Instanton effects in N=1 brane models and the Kahler metric of twisted matter

TL;DR

This work develops a string-theoretic construction of ${\cal N}=1$ gauge theories from magnetized D9-branes on a $(\mathcal{T}_2^{(1)} \times \mathcal{T}_2^{(2)} \times \mathcal{T}_2^{(3)})/(\mathbb{Z}_2 \times \mathbb{Z}_2)$ orbifold, and studies Euclidean D5 instantons that wrap the internal space. By computing mixed annulus amplitudes, the authors extract non-holomorphic contributions tied to the matter Kähler metrics and demonstrate how they combine with field redefinitions to yield holomorphic instanton-induced superpotentials, notably reproducing the ADS/TVY form for $k=1$ in ${\cal N}=1$ SQCD with $N_F=N_a-1$. The analysis connects the one-loop annulus corrections to the Wilsonian gauge coupling and the Kähler metrics, showing that the holomorphic superpotential emerges only after the proper holomorphic redefinitions of couplings and matter fields, consistent with the Dixon-Kaplunovsky-Louis-Lust framework. They further relate these results to the holomorphy of Yukawa couplings in magnetized brane models, providing cross-checks with field-theory limits and existing results. The findings illuminate how stringy instantons encode non-perturbative dynamics in ${\cal N}=1$ brane setups and offer a precise handle on the Kähler geometry of twisted matter, with potential phenomenological implications for non-perturbative superpotential contributions in realistic string vacua.

Abstract

We consider locally consistent systems of magnetized D9 branes on an orbifolded six-torus which support N=1 gauge theories. In such realizations, the matter multiplets arise from "twisted" strings connecting different stacks of branes. The introduction of Euclidean 5 branes (E5) wrapped on the six-dimensional compact space leads to instanton effects. For instance, if the system is engineered so as to yield SQCD, a single E5 brane may account for the ADS/TVY superpotential. We discuss the subtle interplay that exists between the annuli diagrams with an E5 boundary and the holomorphicity properties of the effective low-energy action of the N=1 theory. The consistency of this picture allows to obtain information on the Kahler metric of the chiral matter multiplets arising from twisted strings.

Figures (4)

• Figure 1: Schematization of the brane system we consider, and of its spectrum of chiral multiplets; see the text for more details.
• Figure 2: The flavored moduli of instantonic E$5_a$ branes in presence of D$9_b$ and D$9_c$ branes; see the text for more details.
• Figure 3: Disk interactions between the moduli and the chiral scalars which survive in the field theory limit
• Figure 4: A disk diagram leading to a Yukawa coupling.