PIRSA:13040141 Scientific Series Quantum Fields and Strings

DOI10.48660/13040141

Series: Quantum Fields and Strings

Lapan, J. (2013). Gromov-Witten Invariants from 2D Gauge Theories. Perimeter Institute. https://pirsa.org/13040141

Lapan, Joshua. Gromov-Witten Invariants from 2D Gauge Theories. Perimeter Institute, Apr. 30, 2013, https://pirsa.org/13040141 

@misc{ pirsa_PIRSA:13040141,
  doi = {10.48660/13040141},
  url = {https://pirsa.org/13040141},
  author = {Lapan, Joshua},
  keywords = {Quantum Fields and Strings},
  language = {en},
  title = {Gromov-Witten Invariants from 2D Gauge Theories},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {apr},
  note = {PIRSA:13040141 see, \url{https://pirsa.org}}
}

Abstract

It has been known for twenty years that a class of two-dimensional gauge theories are intimately connected to toric geometry, as well as to hypersurfaces or complete intersections in a toric varieties, and to generalizations thereof.  Under renormalization group flow, the two-dimensional gauge theory flows to a conformal field theory that describes string propagation on the associated geometry.  This provides a connection between certain quantities in the gauge theory and topological invariants of the associated geometry.  In this talk, I will explain how recent results show that, for Calabi-Yau geometries, the partition function for each gauge theory computes the Kahler potential on the Kahler moduli of the associated geometry.  The result is expressed in terms of a Barnes' integral and is readily evaluated in a series expansion around special points in the moduli space (e.g., large volume), providing a fairly efficient way to compute Gromov-Witten invariants of the associated geometry.

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