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

Abstract

We present off-shell N = 2 supergravity actions, which exhibit spontaneously broken local supersymmetry and allow for de Sitter vacua for certain values of the parameters. They are obtained by coupling the standard N = 2 supergravity-matter systems to the Goldstino superfields introduced in arXiv:1105.3001 and arXiv:1607.01277 in the rigid supersymmetric case. These N = 2 Goldstino superfields include nilpotent chiral and linear supermultiplets. We also describe a new reducible N = 1 Goldstino supermultiplet.

A superfield constraint for N $$ \mathcal{N} $$ = 2 → N $$ \mathcal{N} $$ = 0 breaking

“…As we shall see, however, away from a singular corner the solution of C 3 implements the total breaking of supersymmetry. Let us also stress that the setting that we are exploring for the total breaking differs from the one captured by extensions of the N = 2 Volkov-Akulov Lagrangian (see [68][69][70] for a recent comprehensive discussion): when starting from an N = 2 vector multiplet, the low-energy dynamics that we are describing involves a vector field A µ , in addition to the expected goldstini. As we shall see, the N = 2 vector multiplet will enter the equations and the effective Lagrangian only through the abelian field strength, as in the Born-Infeld construction of [55] or in the model of [7,8] that rests on the constraints X 2 = XW α = 0, so that the final spectrum will include a massless vector field.…”

Nilpotent $$ \mathcal{N}=1 $$ tensor multiplet

“…It should be pointed out that cubic nilpotency conditions have been discussed in the literature [18,[31][32][33][34] for two N = 1 superfields, one of which is the nilpotent chiral scalar X subject to the only constraint (1.1), as proposed in [17,18]. Cubic nilpotency conditions for a single N = 2 Goldstino superfield have been proposed in [13,35,36]. This paper is organised as follows.…”

“…These Goldstino superfields include: (i) the irreducible chiral scalar proposed in [16,25]; (ii) the reducible chiral scalar of [17,18]; (iii) the deformed complex linear scalar introduced in [20]; (iv) the complex linear scalar of [26][27][28]; (v) the irreducible real scalar proposed in [12]; (vi) the reducible real scalar of [13]. In the (v) and (vi) cases, there are actually three nilpotency conditions [12,13]:…”

Liberated $$ \mathcal{N} $$ = 1 supergravity

“…However, this is not the full story. An inspection of the term (3.5) will show that a conservative evaluation of the worse possible divergencies which can appear in the fermionic sector have the form 30) where the superscripts U (n) refer to derivatives with respect to A I or A J . Therefore, if we have a function U (and its derivatives) which goes to zero faster than g IJ F I F J nmax , then the divergent terms will be damped, and the limit where supersymmetry gets restored will exist.…”