Two-loop vacuum energy for Calabi-Yau orbifold models

TL;DR

This paper computes the two-loop vacuum energy for specific Calabi-Yau orbifold models in heterotic string theory, revealing vanishing contributions in some models and supersymmetry breaking in others, using advanced supermoduli space techniques.

Contribution

It provides a precise two-loop vacuum energy calculation for Z_2 x Z_2 Calabi-Yau orbifolds in heterotic strings, employing supermoduli space integration methods.

Findings

Interior supermoduli contribution vanishes for both heterotic strings.

Boundary contribution vanishes for E8 x E8 but not for Spin(32)/Z2, breaking supersymmetry.

Type II superstring vacuum energy vanishes for these orbifolds.

Abstract

A precise evaluation of the two-loop vacuum energy is provided for certain Z_2 x Z_2 Calabi-Yau orbifold models in the Heterotic string. The evaluation is based on the recent general prescription for superstring perturbation theory in terms of integration over cycles in supermoduli space, implemented at two-loops with the gauge-fixing methods based on the natural projection of supermoduli space onto moduli space using the super-period matrix. It is shown that the contribution from the interior of supermoduli space (computed with the procedure that has been used in previous two-loop computations) vanishes identically for both the E_8 x E_8 and Spin (32)/Z_2 Heterotic strings. The contribution from the boundary of supermoduli space is also evaluated, and shown to vanish for the E_8 x E_8 string but not for the Spin (32)/Z_2 string, thus breaking supersymmetry in this last model. As a byproduct, the vacuum energy in Type II superstrings is shown to vanish as well for these orbifolds.