Type IIB 2-form fields and gauge coupling constant of 4D ${\cal N}=2$ super QCD

Abstract

We study the relation between the Type IIB (NSNS and RR) 2-form fields and the (complex) gauge coupling constant of the 4D N=2 SU(Nc) super Yang-Mills theory with Nf fundamental matters. We start from the analysis of the D2-brane world volume theory with heavy Nc quarks on the Nf D6 supergravity background. After a sequence of T- and S-dualities, we obtain the (generalized) 2-forms in the configuration with Nc D5-branes wrapping on the vanishing two-cycle under the influence of the background. These 2-forms shows the same behavior as the gauge coupling constant of the 4D N=2 super QCD. The background reduces to the Z_{Nf} orbifold in the twelve-dimensional space-time formally realized by introducing the two parameters as the additional space coordinates. The 10D gravity dual is suggested as the 2D flip in this twelve-dimensional space-time. In the case of Nf=2Nc, this gravity dual becomes AdS_5 \times S^5/Z_2 with D3-charge which depends on the constant generalized NSNS 2-form. This is the result expected from the M-theory QCD configuration. Based on the known exact result, we also discuss this configuration after including the nonperturbative effect.