Two-Sphere Partition Functions and Gromov-Witten Invariants

Abstract

Many N=(2,2) two-dimensional nonlinear sigma models with Calabi-Yau target spaces admit ultraviolet descriptions as N=(2,2) gauge theories (gauged linear sigma models). We conjecture that the two-sphere partition function of such ultraviolet gauge theories -- recently computed via localization by Benini et al. and Doroud et al. -- yields the exact Kähler potential on the quantum Kähler moduli space for Calabi-Yau threefold target spaces. In particular, this allows one to compute the genus zero Gromov-Witten invariants for any such Calabi-Yau threefold without the use of mirror symmetry. More generally, when the infrared superconformal fixed point is used to compactify string theory, this provides a direct method to compute the spacetime Kähler potential of certain moduli (e.g., vector multiplet moduli in type IIA), exactly in α'. We compute these quantities for the quintic and for Rødland's Pfaffian Calabi-Yau threefold and find agreement with existing results in the literature. We then apply our methods to a codimension four determinantal Calabi-Yau threefold in P^7, recently given a nonabelian gauge theory description by the present authors, for which no mirror Calabi-Yau is currently known. We derive predictions for its Gromov-Witten invariants and verify that our predictions satisfy nontrivial geometric checks.

25 pages + 2 appendices; v2 corrects a divisor in Kähler moduli space and includes a new calculation that confirms a geometric prediction; v3 contains minor update of Gromov-Witten invariant extraction procedure

References in corpus (6)

• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Exact Results in D=2 Supersymmetric Gauge Theories
• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• GLSM's for partial flag manifolds
• A cascade of determinantal Calabi--Yau threefolds
• A framework for tropical mirror symmetry

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• New Methods for Characterizing Phases of 2D Supersymmetric Gauge Theories
• Perturbative Corrections to Kahler Moduli Spaces
• The Stringy Instanton Partition Function
• Exact Partition Functions on RP2 and Orientifolds
• A few Ricci-flat stacks as phases of exotic GLSM's
• Exact results for boundaries and domain walls in 2d supersymmetric theories
• Semichiral Fields on S^2 and Generalized Kähler Geometry
• Factorization of the 3d superconformal index
• Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$
• On gauged linear sigma models with torsion
• N=(4,4) Vector Multiplets on Curved Two-Manifolds
• Stringy Instanton Counting and Topological Strings