Abstract
Using the exact formula for the A-twisted correlation functions of the two dimensional $\mathcal{N}=(2,2)$ gauged linear sigma model, we reconsider the computation of the B-model Yukawa couplings of the local toric Calabi-Yau varieties. Our analysis is based on an exact result that has been evaluated from the supersymmetric localization technique and careful treatment of its application. We provide a detailed description of a procedure to investigate the local B-model Yukawa couplings and also test our prescription by comparing the results with known expressions evaluated from the local mirror symmetry approach. In particular, we find that the ambiguities of classical intersection numbers of a certain class of local toric Calabi-Yau varieties discovered previously can be interpreted as degrees of freedom of the twisted mass deformations.
Highlights
The 2D N = (2, 2) gauged linear sigma model (GLSM) [1] has played significant roles in the study of topological quantum field theories and mirror symmetry
After the work of Ref. [1], the topological A-twisted version of the GLSM was studied in Ref. [3] and the genus-zero correlation functions were exactly computed for the A-models with target space a toric variety or a toric Calabi–Yau hypersurface
We have thoroughly investigated the relationship between the topological B-model Yukawa couplings for backgrounds with non-compact directions and the exact localization formula for the A-twisted correlation functions of the 2D N = (2, 2) gauged linear sigma models
Summary
[3] and the genus-zero correlation functions were exactly computed for the A-models with target space a toric variety or a toric Calabi–Yau hypersurface These developments led to a conjecture called the toric residue mirror conjecture [4,5] The aim of this work is to fill this gap and establish an explicit formalism to investigate the local B-model Yukawa couplings from the A-twisted GLSM correlation functions on local toric Calabi–Yau varieties. We propose how to determine the proper mass deformations to conduct the exact calculation of the A-twisted GLSM correlators and check that the resulting A-twisted correlators coincide with known results for the B-model Yukawa couplings evaluated by the local mirror symmetry approach [22,23,24]. As shown in Ref. [15], the supersymmetric localization formula considerably simplifies the exact calculations of the A-twisted correlation functions and realizes the quantum cohomology relations appropriately
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