On a supersymmetric completion of the R^4 term in IIB supergravity

TL;DR

This paper investigates the possibility of constructing a supersymmetric invariant containing the $R^4$ term in type IIB supergravity, finding obstructions that prevent such a construction from being realized as a chiral superpotential.

Contribution

It demonstrates that the supersymmetric $R^4$ invariant in IIB supergravity cannot be formulated as a chiral superpotential due to fundamental obstructions.

Findings

Obstruction to the existence of a chiral measure in IIB superspace.

The superfield containing all IIB supergravity fields does not support a chiral superpotential.

The $R^4$ term cannot be derived from a scalar chiral superpotential in IIB supergravity.

Abstract

We analyze the possibility of constructing a supersymmetric invariant that contains the $R^4$ term among its components as a superpotential term in type IIB on-shell superspace. We consider a scalar superpotential, i.e. an arbitrary holomorphic function of a chiral scalar superfield. In general, IIB superspace does not allow for the existence of chiral superfields, but the obstruction vanishes for a specific superfield, the dilaton superfield. This superfield contains all fields of type IIB supergravity among its components, and its existence is implied by the solution of the Bianchi identities. The construction requires the existence of an appropriate chiral measure, and we find an obstruction to the existence of such a measure. The obstruction is closely related to the obstruction for the existence of chiral superfields and is non-linear in the fields. These results imply that the IIB superinvariant related to the $R^4$ term is not associated with a scalar chiral superpotential.