Computing parallel/coincident phase D-brane superpotentials and Type-Ⅱ/F-theory duality  

作　　者：Xiao-Tian Jiang Fu Zhong Yang 蒋笑添;杨富中(University of Chinese Academy of Sciences, Beijing 100049, China)

机构地区：University of Chinese Academy of Sciences,Beijing 100049,China

出　　处：《Chinese Physics C》2018年第9期37-46,共10页中国物理C（英文版）

基　　金：Supported by NSFC(11475178) and Y4JT01VJ01

摘　　要：In this paper we study the parallel phase and the coincident phase of D-brane systems with the compactification of one closed modulus. D-brane systems with two phases are described by different 4-folds in terms of Type-Ⅱ/F-theory duality, and the phase transitions are related by the blow-up from a 4-fold with singularities to a 4-fold without. In terms of gauge theory, the phase transition corresponds to the enhancement of gauge group U（1）×U（1）→U（2） connecting the Coulomb branch and the Higgs branch. For the sextic and octic with two D-branes,using mirror symmetry and Type-Ⅱ/F theory duality, A-model superpotentials are obtained from the B-model side for the two phases, and the U（1） Ooguri-Vafa invariants for the parallel phase and U（2） Ooguri-Vafa invariants for the coincident phase are extracted from the A-model superpotential. The difference between the invariants of the two phases is evidence of the phase transition between the Coulomb branch and the Higgs branch.In this paper we study the parallel phase and the coincident phase of D-brane systems with the compactification of one closed modulus. D-brane systems with two phases are described by different 4-folds in terms of Type-Ⅱ/F-theory duality, and the phase transitions are related by the blow-up from a 4-fold with singularities to a 4-fold without. In terms of gauge theory, the phase transition corresponds to the enhancement of gauge group U（1）×U（1）→U（2） connecting the Coulomb branch and the Higgs branch. For the sextic and octic with two D-branes,using mirror symmetry and Type-Ⅱ/F theory duality, A-model superpotentials are obtained from the B-model side for the two phases, and the U（1） Ooguri-Vafa invariants for the parallel phase and U（2） Ooguri-Vafa invariants for the coincident phase are extracted from the A-model superpotential. The difference between the invariants of the two phases is evidence of the phase transition between the Coulomb branch and the Higgs branch.

关 键 词：Ooguri-Vafa invariants TypeⅡ/F-theory duality phase transition 

分 类 号：O414.13[理学—理论物理]