Consistent Decoupling of Heavy Scalars and Moduli in N=1 Supergravity

TL;DR

This paper establishes criteria for decoupling heavy fields in N=1 supergravity, ensuring low energy physics remains unaffected by heavy fields, which is crucial for inflation models and de Sitter vacua.

Contribution

It provides a new sufficient condition for supersymmetric decoupling based on the Kahler invariant function G, clarifying when heavy fields can be integrated out without affecting low energy dynamics.

Findings

Decoupling condition is G = L(light, heavy) for supersymmetric cases.

Standard additive ansatz for K and W does not generally satisfy decoupling.

The paper discusses conditions under which decoupling holds in supergravity models.

Abstract

We consider the conditions for integrating out heavy chiral fields and moduli in N=1 supergravity, subject to two explicit requirements. First, the expectation values of the heavy fields should be unaffected by low energy phenomena. Second, the low energy effective action should be described by N=1 supergravity. This leads to a working definition of decoupling in N=1 supergravity that is different from the usual condition of gravitational strength couplings between sectors, and that is the relevant one for inflation with moduli stabilization, where some light fields (the inflaton) can have long excursions in field space. It is also important for finding de Sitter vacua in flux compactifications and KKLT scenarios, since failure of the decoupling condition invalidates the implicit assumption that the stabilization and uplifting potentials have a low energy supergravity description. We derive a sufficient condition for supersymmetric decoupling, namely, that the Kahler invariant function G = K + log |W|^2 is of the form G = L(light, (heavy)) with H and L arbitrary functions, which includes the particular case G = L(light) + H(heavy). The consistency condition does not hold in general for the ansatz K = K(light) + K(heavy), W = W(light) + W(heavy) and we discuss under what circumstances it does hold.