Non-perturbative effective interactions from fluxes

TL;DR

The work investigates non-perturbative interactions arising from D-brane instantons in flux compactifications, using a local C^3/(Z_2×Z_2) quiver with fractional D3/D(-1) systems to realize gauge and stringy instantons. By combining moduli-space integrals, disk-diagram couplings, and flux-induced deformations via G_3, the authors derive a rich set of non-perturbative F- and D-terms, including ADS-type superpotentials, Beasley-Witten multi-fermion terms, and both holomorphic and non-holomorphic flux-induced interactions. They show how G_{(3,0)} and G_{(0,3)} components generate soft terms and induce novel effective operators, with explicit results for one-instanton sectors and generalizations to multi-instanton configurations. A notable finding is that stringy instantons can yield holomorphic non-perturbative superpotentials in the presence of flux, even without orientifold projections, and that fluxes can lift otherwise unwanted neutral zero modes, broadening the landscape of moduli stabilization and SUSY-breaking mechanisms in brane-world setups.

Abstract

Motivated by possible implications on the problem of moduli stabilization and other phenomenological aspects, we study D-brane instanton effects in flux compactifications. We focus on a local model and compute non-perturbative interactions generated by gauge and stringy instantons in a N = 1 quiver theory with gauge group U(N_0) x U(N_1) and matter in the bifundamentals. This model is engineered with fractional D3-branes at a C^3/(Z_2 x Z_2) singularity, and its non-perturbative sectors are described by introducing fractional D-instantons. We find a rich variety of instanton-generated F- and D-term interactions, ranging from superpotentials and Beasley-Witten like multi-fermion terms to non-supersymmetric flux-induced instanton interactions.

Figures (7)

• Figure 1: The quiver diagram encoding the field content and the charges for fractional D-branes of the orbifold $\mathbb{C}^3/(\mathbb{Z}_2\times\mathbb{Z}_2)$. The dots represent the branes associated with the irrep $R_A$ of the orbifold group. A stack of $N_A$ such branes supports a $\mathrm{U}(N_A)$ gauge theory. An oriented link from the $A$-th to the $B$-th dot corresponds to a chiral multiplet transforming in the $({N_A},{\overline N_B})$ representation of the gauge group and in the $R_A \otimes R_B$ representation of the orbifold group.
• Figure 2: This simple quiver gauge theory is (from the point of view of one of the nodes) just $\mathcal{N}=1$ SQCD.
• Figure 3: D3/D$(-1)$-quiver for SQCD with a) gauge instantons and b) stringy instantons. Filled and empty circles represent stacks of D3 and D$(-1)$ branes, solid lines stand for chiral bifundamental matter, dashed lines for charged instanton moduli. A single dashed line represents the fermions $\mu$, while a double dashed line is a $(\mu,w)$ pair.
• Figure 4: Disk diagrams leading to the interaction between the scalar $\phi(x)$, or its superpartner $\psi_\alpha(x)$, and the fermionic instanton moduli $\mu^3$ and $\bar{\mu}^2$.
• Figure 5: An example of a disk interaction between the (anti-holomorphic) scalar $\bar{\phi}(x)$ and the instanton moduli leading to the coupling (\ref{['barphimumu']}).