Suresh Govindarajan

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, exceptional sheaves and quivers on Calabi-Yau manifolds: From Mukai to McKay

Abstract We present a method based on mutations of helices which leads to the construction (in the large-volume limit) of exceptional coherent sheaves associated with the (∑ala=0) orbits in Gepner models. This is explicitly verified for a few examples including some cases where the ambient weighted projective space has singularities not inherited by the Calabi–Yau hypersurface. The method is based on two conjectures which lead to the analog, in the general case, of the Beilinson quiver for P n . We discuss how one recovers the McKay quiver using the gauged linear sigma model (GLSM) near the orbifold or Gepner point in Kahler moduli space.

On D-branes from gauged linear sigma models

Abstract We study both A-type and B-type D-branes in the gauged linear sigma model by considering worldsheets with boundary. The boundary conditions on the matter and vector multiplet fields are first considered in the large-volume phase/non-linear sigma model limit of the corresponding Calabi–Yau manifold, where we find that we need to add a contact term on the boundary. These considerations enable to us to derive the boundary conditions in the full gauged linear sigma model, including the addition of the appropriate boundary contact terms, such that these boundary conditions have the correct non-linear sigma model limit. Most of the analysis is for the case of Calabi–Yau manifolds with one Kahler modulus (including those corresponding to hypersurfaces in weighted projective space), though we comment on possible generalisations.

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.

BKM Lie superalgebras from dyon spectra in ZN CHL orbifolds for composite N

We show that the generating function of electrically charged

Tachyon condensation on the elliptic curve

\frac{1}{2}

BKM Lie superalgebras from counting twisted CHL dyons

-BPS states in