Type IIB 2-form Fields and Gauge Coupling Constant of 4D N=2 super QCD

TL;DR

This paper explores the connection between Type IIB 2-form fields and the gauge coupling in 4D N=2 super QCD, using dualities and supergravity backgrounds to relate string theory constructs to gauge theory parameters.

Contribution

It provides a novel analysis linking Type IIB 2-forms to gauge couplings in N=2 super QCD through dualities and supergravity backgrounds, including nonperturbative effects.

Findings

2-forms mimic gauge coupling behavior

Background reduces to Z_{Nf} orbifold in 12D space

Nf=2Nc case yields AdS_5 x S^5/Z_2 with D3-charge

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.