On the Instanton Contributions to the Masses and Couplings of $E_6$ Singlets
P. Berglund, P. Candelas, X. de la Ossa, E. Derrick, J. Distler, T. Hubsch
TL;DR
This work investigates instanton effects on E6 singlets in (2,2) Calabi–Yau compactifications, focusing on the quintic and the classical structure of singlet deformations. It shows that although individual worldsheet instantons can contribute nontrivially to singlet masses, these contributions cancel in total, implying the singlet mass and related superpotential terms often vanish. The authors also analyze Yukawa couplings involving singlets and 27/27bar states, demonstrating that first-order instanton corrections vanish once contact terms are properly included, consistent with the vanishing of singlet-related superpotential terms to all orders under reasonable assumptions. The results hinge on a detailed treatment of zero modes, deformation theory, and the interplay between integrability, polynomial deformations, and instanton sums, with broader implications for (0,2) vacua and model-building in string theory.
Abstract
We consider the gauge neutral matter in the low--energy effective action for string theory compactification on a \cym\ with $(2,2)$ world--sheet supersymmetry. At the classical level these states (the \sing's of $E_6$) correspond to the cohomology group $H^1(\M,{\rm End}\>T)$. We examine the first order contribution of instantons to the mass matrix of these particles. In principle, these corrections depend on the \K\ parameters $t_i$ through factors of the form $e^{2\p i t_i}$ and also depend on the complex structure parameters. For simplicity we consider in greatest detail the quintic threefold $\cp4[5]$. It follows on general grounds that the total mass is often, and perhaps always, zero. The contribution of individual instantons is however nonzero and the contribution of a given instanton may develop poles associated with instantons coalescing for certain values of the complex structure. This can happen when the underlying \cym\ is smooth. Hence these poles must cancel between the coalescing instantons in order that the superpotential be finite. We examine also the \Y\ couplings involving neutral matter \ysing\ and neutral and charged fields \ymix, which have been little investigated even though they are of phenomenological interest. We study the general conditions under which these couplings vanish classically. We also calculate the first--order world--sheet instanton correction to these couplings and argue that these also vanish.