D-instanton derivation of multi-fermion F-terms in supersymmetric QCD

TL;DR

This work uses a D-instanton realization of gauge theory instantons on D3-branes, arranged on a ${\mathbb C}^3/({\mathbb Z}_2\times{\mathbb Z}_2)$ orbifold, to derive nonperturbative multi-fermion $F$-terms in ${\mathcal N}=1$ SQCD. The method expresses instanton effects as integrals over the instanton moduli (the ADHM data) extracted from the D3-D3, D(-1)-D(-1), and D3-D(-1) sectors, producing chiral terms that deform the moduli space, consistent with Seiberg’s quantum moduli-space structure. For $SU(2)$ with $N_f=N_c=2$, the derived four-fermion interactions reproduce Beasley–Witten’s results, while the symplectic case $USp(2N_c)$ yields simpler expressions and confirms deformations for $N_f=N_c+1$ and higher-fermion terms for larger flavor numbers. Overall, the paper provides a string-theoretic derivation of moduli-space deformations via D-instanton effects and offers a framework for calculating nonperturbative F-terms in SQCD and related gauge theories. $

Abstract

We investigate effects of field theory instantons by considering D-instantons in a suitable D3-brane background. In supersymmetric QCD with SU(N_c) gauge group with N_f=N_c flavors, the moduli space of vacua is deformed by instantons. This effect can be described by the chiral interactions which are called multi-fermion F-terms. We derive these chiral interaction terms as D-instanton effects in the presence of D3-branes. For SU(2), the obtained result agrees with the previous result worked out by Beasley and Witten [hep-th/0409149]. We also explicitly work out those for the case of the symplectic gauge group, and show that they describe the deformation of the moduli space.