2016/08/31 by David R. Morrison
Physics and Astronomy · Mathematics · #hep-th #math-ph #math.MP
paper · pdf · doi:10.1088/1751-8121/aa6f65
This is a contribution to the review volume `Localization techniques in quantum field theories' (eds. V. Pestun and M. Zabzine): arXiv:1608.02952 and at https://arxiv.org/src/1608.02952/anc/LocQFT.pdf or http://pestun.ihes.fr/pages/LocalizationReview/LocQFT.pdf This article reviews portions of hep-th/9412236, hep-th/9508107, arXiv:1208.6244, arXiv:1305.3278, arXiv:1308.2157, and arXiv:1509.08511
arxiv created 2016/10/15 · arxiv updated 2017/10/25
We give a pedagogical review of the computation of Gromov-Witten invariants via localization in 2D gauged linear sigma models. We explain the relationship between the two-sphere partition function of the theory and the Kahler potential on the conformal manifold. We show how the Kahler potential can be assembled from classical, perturbative, and non-perturbative contributions, and explain how the non-perturbative contributions are related to the Gromov-Witten invariants of the corresponding Calabi-Yau manifold. We then explain how localization enables efficient calculation of the two-sphere partition function and, ultimately, the Gromov-Witten invariants themselves.