## Advances in Theoretical and Mathematical Physics

- Adv. Theor. Math. Phys.
- Volume 10, Number 1 (2006), 77-121.

### GLSMs for gerbes (and other toric stacks)

#### Abstract

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.

#### Article information

**Source**

Adv. Theor. Math. Phys., Volume 10, Number 1 (2006), 77-121.

**Dates**

First available in Project Euclid: 30 July 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.atmp/1154236239

**Mathematical Reviews number (MathSciNet)**

MR2222223

**Zentralblatt MATH identifier**

1119.14038

**Subjects**

Primary: 81T30: String and superstring theories; other extended objects (e.g., branes) [See also 83E30]

Secondary: 14M25: Toric varieties, Newton polyhedra [See also 52B20] 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]

#### Citation

Pantev, Tony; Sharpe, Eric. GLSMs for gerbes (and other toric stacks). Adv. Theor. Math. Phys. 10 (2006), no. 1, 77--121. https://projecteuclid.org/euclid.atmp/1154236239