arXiv subjects
Publications and source records attributed to Jan Troost.
We provide generating functions for the perturbative massive string spectrum which are covariant with respect to the SO(9) little group, and which contain all the representation theoretic content of the spectrum. Generating functions for perturbative bosonic, Type II, Heterotic and Type I string theories are presented, and generalizations are discussed.
We construct a non-chiral current algebra in two dimensions consistent with conformal invariance. We show that the conformal current algebra is realized in non-linear sigma-models on supergroup manifolds with vanishing dual Coxeter number, with or without a Wess-Zumino term. The current algebra is computed using two distinct methods. First we exploit special algebraic properties of supergroups to compute the exact two- and three-point functions of the currents and from them we infer the current algebra. The algebra is also calculated by using conformal perturbation theory about the Wess-Zumino-Witten point and resumming the perturbation series. We also prove that these models realize a non-chiral Kac-Moody algebra and construct an infinite set of commuting operators that is closed under the action of the Kac-Moody generators. The supergroup models that we consider include models with applications to statistical mechanics, condensed matter and string theory. In particular, our results may help to systematically solve and clarify the quantum integrability of PSU(n|n) models and their cosets, which appear prominently in string worldsheet models on anti-deSitter spaces.
We compute the algebra of left and right currents for a principal chiral model with arbitrary Wess-Zumino term on supergroups with zero Killing form. We define primary fields for the current algebra that match the affine primaries at the Wess-Zumino-Witten points. The Maurer-Cartan equation together with current conservation tightly constrain the current-current and current-primary operator product expansions. The Hilbert space of the theory is generated by acting with the currents on primary fields. We compute the conformal dimensions of a subset of these states in the large radius limit. The current algebra is shown to be consistent with the quantum integrability of these models to several orders in perturbation theory.
We first clarify the relation between boundary perturbations of AdS3 in general relativity, and exactly marginal worldsheet vertex operators in AdS3 string theory with Neveu-Schwarz Neveu-Schwarz flux. The latter correspond to solutions of the higher derivative low-energy tree level effective action to all orders in the string length over the curvature radius. We then calculate the exact expression of the boundary energy momentum tensor including all these higher derivative corrections in a purely bosonic string theory. The bottom-line is a canonical shift in the normalization of the boundary energy-momentum tensor corresponding to a shift in the curvature radius over the string length squared by the dual Coxeter number of the SL(2,R) subalgebra of the space-time Virasoro algebra. That allows us to derive the value of the Brown-Henneaux central charge including all tree level higher derivative corrections in bosonic string theory, in a scheme dictated by the worldsheet conformal field theory.
We analyze various perspectives on the elliptic genus of non-compact supersymmetric coset conformal field theories with central charge larger than three. We calculate the holomorphic part of the elliptic genus via a free field description of the model, and show that it agrees with algebraic expectations. The holomorphic part of the elliptic genus is directly related to an Appell-Lerch sum and behaves anomalously under modular transformation properties. We analyze the origin of the anomaly by calculating the elliptic genus through a path integral in a coset conformal field theory. The path integral codes both the holomorphic part of the elliptic genus, and a non-holomorphic remainder that finds its origin in the continuous spectrum of the non-compact model. The remainder term can be shown to agree with a function that mathematicians introduced to parameterize the difference between mock theta functions and Jacobi forms. The holomorphic part of the elliptic genus thus has a path integral completion which renders it non-holomorphic and modular.
String theory on AdS3 space-times with boundary conditions that allow for black hole states has global asymptotic symmetries which include an infinite dimensional conformal algebra. Using the conformal current algebra for sigma-models on PSU(1,1|2), we explicitly construct the R-symmetry and Virasoro charges in the worldsheet theory describing string theory on AdS3 X S3 with Ramond-Ramond fluxes. We also indicate how to construct the full boundary superconformal algebra. The boundary superconformal algebra plays an important role in classifying the full spectrum of string theory on AdS3 with Ramond-Ramond fluxes, and in the microscopic entropy counting in D1-D5 systems.
We provide the backreaction of the T-fold doubly T-dual to a background with NSNS three-form flux on a three-torus. We extend the backreacted T-fold to include cases with a flux localized in one out of three directions. We analyze the resulting monodromy domain walls and vortices. In these backgrounds, we give an analysis of the action of T-duality on observables like charges and Wilson surfaces. We analyze arguments for the existence of regions in the configuration space of second quantized string theory that cannot be reduced to geometry. Finally, by allowing for space-dependent moduli, we find a supergravity solution which is a T-fold with hyperbolic monodromies.
We exhibit bound states in the spectrum of non-compact D-branes in N=2 Liouville conformal field theory. We interpret these states in the study of D-branes in the near-horizon limit of Neveu-Schwarz five-branes spread on a topologically trivial circle. We match semi-classical di-electric and repulsion effects with exact conformal field theory results and describe the fate of D-branes hitting NS5-branes. We also show that the bound states can give rise to massless vector and hyper multiplets in a low-energy gauge theory on D-branes deep inside the throat.
