SL(2,R)-invariant IIB Brane Actions

TL;DR

The work addresses the problem of making IIB brane actions manifestly $SL(2,\mathbb{R})$ (via $SU(1,1)$) covariant by incorporating an $SU(1,1)$ doublet of worldvolume vectors and constrained charges. It develops a universal Wess-Zumino term $\mathcal{L}_{\rm WZ} = q \cdot \mathcal{C}\, e^{q \mathcal{F}_{(2)}}$ together with a universal kinetic term, yielding a single expression for all branes with $p=-1,1,3,5,7,9$, including the D7/D9 cases via charge restrictions $q_{\alpha\beta} = q_\alpha q_\beta$. The paper provides explicit actions for each special case and clarifies when a single Born-Infeld vector suffices (notably for the 7-brane conjugacy class with $\det q_{\alpha\beta}=0$) and when obstructions arise for other classes. This unified framework clarifies the role of $SU(1,1)$ charges, the field redefinitions required to achieve gauge invariance, and the duality structure underpinning IIB brane dynamics, with implications for future fermionic extensions and kappa-symmetry.

Abstract

We give a universal SL(2,R)-invariant expression for all IIB p-brane actions with p=-1,1,3,5,7,9. The Wess-Zumino terms in the brane actions are determined by requiring (i) target space gauge invariance and (ii) the presence of a single Born-Infeld vector. We find that for p=7 (p=9) brane actions with these properties only exist for orbits that contain the standard D7-brane (D9-brane). We comment about the actions for the other orbits.