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

TL;DR

The authors investigate whether the IIB $R^4$ correction can arise from a scalar chiral superpotential in on-shell IIB superspace. By constructing a non-linear dilaton superfield $V$ and attempting to define a chiral measure $oldsymbol{ riangle}$, they show a non-linear obstruction prevents a purely chiral half-superspace action, implying the $R^4$ term is not realizable as such a superpotential. Their component analysis yields the $R^4$ coefficient associated with the Eisenstein series $E_5$, and while $E_5$ is SL(2,Z) invariant, its weak-coupling expansion conflicts with known closed-string perturbation theory, indicating this is not the physical string-theory $R^4$ invariant. The work provides valuable techniques for studying higher-derivative invariants in IIB and guides future attempts to realize the correct supersymmetric completion of $R^4$ (and analogous terms) in other theories.

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.