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

Abstract

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.

66 pages, 3 figures; v2: refs. added; v3: minor changes and corrections -- version published in J.Geom.Phys

References in corpus (8)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• Sphere Partition Functions and the Zamolodchikov Metric
• Phases Of N=2 Theories In 1+1 Dimensions With Boundary
• Homological projective duality for Grassmannians of lines
• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• GLSM's for partial flag manifolds
• Mirror Symmetry for Toric Branes on Compact Hypersurfaces
• Stringy $E$-functions of Pfaffian-Grassmannian double mirrors

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• GLSM realizations of maps and intersections of Grassmannians and Pfaffians
• The Geometry of Gauged Linear Sigma Model Correlation Functions
• A pair of Calabi-Yau manifolds from a two parameter non-Abelian gauged linear sigma model
• Equivariant A-twisted GLSM and Gromov--Witten invariants of CY 3-folds in Grassmannians
• On genus one fibered Calabi-Yau threefolds with 5-sections
• GLSMs for exotic Grassmannians
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM
• Anomalies and Holomorphy in Supersymmetric Chern-Simons-Matter Theories