Two-Sphere Partition Functions and Gromov–Witten Invariants

By H. Jockers, Vijaya Kumar, Joshua M. Lapan, D. Morrison, M. Romo. 2012

189 citations recorded by the source corpus.

Many $${\mathcal{N}=(2,2)}$$N=(2,2) two-dimensional nonlinear sigma models with Calabi–Yau target spaces admit ultraviolet descriptions as $${\mathcal{N}=(2,2)}$$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 $${\mathbb{P}^{7}}$$P7 , 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.

Subfields: Geometry and Topology, Nuclear and High Energy Physics

View Paper: https://www.semanticscholar.org/paper/849652aac37bc2255b48f54bba477c5f91208d77

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Geometry and Topology

In Nuclear and High Energy Physics

Citations in the corpus

Sphere partition functions and the Zamolodchikov metric (2014, background): “Our explicit construction of these counterterms gives a microscopic realization of the Kähler ambiguities implied by the proof [15] that the exact two-sphere partition function [18,17,19] computes the Kähler potential K on the conformal manifold Sc × Stc [14,15] ZAS2 = e −Ktc ZBS2 = e −Kc .”
Supersymmetry on curved spaces and holography (2012, methodology): “In fact, in [32] the authors have computed new Gromov-Witten invariants for Calabi-Yau manifolds without known mirror.”
Correlation functions of Coulomb branch operators (2016, background): “For SCFTs with one exactly marginal coupling and a one-dimensional Coulomb branch, namely for N = 2 SU(2) SQCD with four fundamental hypermultiplets Extending the earlier result in two-dimensional N = (2, 2) SCFTs [5, 7–9].”
A topologically twisted index for three-dimensional supersymmetric theories (2015, methodology): “The partition function on the sphere with no twist have also been computed via localization in [18, 19] and has led to a re-interpretation of the Kähler geometry of the Calabi-Yau moduli space [60, 61].”
Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary (2013, background): “Interestingly, it was observed in some examples [5] that it computes the Kähler potential for the family of superconformal fixed points of the theory.”