Suresh Govindarajan

We study fractional 2p -branes and their intersection numbers in non-compact orbifolds as well the continuation of these objects in Kähler 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. © SISSA 2005.

We systematically study and obtain the large-volume analogues of fractional two-branes on resolutions of the orbifolds ℂ3/ℤ 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 ℂ3/ ℤ3 and ℂ3/ℤ5. © SISSA 2006.

We consider Landau-Ginzburg (LG) models with boundary conditions preserving 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 corresponding 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 boundary conditions and determine their consistency with A-type N = 2 supersymmetry. This enables us to provide a microscopic description of special lagrangian submanifolds in ℂn due to Harvey and Lawson. We generalise this construction to the case of hypersurfaces in ℙn. We find that the boundary conditions must necessarily have vanishing Poisson bracket with the combination (W(φ) - W̄(φ̄)), where W(φ) is the appropriate superpotential for the hypersurface. An interesting application considered is the T3 supersymmetric cycle of the quintic in the large complex structure limit.

As a first step to a detailed study of orientifolds of Gepner models associated with Calabi-Yau manifolds, we construct crosscap states associated with anti-holomorphic involutions (with fixed points) of Calabi-Yau manifolds. We argue that these orientifolds are dual to M-theory compactifications on (singular) seven-manifolds with G2 holonomy. Using the spacetime picture as well as the M-theory dual, we discuss aspects of the orientifold that should be obtained in the Gepner model. This is illustrated for the case of the quintic. © SISSA/ISAS 2004.