D-brane monodromies from a matrix-factorization perspective

The aim of this work is to analyze Kaehler moduli space monodromies of string compactifications. This is achieved by investigating the monodromy action upon D-brane probes, which we model in the Landau-Ginzburg phase in terms of matrix factorizations. The two-dimensional cubic torus and the quintic Calabi-Yau hypersurface serve as our two prime examples.Comment: 49 pages, 5 figures, harvmac; v2: minor changes and corrected typo

The Geometry of Gauged Linear Sigma Model Correlation Functions

Applying advances in exact computations of supersymmetric gauge theories, we study the structure of correlation functions in two-dimensional N=(2,2) Abelian and non-Abelian gauge theories. We determine universal relations among correlation functions, which yield differential equations governing the dependence of the gauge theory ground state on the Fayet-Iliopoulos parameters of the gauge theory. For gauge theories with a non-trivial infrared N=(2,2) superconformal fixed point, these differential equations become the Picard-Fuchs operators governing the moduli-dependent vacuum ground state in a Hilbert space interpretation. For gauge theories with geometric target spaces, a quadratic expression in the Givental I-function generates the analyzed correlators. This gives a geometric interpretation for the correlators, their relations, and the differential equations. For classes of Calabi-Yau target spaces, such as threefolds with up to two Kahler moduli and fourfolds with a single Kahler modulus, we give general and universally applicable expressions for Picard-Fuchs operators in terms of correlators. We illustrate our results with representative examples of two-dimensional N=(2,2) gauge theories.Comment: 76 pages, v2: references added and minor improvement

N=1 Sigma Models in AdS_4

We study sigma models in AdS_4 with global N=1 supersymmetry and find that they differ significantly from their flat-space cousins -- the target space is constrained to be a Kahler manifold with an exact Kahler form, the superpotential transforms under Kahler transformations, the space of supersymmetric vacua is generically a set of isolated points even when the superpotential vanishes, and the R-symmetry is classically broken by the cosmological constant. Remarkably, the exactness of the Kahler class is also required for the sigma model to arise as a decoupling limit of N=1 supergravity, and ensures the vanishing of gravitational anomalies. As simple applications of these results, we argue that fields with AdS_4 scale masses are ubiquitous in, for example, type IIB N=1 AdS_4 vacua stabilized near large volume; we also show that the Affleck-Dine-Seiberg runaway of N_f < N_c SQCD is regulated by considering the theory in AdS_4.Comment: 32 pages; v2: minor changes and references added; v3: discussion in sect. 5 extended, version published in JHE