: intro expanded, references added, typos corrected, footnote added on p31; renumbering of sections; main theorem reformulated for clarity, but contents unchanged. Minor revisions in v3: typos corrected, footnotes 5, 6 added, lemma 1 and section 3.3.2 rewritten for greater generality, section 3.3 review removed. To appear in Comm. Math. Phy

The partition function of the supersymmetric two-dimensional black hole and little string theory

We compute the partition function of the supersymmetric two-dimensional Euclidean black hole geometry described by the SL(2,R)/U(1) superconformal field theory. We decompose the result in terms of characters of the N=2 superconformal symmetry. We point out puzzling sectors of states besides finding expected discrete and continuous contributions to the partition function. By adding an N=2 minimal model factor of the correct central charge and projecting on integral N=2 charges we compute the partition function of the background dual to little string theory in a double scaling limit. We show the precise correspondence between this theory and the background for NS5-branes on a circle, due to an exact description of the background as a null gauging of SL(2,R) x SU(2). Finally, we discuss the interplay between GSO projection and target space geometry.Comment: JHEP class, 35 pages, no figures; v2: minor changes, typos corrected, published versio

Type IIB orientifolds on Gepner points

We study various aspects of orientifold projections of Type IIB closed string theory on Gepner points in different dimensions. The open string sector is introduced, in the usual constructive way, in order to cancel RR charges carried by orientifold planes. Moddings by cyclic permutations of the internal N=2 superconformal blocks as well as by discrete phase symmetries are implemented. Reduction in the number of generations, breaking or enhancements of gauge symmetries and topology changes are shown to be induced by such moddings. Antibranes sector is also considered; in particular we show how non supersymmetric models with antibranes and free of closed and open tachyons do appear in this context. A systematic study of consistent models in D=8 dimensions and some illustrative examples in D=6 and D=4 dimensions are presented.Comment: 67 pages, no figures References added, typos correcte

SL(2,R)/U(1) Supercoset and Elliptic Genera of Non-compact Calabi-Yau Manifolds

We first discuss the relationship between the SL(2;R)/U(1) supercoset and N=2 Liouville theory and make a precise correspondence between their representations. We shall show that the discrete unitary representations of SL(2;R)/U(1) theory correspond exactly to those massless representations of N=2 Liouville theory which are closed under modular transformations and studied in our previous work hep-th/0311141. It is known that toroidal partition functions of SL(2;R)/U(1) theory (2D Black Hole) contain two parts, continuous and discrete representations. The contribution of continuous representations is proportional to the space-time volume and is divergent in the infinite-volume limit while the part of discrete representations is volume-independent. In order to see clearly the contribution of discrete representations we consider elliptic genus which projects out the contributions of continuous representations: making use of the SL(2;R)/U(1), we compute elliptic genera for various non-compact space-times such as the conifold, ALE spaces, Calabi-Yau 3-folds with A_n singularities etc. We find that these elliptic genera in general have a complex modular property and are not Jacobi forms as opposed to the cases of compact Calabi-Yau manifolds.Comment: 39 pages, no figure; v2 references added, minor corrections; v3 typos corrected, to appear in JHEP; v4 typos corrected in eqs. (3.22) and (3.44

g-Functions and gluon scattering amplitudes at strong coupling

We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling by calculating the area of the minimal surfaces in AdS_3 based on the associated thermodynamic Bethe ansatz system. The remainder function of the amplitudes is computed by evaluating the free energy, the T- and Y-functions of the homogeneous sine-Gordon model. Using conformal field theory (CFT) perturbation, we examine the mass corrections to the free energy around the CFT point corresponding to the regular polygonal Wilson loop. Based on the equivalence between the T-functions and the g-functions, which measure the boundary entropy, we calculate corrections to the T- and Y-functions as well as express them at the CFT point by the modular S-matrix. We evaluate the remainder function around the CFT point for 8 and 10-point amplitudes explicitly and compare these analytic expressions with the 2-loop formulas. The two rescaled remainder functions show very similar power series structures.Comment: 51 pages, 4 figures, v2: some comments and references added, based on the published version, v3: minor change