Chern-Simons theory on L(p, q) lens spaces and Gopakumar-Vafa duality

JOURNAL OF GEOMETRY AND PHYSICS

卷:60

Article

Brini, Andrea^1,2  Griguolo, Luca^3,4  Seminara, Domenico^5,6  Tanzini, Alessandro^1,2 

[1] Int Sch Adv Studies SISSA ISAS, Math Phys Sector, I-34014 Trieste, Italy

[2] Ist Nazl Fis Nucl, Sez Trieste, Milan, Italy

[3] Univ Parma, Dipartimento Fis, I-43100 Parma, Italy

[4] Ist Nazl Fis Nucl, Grp Collegato Parma, I-43100 Parma, Italy

[5] Univ Florence, Dipartimento Fis, I-50121 Florence, Italy

[6] Ist Nazl Fis Nucl, Sez Firenze, I-50019 Sesto Fiorentino, Italy

关键词: Chern-Simons theory;    Gopakumar-Vafa;    Large N duality;    Open-closed duality;    Topological strings;    Geometric transitions;    Random matrices;   

DOI  :  10.1016/j.geomphys.2009.11.006

来源: Elsevier

【 摘 要 】

We consider aspects of Chern-Simons theory on L(p, q) lens spaces and its relation with matrix models and topological string theory on Calabi-Yau threefolds, searching for possible new large N dualities via geometric transition for non-SU(2) cyclic quotients of the conifold. To this aim we find, on one hand, a useful matrix integral representation of the SU(N) CS partition function in a generic flat background for the whole L(p. q) family and provide a solution for its large N dynamics; on the other hand, we perform in full detail the construction of a family of would-be dual closed string backgrounds through conifold geometric transition from T*L(p, q). We can then explicitly prove the claim in [5] that Gopakumar-Vafa duality in a fixed vacuum fails in the case q > 1, and briefly discuss how it could be restored in a non-perturbative setting. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free