D=10, N=IIB Supergravity: Lorentz-invariant actions and duality

TL;DR

This work delivers a set of manifestly Lorentz-invariant and supersymmetric Lagrangians for D=10 Type IIB supergravity in the presence of a chiral 4-form by employing the PST construction with a single auxiliary scalar. It develops duality-symmetric formulations that pair the gauge potentials with their Hodge duals (A_2/A_6 and A_0/A_8) under the SL(2,R) (SU(1,1)) duality, incorporating an SU(1,1) triplet of eight-forms to encode scalar duals. The paper provides explicit component actions, supersymmetry transformations, and a demonstration that these duality-symmetric theories reproduce the standard IIB equations of motion, thereby offering covariant and symmetry-rich frameworks for the theory. These constructions have potential implications for brane couplings, dual descriptions, and perturbative analyses, including linearized duality and Lorentz anomaly considerations on trivial manifolds. Overall, the authors clarify the duality structure of IIB supergravity and extend covariant Lagrangian formulations to fully duality-symmetric settings.

Abstract

We present a manifestly Lorentz invariant and supersymmetric component field action for $D = 10$, type $IIB$ supergravity, using a newly developed method for the construction of actions with chiral bosons, which implies only a single scalar non propagating auxiliary field. With the same method we construct also an action in which the complex two-form gauge potential and its Hodge-dual, a complex six-form gauge potential, appear in a symmetric way in compatibility with supersymmetry and Lorentz invariance. The duals of the two physical scalars of the theory turn out to be described by a $SL(2,R)$ triplet of eight-forms whose curvatures are constrained by a single linear relation. We present also a supersymmetric action in which the basic fields and their duals, six-form and eight-form potentials, appear in a symmetric way. All these actions are manifestly invariant under the global $SL(2,R)$-duality group of $D = 10$, $IIB$ supergravity and are equivalent to each other in that their dynamics corresponds to the well known equations of motion of $ D=10$, $IIB$ supergravity.