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

TL;DR

The paper addresses integrating out heavy moduli in $N=1$ supergravity while preserving a consistent low-energy $N=1$ description and unaltered heavy vevs. It shows that a sufficient decoupling condition is that the Kahler-invariant function satisfies $\\widehat{G} = f(L,\bar L, g(H,\bar H))$, which guarantees a block-diagonal Kähler metric and Hessian, enabling a stable light-sector theory and potential BPS embedding. It also demonstrates that common separable forms $K = K_{\text{heavy}} + K_{\text{light}}$ and $W = W_{\text{heavy}} + W_{\text{light}}$ generally fail to decouple, with important implications for inflation and moduli stabilization in KKLT/LVS scenarios. This provides a practical criterion to assess the viability of compactifications and helps clarify why some models naturally support decoupled heavy moduli while others do not.

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.