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

We study the relation between the Type IIB (NSNS and RR) 2-form fields and the (complex) gauge coupling constant of the 4D SU(N _c ) super Yang-Mills theory with N _f fundamental matter particles. We start from the analysis of the D2-brane world-volume theory with heavy N _c quarks on the N _f D6 supergravity background. After a sequence of T- and S-dualities, we obtain the (generalized) 2-forms in the configuration with N _c D5-branes wrapping on a vanishing two-cycle under the influence of the background. These 2-forms show the same behavior as the gauge coupling constant of the 4D super QCD. The background reduces to the orbifold in the twelve-dimensional space-time formally realized by introducing the two parameters as additional space coordinates. The 10D gravity dual is suggested as the 2D flip in this twelve-dimensional space-time. In the case of N _f = 2N _c , this gravity dual becomes AdS₅ x S⁵/Z₂ with a 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 non-perturbative effects.Received: 2 May 2003, Revised: 21 July 2003, Published online: 19 September 2003