# Phase transitions, double-scaling limit, and topological strings

## Abstract

Topological strings on Calabi-Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi-Yau threefolds given by a bundle over a two-sphere. This theory can be regarded as a q-deformation of Hurwitz theory, and it has a conjectural nonperturbative description in terms of q-deformed 2D Yang-Mills theory. We solve the planar model and find a phase transition at small radius in the universality class of 2D gravity. We give strong evidence that there is a double-scaled theory at the critical point whose all-genus free energy is governed by the Painleve I equation. We compare the critical behavior of the perturbative theory to the critical behavior of its nonperturbative description, which belongs to the universality class of 2D supergravity, and we comment on possible implications for nonperturbative 2D gravity. We also give evidence for a new open/closed duality relating these Calabi-Yau backgrounds to open strings with framing.

- Authors:

- Center for Theoretical Physics, MIT, Cambridge, Massachusetts 02139 (United States)
- Dipartimento di Fisica, Universita di Parma, INFN Gruppo Collegato di Parma, Parco Area delle Scienze 7/A, 43100 Parma (Italy)
- Department of Physics, Theory Division, CERN, Geneva 23, CH-1211 (Switzerland)
- Dipartimento di Fisica, Polo Scientifico Universita di Firenze, INFN Sezione di Firenze Via G. Sansone 1, 50019 Sesto Fiorentino (Italy)

- Publication Date:

- OSTI Identifier:
- 21011119

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. D, Particles Fields; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevD.75.046004; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; COMPARATIVE EVALUATIONS; DUALITY; FREE ENERGY; GRAVITATION; PHASE TRANSFORMATIONS; QUANTUM FIELD THEORY; STRING MODELS; SUPERGRAVITY; TOPOLOGY; YANG-MILLS THEORY

### Citation Formats

```
Caporaso, Nicola, Griguolo, Luca, Pasquetti, Sara, Marino, Marcos, and Seminara, Domenico.
```*Phase transitions, double-scaling limit, and topological strings*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVD.75.046004.

```
Caporaso, Nicola, Griguolo, Luca, Pasquetti, Sara, Marino, Marcos, & Seminara, Domenico.
```*Phase transitions, double-scaling limit, and topological strings*. United States. doi:10.1103/PHYSREVD.75.046004.

```
Caporaso, Nicola, Griguolo, Luca, Pasquetti, Sara, Marino, Marcos, and Seminara, Domenico. Thu .
"Phase transitions, double-scaling limit, and topological strings". United States.
doi:10.1103/PHYSREVD.75.046004.
```

```
@article{osti_21011119,
```

title = {Phase transitions, double-scaling limit, and topological strings},

author = {Caporaso, Nicola and Griguolo, Luca and Pasquetti, Sara and Marino, Marcos and Seminara, Domenico},

abstractNote = {Topological strings on Calabi-Yau manifolds are known to undergo phase transitions at small distances. We study this issue in the case of perturbative topological strings on local Calabi-Yau threefolds given by a bundle over a two-sphere. This theory can be regarded as a q-deformation of Hurwitz theory, and it has a conjectural nonperturbative description in terms of q-deformed 2D Yang-Mills theory. We solve the planar model and find a phase transition at small radius in the universality class of 2D gravity. We give strong evidence that there is a double-scaled theory at the critical point whose all-genus free energy is governed by the Painleve I equation. We compare the critical behavior of the perturbative theory to the critical behavior of its nonperturbative description, which belongs to the universality class of 2D supergravity, and we comment on possible implications for nonperturbative 2D gravity. We also give evidence for a new open/closed duality relating these Calabi-Yau backgrounds to open strings with framing.},

doi = {10.1103/PHYSREVD.75.046004},

journal = {Physical Review. D, Particles Fields},

number = 4,

volume = 75,

place = {United States},

year = {Thu Feb 15 00:00:00 EST 2007},

month = {Thu Feb 15 00:00:00 EST 2007}

}