Moduli Dependent Non-Holomorphic Contributions of Massive States to Gravitational Couplings and $C^2$-Terms in $Z_N$-Orbifold Compactifications

TL;DR

This paper investigates how massive states in certain supergravity theories contribute non-holomorphic terms at one loop, affecting gravitational couplings and potentially canceling problematic $C^2$-terms in $Z_N$-orbifold compactifications.

Contribution

It demonstrates that moduli-dependent non-holomorphic contributions from massive states can cancel $C^2$-terms in $Z_N$-orbifold models at one loop.

Findings

Massive states contribute non-holomorphic terms to gravitational couplings.

Such contributions can cancel naked $C^2$-terms.

$\mathcal{R}^2$-terms can arise without cancellation.

Abstract

It is pointed out that massive states in D=4, N=1 supergravity-matter theories can, in general, at the 1-loop level contribute non-holomorphic terms to quadratic gravitational couplings. It is then shown in the context of $(2,2)$-symmetric $Z_N$-orbifold theories that, for constant moduli backgrounds, the inclusion of such contributions can result in the cancellation of naked $C^2$-terms. ${\cal R}^2$-terms can also arise but, being ghost free, need not cancel.