A Note on Poly-Instanton Effects in Type IIB Orientifolds on Calabi-Yau Threefolds

TL;DR

The paper identifies sufficient geometric and topological conditions for poly-instanton corrections in Type IIB orientifolds with O7/O3, focusing on Euclidean D3-brane instantons wrapping divisors. It derives zero-mode criteria using equivariant cohomology and demonstrates how a single Wilson-line modulino in H^1_+(E,O) enables poly-instanton corrections. Through three explicit toric Calabi-Yau examples, it shows setups where poly-instantons exist (Example A and C) and one where they are blocked by extra zero modes (Example B), illustrating the sensitivity to D7-brane content and tadpole cancellation. The results hint at novel moduli-stabilization pathways, including LARGE volume-type realizations, and set the stage for further detailed stabilization and inflation analyses.

Abstract

The zero mode structure for the generation of poly-instanton corrections for Euclidian D3-branes wrapping complex surfaces in Type IIB orientifolds with O7- and O3-planes is analyzed. Working examples of such surfaces and explicit embeddings into compact Calabi-Yau threefolds are presented, with special emphasis on geometries capable of realizing the LARGE volume scenario.

Figures (5)

• Figure 1: Relative positions of $O7$-planes and divisor $W$ for example A with involution $\sigma: x_7 \leftrightarrow -x_7$.
• Figure 2: Relative position of $O7$-planes and divisor $W$ for example A with involution $\sigma: x_4 \leftrightarrow -x_4$.
• Figure 3: Relative position of $O7$-planes and divisor $W$ for example B with involution $\sigma: x_4 \leftrightarrow -x_4$.
• Figure 4: Relative position of $O7$-planes and divisor $W$ for example B with involution $\sigma: x_2 \leftrightarrow -x_2$.
• Figure 5: Relative position of $O7$-planes and divisor $W$ for example C with involution $\sigma: x_3 \leftrightarrow -x_3$.