Using the pure spinor formalism on the world-sheet, we derive the T-duality rules for all target space couplings in an efficient manner. The world-sheet path integral derivation is a proof of the equivalence of the T-dual Ramond-Ramond backgrounds which is valid non-perturbatively in the string length over the curvature radius and to all orders in perturbation theory in the string coupling.
We study non-compact Gepner models that preserve sixteen or eight supercharges in type II string theories. In particular, we develop an orbifolded Landau-Ginzburg description of these models analogous to the Landau-Ginzburg formulation of compact Gepner models. The Landau-Ginzburg description provides an easy and direct access to the geometry of the singularity associated to the non-compact Gepner models. Using these tools, we are able to give an intuitive account of the chiral rings of the models, and of the massless moduli in particular. By studying orbifolds of the singular linear dilaton models, we describe mirror pairs of non-compact Gepner models by suitably adapting the Greene-Plesser construction of mirror pairs for the compact case. For particular models, we take a large level, low curvature limit in which we can analyze corrections to a flat space orbifold approximation of the non-compact Gepner models. This gives rise to a counting of moduli which differs from the toric counting in a subtle way.
We define a wave-function for string theory cosmological backgrounds. We give a prescription for computing its norm following an earlier analysis within general relativity. Under Euclidean continuation, the cosmologies we discuss in this paper are described in terms of compact parafermionic worldsheet systems. To define the wave-function we provide a T-fold description of the parafermionic conformal field theory, and of the corresponding string cosmology. In specific examples, we compute the norm of the wave-function and comment on its behavior as a function of moduli.
We study D-branes in the superstring background R^{3,1} \times SL(2,R)_{k=1}/U(1) which are extended in the cigar direction. Some of these branes are new. The branes realize flavor in the four dimensional N=1 gauge theories on the D-branes localized at the tip of the cigar. We study the analytic properties of the boundary conformal field theories on these branes with respect to their defining parameter and find non-trivial monodromies in this parameter. Through this approach, we gain a better understanding of the brane set-ups in ten dimensions involving wrapped NS5-branes. As one application, using the boundary conformal field theory description of the electric and magnetic D-branes, we can understand electric-magnetic (Seiberg) duality in N=1 SQCD microscopically in a string theoretic context.
We exhibit exact conformal field theory descriptions of SO(N) and Sp(N) pairs of Seiberg-dual gauge theories within string theory. The N=1 gauge theories with flavour are realized as low energy limits of the worldvolume theories on D-branes in unoriented non-critical superstring backgrounds. These unoriented backgrounds are obtained by constructing exact crosscap states in the SL(2,R)/U(1) coset conformal field theory using the modular bootstrap method. Seiberg duality is understood by studying the behaviour of the boundary and crosscap states under monodromy in the closed string parameter space.
Firstly, we generalize a semi-classical limit of open strings on D-branes in group manifolds. The limit gives rise to rigid open strings, whose dynamics can efficiently be described in terms of a matrix algebra. Alternatively, the dynamics is coded in group theory coefficients whose properties are translated in a diagrammatical language. In the case of compact groups, it is a simplified version of rational boundary conformal field theories, while for non-compact groups, the construction gives rise to new associative products. Secondly, we argue that the intuitive formalism that we provide for the semi-classical limit, extends to the case of quantum groups. The associative product we construct in this way is directly related to the boundary vertex operator algebra of open strings on symmetry preserving branes in WZW models, and generalizations thereof, e.g. to non-compact groups. We treat the groups SU(2) and SL(2,R) explicitly. We also discuss the precise relation of the semi-classical open string dynamics to Berezin quantization and to star product theory.
We review and extend evidence for the validity of a generalized Verlinde formula in particular non-rational conformal field theories. We identify a subset of representations of the chiral algebra in non-rational conformal field theories that give rise to an analogue of the relation between modular S-matrices and fusion coefficients in rational conformal field theories. To that end we review and extend the Cardy-type brane calculations in bosonic and supersymmetric Liouville theory (and its duals) as well as in the hyperbolic three-plane H3+. We analyze the three-point functions of Liouville theory and of H3+ in detail to directly identify the fusion coefficients from the operator product expansion.
We briefly review superstring theories, highlighting the important concepts, developments, and open problems of the subject.
We clarify some aspects of the map between the c=1 string theory at self-dual radius and the topologically twisted cigar at level one. We map the ZZ and FZZT D-branes in the c=1 string theory at self dual radius to the localized and extended branes in the topological theory on the cigar. We show that the open string spectrum on the branes in the two theories are in correspondence with each other, and their two point correlators are equal. We also find a representation of an extended N=2 algebra on the worldsheet which incorporates higher spin currents in terms of asymptotic variables on the cigar.
We study the topologically twisted cigar, namely the SL(2,R)/U(1) superconformal field theory at arbitrary level, and find the BRST cohomology of the topologically twisted N=2 theory. We find a one to one correspondence between the spectrum of the twisted coset and singular vectors in the Wakimoto modules constructed over the SL(2,R) current algebra. The topological cigar cohomology is the crucial ingredient in calculating the closed string spectrum of topological strings on non-compact Gepner models.