GLSMs, joins, and nonperturbatively-realized geometries

Abstract

In this work we give a gauged linear sigma model (GLSM) realization of pairs of homologically projective dual Calabi-Yaus that have recently been constructed in the mathematics literature. Many of the geometries can be realized mathematically in terms of joins. We discuss how joins can be described in terms of GLSMs and how the associated Calabi-Yaus arise as phases in the GLSMs. Due to strong-coupling phenomena in the GLSM, the geometries are realized via a mix of perturbative and non-perturbative effects. We apply two-dimensional gauge dualities to construct dual GLSMs. Geometries that are realized perturbatively in one GLSM, are realized non-perturbatively in the dual, and vice versa.

arXiv comment76 pages, 6 figures; v2: references added

References in corpus (25)

• Phases of $N=2$ Theories In Two Dimensions
• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
• The Verlinde Algebra And The Cohomology Of The Grassmannian
• Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N=(2,2) Theories
• Cluster decomposition, T-duality, and gerby CFT's
• GLSM's for gerbes (and other toric stacks)
• Cohomology of Line Bundles: A Computational Algorithm
• Non-birational twisted derived equivalences in abelian GLSMs
• Homological projective duality for Grassmannians of lines
• Tables of Calabi--Yau equations
• Notes on gauging noneffective group actions
• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• GLSM's for partial flag manifolds
• Differential equations, mirror maps and zeta values
• The long flow to freedom
• Linear Sigma Models With Strongly Coupled Phases -- One Parameter Models
• A proposal for nonabelian (0,2) mirrors
• PALP - a User Manual
• Calabi-Yau manifolds realizing symplectically rigid monodromy tuples
• GLSM realizations of maps and intersections of Grassmannians and Pfaffians
• A pair of Calabi-Yau manifolds from a two parameter non-Abelian gauged linear sigma model
• A cascade of determinantal Calabi--Yau threefolds
• Smoothing Calabi-Yau toric hypersurfaces using the Gross-Siebert algorithm
• Calabi--Yau 3-folds from projective joins of del Pezzo manifolds
• Categorical joins

Cited by in corpus (8)

• Quantum symmetries in orbifolds and decomposition
• A generalization of decomposition in orbifolds
• Modular Curves and the Refined Distance Conjecture
• On genus one fibered Calabi-Yau threefolds with 5-sections
• Smoothing Calabi-Yau toric hypersurfaces using the Gross-Siebert algorithm
• Correlation functions in massive Landau-Ginzburg orbifolds and tests of dualities
• Noncommutative resolutions and CICY quotients from a non-abelian GLSM
• Mirror Symmetry of Calabi-Yau Manifolds Fibered by (1,8)-Polarized Abelian Surfaces