Non-perturbative SQCD Superpotentials from String Instantons

TL;DR

This work provides a concrete string-theoretic derivation of the Affleck-Dine-Seiberg non-perturbative superpotential for ${\cal N}=1$ SQCD with $N_f=N_c-1$ by embedding the gauge theory in a local Type IIA setup with intersecting D6-branes and a single E2-instanton inside the color stack. By explicitly computing disc amplitudes and performing the full fermionic and bosonic zero-mode integrations, the authors recover the ADS form $W = {\Lambda^{3N_c-N_f}}/{\det(M_{ff'})}$ in the field theory limit, and extend the analysis to ${\rm USp}(2N_c)$ SQCD to obtain the corresponding Pfaffian-based superpotential. The paper further discusses generalizations to ${\rm SO}(N_c)$ and outlines how stringy corrections (worldsheet instantons, massive string modes) modify the simple field-theory result away from the strict limit. Overall, the results validate the string-instanton calculus of Blumenhagen et al. as a mechanism for encoding non-perturbative gauge dynamics and illustrate the role of ADHM data in the stringy derivation of non-perturbative superpotentials.

Abstract

The Affleck-Dine-Seiberg instanton generated superpotential for SQCD with Nf=Nc-1 flavours is explicitly derived from a local model of engineered intersecting D6-branes with a single E2-instanton. This computation extends also to symplectic gauge groups with Nf=Nc flavours.

Figures (5)

• Figure 1: Relation between instantonic one-loop amplitudes and corresponding � gauge �threshold corrections.
• Figure 2: Local SQCD brane configuration with resulting zero modes.
• Figure 3: Four-point massless string exchange and four-point vertex interaction.
• Figure 4: Brane configuration for an instanton in an $USp(2N_c)$ gauge theory. The dashed line represents the orientifold plane.
• Figure 5: Brane configuration for an instanton in an $SO(N)$ gauge theory. The dashed line represents the orientifold plane.