Open Access
January 2006 GLSMs for gerbes (and other toric stacks)
Tony Pantev, Eric Sharpe
Adv. Theor. Math. Phys. 10(1): 77-121 (January 2006).


In this paper, we will discuss gauged linear sigma model descriptions of toric stacks. Toric stacks have a simple description in terms of (symplectic, GIT) ${\bf C}^{\times}$ quotients of homogeneous coordinates, in exactly the same form as toric varieties. We describe the physics of the gauged linear sigma models that formally coincide with the mathematical description of toric stacks and check that physical predictions of those gauged linear sigma models exactly match the corresponding stacks. We also see in examples that when a given toric stack has multiple presentations in a form accessible as a gauged linear sigma model, that the IR physics of those different presentations matches, so that the IR physics is presentation-independent, making it reasonable to associate CFTs to stacks, not just presentations of stacks. We discuss mirror symmetry for stacks, using Morrison-Plesser-Hori-Vafa techniques to compute mirrors explicitly, and also find a natural generalization of Batyrev's mirror conjecture. In the process of studying mirror symmetry, we find some new abstract CFTs, involving fields valued in roots of unity.


Download Citation

Tony Pantev. Eric Sharpe. "GLSMs for gerbes (and other toric stacks)." Adv. Theor. Math. Phys. 10 (1) 77 - 121, January 2006.


Published: January 2006
First available in Project Euclid: 30 July 2006

zbMATH: 1119.14038
MathSciNet: MR2222223

Primary: 81T30
Secondary: 14M25 , 14N35

Rights: Copyright © 2006 International Press of Boston

Vol.10 • No. 1 • January 2006
Back to Top