Full diffeomorphism and Lorentz invariance in 4D $$ \mathcal{N}=1 $$ superfield description of 6D SUGRA

Abstract

Abstract:We complete the four-dimensional N = 1 superfield description of sixdimensional supergravity. The missing ingredients in the previous works are the superfields that contain the sechsbein e ν 4 , e ν 5 , e 4 µ , e 5 µ and the second gravitino. They are necessary to make the action invariant under the diffeomorphisms and the Lorentz transformations involving the extra dimensions. We find the corresponding superfield transformation laws, and show the invariance of the action under them. We also check that the resultant action reproduces the known superfield description of five-dimensional supergravity through the dimensional reduction.

$$ \mathcal{N}=1 $$ superfield description of BPS solutions in 6D gauged SUGRA with 3-branes

“…In this paper, we express the BPS backgrounds in the N = 1 superfield language. As we have shown in our previous work [14], the relation between the superfields and the usual component fields of 6D SUGRA is not simple. Thus expressing the known background configurations in terms of the superfields is a nontrivial task.…”

“…[12], and extended the result to SUGRA by inserting the superfields that contain the fields in the Weyl multiplets in refs. [13,14]. The N = 1 superfield action is also a good starting point to derive 4D effective theory keeping the N = 1 SUSY structure, just we did in five-dimensional SUGRA [15]- [20].…”

“…The paper is organized as follows. In the next section, we briefly review our previous work [14], and provide the bulk and the brane actions in terms of N = 1 superfields. Section 3 is the main part of this paper.…”

Eleven-dimensional supergravity in 4D, N = 1 superspace

“…Finally, it would be desirable to understand the truncations of this formulation of eleven-dimensional supergravity to other dimensions. This would make contact with (and potentially simplify) the phenomenological literature on five-dimensional supergravity [24,26,[38][39][40][41] and extensions to six-dimensions [42][43][44].…”

Five-dimensional supergravity in N = 1/2 superspace

“…Such a "superfield Noether procedure" is guaranteed to be possible when the offshell superspace exists and, indeed, it was used to construct five-and six-dimensional matter-coupled supergravity in various approximations in [14][15][16][17][18][19][20][21][22][23]. In the cases in which an off-shell superspace does not exist, it is not obvious that the procedure will work.…”