Dirac-Born-Infeld-Volkov-Akulov and Deformation of Supersymmetry

TL;DR

This paper develops explicit all-order deformations of the d=10 and d=4 Maxwell supermultiplets that realize both deformed linear supersymmetries and Volkov–Akulov type nonlinear supersymmetries, aligning with the string-tension expansion of Dirac–Born–Infeld actions derived from D9 and D3 branes. It then extends the construction to half-maximal cases in d=6 and d=4 using a new class of vector branes (Vp-branes), yielding complete DBI–VA models in each case and providing explicit symmetry transformations and algebras. The results are obtained through complementary bottom-up deformations of the Maxwell action and top-down brane analyses, with a unique choice of field redefinitions ensuring agreement with the brane actions. The work clarifies how maximal and half-maximal nonlinear SUSYs can be realized in DBI-type theories, offering a framework for further exploration of higher-derivative invariants and duality structures in extended supersymmetry. Overall, the paper presents a coherent, all-orders completion of DBI–VA dynamics across d=10, d=6, and d=4, grounded in brane physics and symmetry considerations, and it suggests avenues for comparing with existing half-maximal constructions and for future development of higher-derivative superconformal invariants.

Abstract

We deform the action and the supersymmetry transformations of the d=10 and d=4 Maxwell supermultiplets so that at each order of the deformation the theory has 16 Maxwell multiplet deformed supersymmetries as well as 16 Volkov-Akulov type non-linear supersymmetries. The result agrees with the expansion in the string tension of the explicit action of the Dirac-Born-Infeld model and its supersymmetries, extracted from D9 and D3 superbranes, respectively. The half-maximal Dirac-Born-Infeld models with 8 Maxwell supermultiplet deformed supersymmetries and 8 Volkov-Akulov type supersymmetries are described by a new class of d=6 vector branes related to chiral (2,0) supergravity, which we denote as `Vp-branes'. We use a space-filling V5 superbrane for the d=6 model and a V3 superbrane for the d=4 half-maximal Dirac-Born-Infeld (DBI) models. In this way we present a completion to all orders of the deformation of the Maxwell supermultiplets with maximal 16+16 supersymmetries in d=10 and 4, and half-maximal 8+8 supersymmetries in d=6 and 4.