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

TL;DR

This paper develops new Lorentz-invariant, supersymmetric actions for D=10 IIB supergravity, incorporating dual potentials and SL(2,R) symmetry, advancing the theoretical understanding of supergravity formulations.

Contribution

It introduces a novel method for constructing Lorentz-invariant actions with chiral bosons, including dual potentials and manifest SL(2,R) symmetry, for D=10 IIB supergravity.

Findings

Constructed a Lorentz-invariant, supersymmetric action with a single auxiliary scalar.

Developed symmetric actions involving complex two-form and six-form potentials.

Demonstrated all actions are equivalent and reproduce known equations of motion.

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.