T. Jayaraman

Worldsheet approaches to D-branes on supersymmetric cycles

We consider D-branes wrapped around supersymmetric cycles of Calabi–Yau manifolds from the viewpoint of N=2 Landau–Ginzburg models with boundary as well as by consideration of boundary states in the corresponding Gepner models. The Landau–Ginzburg approach enables us to provide a target space interpretation for the boundary states. The boundary states are obtained by applying Cardys procedure to combinations of characters in the Gepner models which are invariant under spectral flow. We are able to relate the two descriptions using common discrete symmetries occurring in the two descriptions. We thus provide an extension to the boundary, the bulk correspondence between Landau–Ginzburg orbifolds and the corresponding Gepner models.

D branes on Calabi-Yau manifolds and superpotentials

We show how to compute terms in an expansion of the world-volume superpotential for fairly general D-branes on the quintic Calabi-Yau using linear sigma model techniques, and show in examples that this superpotential captures the geometry and obstruction theory of bundles and sheaves on this Calabi-Yau.

On the Landau-Ginzburg description of boundary CFTs and special lagrangian submanifolds

We consider Landau-Ginzburg (LG) models with boundary conditions pre- serving A-type N = 2 supersymmetry. We show the equivalence of a linear class of boundary conditions in the LG model to a particular class of boundary states in the cor- responding CFT by an explicit computation of the open-string Witten index in the LG model. We extend the linear class of boundary conditions to general non-linear bound- ary conditions and determine their consistency with A-type N = 2 supersymmetry. This enables us to provide a microscopic description of special Lagrangian submani- folds in C n due to Harvey and Lawson. We generalise this construction to the case of hypersurfaces in P n . We nd that the boundary conditions must necessarily have vanishing Poisson bracket with the combination (W () W ()), where W ( )i s the appropriate superpotential for the hypersurface. An interesting application considered is the T 3 supersymmetric cycle of the quintic in the large complex structure limit.

A quantum McKay correspondence for fractional 2p -branes on LG orbifolds

We study fractional 2p -branes and their intersection numbers in non-compact orbifolds as well the continuation of these objects in Kahler moduli space to coherent sheaves in the corresponding smooth non-compact Calabi-Yau manifolds. We show that the restriction of these objects to compact Calabi-Yau hypersurfaces gives the new fractional branes in LG orbifolds constructed by Ashok et. al. in [13]. We thus demonstrate the equivalence of the B-type branes corresponding to linear boundary conditions in LG orbifolds, originally constructed in [2], to a subset of those constructed in LG orbifolds using boundary fermions and matrix factorization of the world-sheet superpotential. The relationship between the coherent sheaves corresponding to the fractional two-branes leads to a generalization of the McKay correspondence that we call the quantum McKay correspondence due to a close parallel with the construction of branes on non-supersymmetric orbifolds. We also provide evidence that the boundary states associated to these branes in a conformal field theory description corresponds to a sub-class of the boundary states associated to the permutation branes in the Gepner model associated with the LG orbifold.

Chiral Rings and Physical States in c < 1 String Theory

Abstract We show how the double cohomology of the string and Felder BRST charges naturally leads to the ring structure of c x p ⋍ y p+1 for the (p + 1, p) model. We also study the states corresponding to the edges of the conformal grid whose inclusion is crucial for the closure of the ring. We introduce candidate operators that correspond to the observables of the matrix models. Their existence is motivated by the relation of one of the screening operators of the minimal model to the zero momentum dilaton.

A proposal for the geometry of W n gravity

Abstract We relate the Teichmuller spaces obtained by Hitchin to the Teichmuller spaces of WAn-gravity. The relationship of this space to W-gravity is obtained by identifying the flat PSL(n + 1, R ) connections of Hitchin to generalised vielbeins and connections. This is explicitly demonstrated for WA2 = W3 gravity. We show how W-diffeomorphisms are obtained in this formulation. We find that particular combinations of the generalised connection play the role of projective connections. We thus obtain W-diffeomorphisms in a geometric fashion without invoking the presence of matter fields. This description in terms of vielbeins naturally provides the measure for the gravity sector in the Polyakov path integral for W-strings.

Fractional two-branes, toric orbifolds and the quantum McKay correspondence

We systematically study and obtain the large-volume analogues of fractional two-branes on resolutions of the orbifolds 3/n. We also study a generalisation of the McKay correspondence proposed in hep-th/0504164 called the quantum McKay correspondence by constructing duals to the fractional two-branes. Details are explicitly worked out for two examples – the crepant resolutions of 3/3 and 3/5.

Genus zero correlation functions in c 1 string theory

We compute [ital N]-point correlation functions of pure vertex operator states (DK states) for minimal models coupled to gravity. We obtain agreement with the matrix model results on analytically continuing in the number of cosmological constant operators and matter-screening operators. We illustrate this for the cases of the (2[ital k][minus]1,2) and ([ital p]+1,[ital p]) models.

Correlation Functions And Multicritical Flows In c < 1 String Theory

We compute all string tree level correlation functions of vertex operators in c < 1 string theory. This is done by using the ring structure of the theory. In order to study the multicritical behavior, we calculate the correlation functions after perturbation by physical vertex operators. We show that the (2k − 1, 2) models can be obtained from the (1, 2) model and the minimal models can be obtained from the (1, p) model by perturbing the action with appropriate physical operators. Our results are consistent with known results from matrix models.

States of nonzero ghost number in c gt 1 matter coupled to 2D gravity

We study c<1 matter coupled to gravity in the Coulomb gas formalism using the double cohomology of the string BRST and Felder BRST charges. We find that states outside the primary conformal grid are related to the states of nonzero ghost number by means of descent equations given by the double cohomology. Some aspects of the Virasoro structure of the Liouville-Fock space are studied. As a consequence, states of nonzero ghost number are easily constructed by “solving” these descent equations. This enables us to map ghost number conserving correlation functions involving nonzero ghost number states into those involving states outside the primary conformal grid.