Supersymmetric Dirac–Born–Infeld action with self-dual mass term

Abstract

We present a self-dual N = 1 supersymmetric Dirac-Born-Infeld action in three dimensions. This action is based on the supersymmetric generalized self-duality in odd dimensions developed originally by Townsend, Pilch and van Nieuwenhuizen. Even though such a self-duality had been supposed to be very difficult to generalize to a supersymmetrically interacting system, we show that Dirac-Born-Infeld action is actually compatible with supersymmetry and self-duality in three-dimensions. The interactions can be further generalized to arbitrary (non)polynomial interactions. As a by-product, we also show that a third-rank field strength leads to a more natural formulation of self-duality in 3D. We also show an interesting role played by the third-rank field strength leading to a supersymmetry breaking, in addition to accommodating a Chern-Simons form.

Self-dual non-Abelian vector multiplet in three dimensions

“…Even though the Abelian supersymmetric DBI action was introduced to self-dual VM [11], our result (6.3) covers the non-Abelian case for the first time after the discovery of self-dual VM in 3D [7].…”

“…Subsequently, we also show that the self-dual VM can be further coupled to supersymmetric Dirac-Born-Infeld (DBI) action [9][10] [11]. By an appropriate identification of mass parameters, we will see that the mass of the self-dual VM can be quantized as the result of Chern-Simons quantization.…”

“…We also see that our system has a close relationship with σ -models for gauge group manifolds, when the minimal coupling is switched off: m → 0, justifying various coefficients in our lagrangians. Subsequently, we also show that the self-dual VM can be further coupled to supersymmetric Dirac-Born-Infeld (DBI) action [9][10] [11]. By an appropriate identification of mass parameters, we will see that the mass of the self-dual VM can be quantized as the result of Chern-Simons quantization.…”

“…As a matter of fact, we can consider the supersymmetric DBI action [10] in 3D [11] at the first non-trivial quartic order:…”

“…Since our formulation has been in off-shell component language, it is not too difficult to introduce more general interactions, such as DBI action [9]. As a matter of fact, we can consider the supersymmetric DBI action [10] in 3D [11] at the first non-trivial quartic order:…”