This two-semester seminar will focus on the physics and mathematics underlying gauged linear sigma models, with the goal of understanding the monomial-divisor mirror map for Calabi-Yau hypersurfaces. Broadly speaking, we will cover:

  • Toric Geometry
    • Crash-course on toric varieties
    • Sheaves & Sheaf cohomology on toric varieties
    • Toric Residues (alg-geom/9410017) and mirror symmetry (math/0203216)
  • GLSMs

Students from both the mathematics and physics departments are encouraged to participate. The student-given talks will aim to develop a healthy mix of the abstract (sheaf cohomology & residues) and the concrete (computing correlators in twisted theories) in a way that is accessible to beginning graduate students and useful for older students as well.

Meeting Information

Meeting Time 10.30-11.30 am
Meeting Location DRL 2C2

Content

This semester we will begin with a thorough treatment of GLSMs, on the level of Witten's Phases (hep-th/9301042) and Morrison & Plesser's Summing the Instantons... (hep-th/9412236). We will continue with explorations of computing A- and B-model correlators using Landau-Ginzburg models and Coloumb branch techniques. Finally, we will explore mirror symmetry in the model, with the goal understanding the toric residue mirror conjecture in math/0203216.

Papers

  • hep-th/9301042 — Phases of N=2 Theories In Two Dimensions
  • hep-th/9412236 — Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
  • hep-th/0501238 — The Coulomb Branch in Gauged Linear Sigma Models

Participants

  • Matt Ballard
  • Patrick Clarke
  • Ron Donagi
  • Josh Guffin
  • Jim Halverson
  • Victor Lu
  • Pooya Ronagh
  • Charlie Siegel
  • Jeffrey Teo

Date Speaker Topic
7 April 2010 Charles Siegel Toric Residues à la Cox
31 March 2010 Josh Guffin The GLSM IV - Correlators and topological models continued
24 March 2010 Josh Guffin The GLSM III - Correlators and topological models
17 March 2010 Cancelled
3 March 2010 Josh Guffin The GLSM II - Quantum aspects
24 February 2010 Josh Guffin The GLSM I - Classical aspects
17 February 2010 Josh Guffin The symplectic quotient construction of toric varieties
10 February 2010 Cancelled due to weather
3 February 2010 Jim Halverson A QFT Primer II
27 January 2010 Jim Halverson A QFT Primer I