Abstract
We derive the component on-shell action of the space-filling D3-brane, {\it i.e.} $N=1$ supersymmetric Born-Infeld action, within the nonlinear realization approach. The covariant Bianchi identity defining the $N=1$, $d=4$ vector supermultiplet has been constructed by introducing a new bosonic Goldstone superfield associated with the generator of the $U(1)$ group, which transforms to each other the spinor generators of unbroken and spontaneously broken $N=1$, $d=4$ supersymmetries. The first component of this Goldstone superfield is the auxiliary field of the vector supermultiplet and, therefore, the Bianchi identity can be properly defined. The component action of the D3-brane has a very simple form, being written in terms of derivatives covariant with respect to spontaneously broken supersymmetry - it just mimics its bosonic counterpart.
Highlights
JHEP08(2015)094 transforms independently from the remaining ones
The covariant Bianchi identity defining the N = 1, d = 4 vector supermultiplet has been constructed by introducing a new bosonic Goldstone superfield associated with the generator of the U(1) group, which transforms to each other the spinor generators of unbroken and spontaneously broken N = 1, d = 4 supersymmetries
Here we are going to demonstrate that the on-shell component action of D3-brane has a very simple form
Summary
The idea how to find the covariant Bianchi identity is rather simple. Let us suppose that we introduced into the game some additional bosonic superfield φ which enters the new Cartan forms as. Where U is the generator defined in (3.2), while φ is the corresponding Goldstone superfield Such a type of modification of the coset element leads to new expressions of the Cartan forms. ΩαQ = cos φ dθα − i sin φ dψα, ΩQα = cos φ dθα + i sin φ dψα ̇ The modifications of these Cartan forms forced us to introduce the new covariant (with respect to N = 2, d = 4 Poincare supergroup and U transformations) derivatives Dα, Dαimplicitly defined as. It is found to be convenient to represent the results of the action of ∇α and ∇αon (3.23) as It is a matter of straightforward but still quite lengthly calculations to check that the r.h.s. of the equations (3.27) are covariantly chiral and antichiral, respectively. We see that the Bianchi identities (3.23) are correct: they are covariant with respect to all symmetries and do not imply the equations of motion
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
