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 Painlevé 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.

Phase transitions, double-scaling limit, and topological strings / N. Caporaso; L. Griguolo; M. Mariño; S. Pasquetti; D. Seminara. - In: PHYSICAL REVIEW D, PARTICLES, FIELDS, GRAVITATION, AND COSMOLOGY. - ISSN 1550-7998. - STAMPA. - 75:(2007), pp. 046004-1-046004-24. [10.1103/PhysRevD.75.046004]

Phase transitions, double-scaling limit, and topological strings

SEMINARA, DOMENICO
2007

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 Painlevé 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.
2007
75
046004-1
046004-24
N. Caporaso; L. Griguolo; M. Mariño; S. Pasquetti; D. Seminara
File in questo prodotto:
File Dimensione Formato  
PhysRevD.75.046004.pdf

Accesso chiuso

Tipologia: Pdf editoriale (Version of record)
Licenza: Tutti i diritti riservati
Dimensione 412.43 kB
Formato Adobe PDF
412.43 kB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/343253
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 38
  • ???jsp.display-item.citation.isi??? 41
social impact