Abstract not found

We study the superpotential of a certain class of N = 1 supersymmetric type II compactifications with fluxes and D-branes. We show that it has an important twodimensional meaning in terms of a chiral ring of the topologically twisted theory on the world-sheet. In the open-closed string B-model, this chiral ring is isomorphic to a certain relative cohomology group V, which is the appropriate mathematical concept to deal with both the open and closed string sectors. The family of mixed Hodge structures on V then implies for the superpotential to have a certain geometric structure. This structure represents a holomorphic, N = 1 supersymmetric generalization of the well-known N = 2 special geometry. It defines an integrable connection on the topological family of open-closed B-models, and a set of special coordinates on the space M of vev’s in N = 1 chiral multiplets. We show that it can be given a very concrete and simple realization for linear sigma models, which leads to a powerful and systematic method for computing the exact non-perturbative N = 1 superpotentials for a broad class of toric D-brane geometries. August

We introduce an integral structure in orbifold quantum cohomology associated to the K-group and the b Γ-class. In the case of compact toric orbifolds, we show that this integral structure matches with the natural integral structure for the Landau-Ginzburg model under mirror symmetry. By assuming the existence of an integral structure, we give a natural explanation for the specialization to a root of unity in Y. Ruan’s crepant resolution conjecture [66].

The quantum cohomology of CP 1 provides a distinguished solution of the third Painlevé (PIII) equation. S. Cecotti and C. Vafa discovered this from a physical viewpoint (see [4], [5]). We shall derive this from a differential geometric viewpoint, using the theory of harmonic maps

Abstract. We exhibit a direct correspondence between the potential defining the H 1,1 small quantum module structure on the cohomology of a Calabi-Yau manifold and the asymptotic data of the A-model variation of Hodge structure. This is done in the abstract context of polarized variations of Hodge structure and Frobenius modules. 1.

We prove that the solution to a pair of nonlinear integral equations arising in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent kernel of the linear integral operator with kernel I.

Abstract. We show that if the Stokes matrix of a connection with a pole of order two and no ramification gives rise, when added to its adjoint, to a positive semi-definite Hermitian form, then the associated integrable twistor structure (or TERP structure, or non-commutative Hodge structure) is pure and polarized. Contents Introduction........................................................ 1 1. Polarized pure twistor structure attached to a flat unitary bundle 3 2. Stokes filtration and Stokes data................................ 8 3. Natural operations on Stokes filtrations and Stokes data........ 14

Abstract: We prove that the solution to a pair of nonlinear integral equations arising in the thermodynamic Bethe Ansatz can be expressed in terms of the resolvent kernel of the linear integral operator with kernel p-(u(θ)+u(θ'}} I.

Abstract. We use a Grassmannian framework to define multi-component tau functions as expectation values of certain multi-component Fermi operators satisfying simple bilinear commutation relations on Clifford algebra. The tau functions contain both positive and negative flows and are shown to satisfy the 2n-component KP hierarchy. The hierarchy equations can be formulated in terms of pseudo-differential equations for n × n matrix wave functions derived in terms of tau functions. These equations are cast in form of Sato– Wilson relations. A reduction process leads to the AKNS, two-component Camassa–Holm and Cecotti–Vafa models and the formalism provides simple formulas for their solutions. Key words: Clifford algebra; tau-functions; Kac–Moody algebras; loop groups; Camassa– Holm equation; Cecotti–Vafa equations; AKNS hierarchy

Abstract. We show that, under a condition called minimality, if the Stokes matrix of a connection with a pole of order two and no ramification gives rise, when added to its adjoint, to a positive semi-definite Hermitian form, then the associated integrable twistor structure (or TERP structure, or non-commutative Hodge structure) is pure and polarized. Contents Introduction........................................................ 1 1. Polarized pure twistor structure attached to a flat unitary bundle 3 2. Stokes filtration and Stokes data................................ 9 3. Natural operations on Stokes filtrations and Stokes data........ 14