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

Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds

In this work we study the phase structure of skew symplectic sigma models, which are a certain class of two-dimensional N = (2,2) non-Abelian gauged linear sigma models. At low energies some of them flow to non-linear sigma models with Calabi-Yau target spaces, which emerge from non-Abelian strong coupling dynamics. The observed phase structure results in a non-trivial duality proposal among skew symplectic sigma models and connects non-complete intersection Calabi-Yau threefolds, that are non-birational among another, in a common quantum Kahler moduli space. As a consequence we find non-trivial identifications of spectra of topological B-branes, which from a modern algebraic geometry perspective imply derived equivalences among Calabi-Yau varieties. To further support our proposals, we calculate the two sphere partition function of skew symplectic sigma models to determine geometric invariants, which confirm the anticipated Calabi-Yau threefold phases. We show that the two sphere partition functions of a pair of dual skew symplectic sigma models agree in a non-trivial fashion. To carry out these calculations, we develop a systematic approach to study higher-dimensional Mellin-Barnes type integrals. In particular, these techniques admit the evaluation of two sphere partition functions for gauged linear sigma models with higher rank gauge groups, but are applicable in other contexts as well.Comment: 66 pages, 3 figures; v2: refs. added; v3: minor changes and corrections -- version published in J.Geom.Phy

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

Perturbative Corrections to Kahler Moduli Spaces

We propose a general formula for perturbative-in-alpha' corrections to the Kahler potential on the quantum Kahler moduli space of Calabi-Yau n-folds, for any n, in their asymptotic large volume regime. The knowledge of such perturbative corrections provides an important ingredient needed to analyze the full structure of this Kahler potential, including nonperturbative corrections such as the Gromov-Witten invariants of the Calabi-Yau n-folds. We argue that the perturbative corrections take a universal form, and we find that this form is encapsulated in a specific additive characteristic class of the Calabi-Yau n-fold which we call the log Gamma class, and which arises naturally in a generalization of Mukai's modified Chern character map. Our proposal is inspired heavily by the recent observation of an equality between the partition function of certain supersymmetric, two-dimensional gauge theories on a two-sphere, and the aforementioned Kahler potential. We further strengthen our proposal by comparing our findings on the quantum Kahler moduli space to the complex structure moduli space of the corresponding mirror Calabi-Yau geometry.Comment: 28 pages; v2: discussion in section 5 extended and refs. adde

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

First images of a possible CO(+)-tail of comet P/Schwassmann-Wachmann 1 observed against the dust coma background

Comet P/Schwassmann-Wachmann 1 was observed with the 2m-Ritchey-Cretien Telescope of the Bulgarian National Observatory, Rozhen, Bulgaria, using the CCD-camera and focal reducer of the Max-Planck-Institute for Aeronomy. Images were taken in a red continuum window and in the 2-0 A(exp 2)Pi - X(exp 2)Sigma(+) band of CO(+) located in the blue part of the spectrum. The red images reveal an extended dust coma. From a comparison of the red and blue images a dust reddening of 13.2 percent per 1000 A is derived. At 642 nm the magnitude of the comet with a square diaphragm of 4.5 arcsec is 16.6. The blue images, taken in the CO(+) band, show a significantly different brightness distribution which is interpreted as presence of a CO(+) coma and tail superimposed on the continuum. A column density of several 10(exp 10) CO(+) molecules cm(exp -2) is derived. The tail thickness of 10(exp 5) km is unexpectedly small. We estimate the CO(+) production rate to about 6 x 10(exp 26) CO(+) particles s(exp -1). This value does not support the idea that the outbursts of this comet are caused by crystallization of amorphous water ice