Brane induced supersymmetry breaking and de Sitter supergravity

Abstract

We obtain a four-dimensional supergravity with spontaneously broken supersymmetry allowing for de Sitter vacua by coupling a superspace action of minimal N = 1, D = 4 supergravity to a locally supersymmetric generalization of the Volkov-Akulov goldstino action describing the dynamics of a space-filling non-BPS 3-brane in N = 1, D = 4 superspace. To the quadratic order in the goldstino field the obtained action coincides with earlier constructions of supergravities with nilpotent superfields, while matching the higher-order contributions will require a non-linear redefinition of fields. In the unitary gauge, in which the goldstino field is set to zero, the action coincides with that of Volkov and Soroka. We also show how a nilpotency constraint on a chiral curvature superfield emerges in this formulation.

Scanning of the supersymmetry breaking scale and the gravitino mass in supergravity

“…Note that now also the function g(φ) will contribute to the gravitino mass [37]. For further discussion on supersymmetry breaking and nonlinear realizations in supergravity see [38][39][40][41][42][43][44][45][46]. Let us now see, following [8], how the empty universe problem can be resolved in the present supersymmetric context.…”

Goldstino superfields in N = 2 $$ \mathcal{N}=2 $$ supergravity

“…Secondly, every Goldstino superfield coupled to supergravity provides a universal positive contribution to the cosmological constant [14,[18][19][20][21], unlike the supersymmetric cosmological term [22] which yields a negative contribution to the cosmological constant. The same property is true for the Goldstino brane [23]. Of course, the observation that the coupling of the Volkov-Akulov theory [24][25][26] to supergravity generates a model-independent positive contribution to the cosmological constant was made long ago in the frameworks of on-shell supergravity [5] and off-shell supergravity [18].…”

“…It tells us that we are dealing with nilpotent N = 2 supergravity. The equation (3.23) is similar to that in spontaneously broken N = 1 supergravity [21,23], see appendix D for a review of the construction of [21]. The supergravity theory (3.15) possesses a dual formulation in which the tensor multiplet compensator is dualised into a polar hypermultiplet compensator [54].…”

“…Secondly, it allows us to express X as a function of the supergravity fields. The nilpotency constraint (D.1) and the equation of motion (D.3) imply that the chiral curvature becomes nilpotent [21,23],…”

From linear to non-linear SUSY and back again

“…While explicit string constructions based on tachyon-free non-BPS systems are known since some time [27][28][29] and their non-linear supersymmetry has been studied in detail [30,31], their connection with the constrained superfields are still not fully understood [32][33][34][35][36][37][38]. This renewal of interest for non-linear realizations also led to various developments on the properties of the supersymmetry breaking sector in local supersymmetry [39][40][41][42][43][44][45][46][47].…”