# Gauged Linear Sigma Models for Noncompact Calabi-Yau Varieties

## Abstract

We study gauged linear sigma models for noncompact Calabi-Yau manifolds described as a line bundle on a hypersurface in a projective space. This gauge theory has a unique phase if the Fayet-Iliopoulos parameter is positive, while there exist two distinct phases if the parameter is negative. In the T-dual theory, on the other hand, we obtain two types of exact massless effective theories: One is the sigma model on a newly obtained Calabi-Yau geometry as a mirror dual, while the other is given by a Landau-Ginzburg theory with a negative power term, indicating N = 2 superconformal field theory on SL(2,R)/U(1). We argue that the effective theories in the original gauged linear sigma model are exactly realized as N = 2 Liouville theories coupled to well-defined Landau-Ginzburg minimal models.

- Authors:

- Korea Institute for Advanced Study, Cheongnyangni-dong, Dongdaemun-gu, Seoul 130-722 (Korea, Republic of)

- Publication Date:

- OSTI Identifier:
- 20729204

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: AIP Conference Proceedings; Journal Volume: 805; Journal Issue: 1; Conference: PASCOS 2005: 11. international symposium on particles, strings, and cosmology, Gyeongju (Korea, Republic of), 30 May - 4 Jun 2005; Other Information: DOI: 10.1063/1.2149743; (c) 2005 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; CONFORMAL INVARIANCE; GAUGE INVARIANCE; GEOMETRY; GINZBURG-LANDAU THEORY; QUANTUM FIELD THEORY; SIGMA MODEL; SL GROUPS; SMOOTH MANIFOLDS; SPACE; U-1 GROUPS

### Citation Formats

```
Kimura, Tetsuji.
```*Gauged Linear Sigma Models for Noncompact Calabi-Yau Varieties*. United States: N. p., 2005.
Web. doi:10.1063/1.2149743.

```
Kimura, Tetsuji.
```*Gauged Linear Sigma Models for Noncompact Calabi-Yau Varieties*. United States. doi:10.1063/1.2149743.

```
Kimura, Tetsuji. Fri .
"Gauged Linear Sigma Models for Noncompact Calabi-Yau Varieties". United States.
doi:10.1063/1.2149743.
```

```
@article{osti_20729204,
```

title = {Gauged Linear Sigma Models for Noncompact Calabi-Yau Varieties},

author = {Kimura, Tetsuji},

abstractNote = {We study gauged linear sigma models for noncompact Calabi-Yau manifolds described as a line bundle on a hypersurface in a projective space. This gauge theory has a unique phase if the Fayet-Iliopoulos parameter is positive, while there exist two distinct phases if the parameter is negative. In the T-dual theory, on the other hand, we obtain two types of exact massless effective theories: One is the sigma model on a newly obtained Calabi-Yau geometry as a mirror dual, while the other is given by a Landau-Ginzburg theory with a negative power term, indicating N = 2 superconformal field theory on SL(2,R)/U(1). We argue that the effective theories in the original gauged linear sigma model are exactly realized as N = 2 Liouville theories coupled to well-defined Landau-Ginzburg minimal models.},

doi = {10.1063/1.2149743},

journal = {AIP Conference Proceedings},

number = 1,

volume = 805,

place = {United States},

year = {Fri Dec 02 00:00:00 EST 2005},

month = {Fri Dec 02 00:00:00 EST 2005}

}