平行/重合D膜超势,Ooguri-Vafa不变量与类型Ⅱ弦理论/F理论对偶

Parallel/coincident D-brane superpotentials,Ooguri-Vafa invariants,and Type Ⅱ/F theory duality

利用类型Ⅱ弦理论/F理论对偶,第一次在平行和重合相区计算一个具体的双D膜系统的超势,并提取Ooguri-Vafa不变量。平行D膜相与重合D膜相间的相变也对应着D膜世界叶上规范理论规范对称性的提升U(1)×…×U(1)→U(n)。计算显示这两个相区的超势截然不同,并给出不同的Ooguri-Vafa不变量。这意味着相变的发生导致两个相区能谱结构的差异。

The superpotential is very important physical observation in the topological string theory,and it determines the F-term of the low-energy effective theory and the string vacuum structure.Ooguri-Vafa invariants,as the counting number of BPS states,can be extracted from the superpotential,giving rise to the energy spectrum of the D-brane system.We compute the superpotentials and Ooguri-Vafa invariants for complicated D-brane system,namely double Dbranes system,in the parallel and coincident phases using the TypeⅡ/F theory duality for the first time.The coincidence of parallel D-branes leads to the enhancement of gauge symmetry U(1)×…×U(1)→U(n)in terms of gauge theory on the worldvolume of the D-branes being known as the phase transition between the parallel D-brane phase and the coincident D-brane phase.We find the difference between the Ooguri-Vafa invariants for the two phases giving rise to the distinct spectra.It can be viewed as an evidence of the phase transition.