On Extended Supersymmetry of 4d Galileons and 3-Brane Effective Actions

Abstract

We use on-shell amplitude methods to systematically analyze the possibility of extended supersymmetry for 4d Galileon models, expanding on previous N = 1 results. Assuming spins ≤ 1, we prove that there exists no N = 4 supersymmetric extension of any 4d Galileons. Thus the Galileons cannot be part of the effective action of a single flat maximally supersymmetric D3-brane, and that explains why such terms do not appear in the α -expansion of the abelian open superstring amplitude. For N = 2 Galileons, we show that the complex scalar Z = φ + iχ of the vector supermultiplet cannot have φ and χ both enjoy enhanced shift symmetry; instead, χ can at best be an R-axion with constant shift symmetry. Using the soft bootstrap, we demonstrate that the quartic DBI-Galileon is incompatible with N = 2 supersymmetry. A similar analysis performed at 7-point shows that a 2-parameter family of N = 2 supersymmetric quintic Galileons coupled with DBI passes the soft bootstrap. Finally, we show how supersymmetric couplings between Galileons and gravitons arise in generalizations of our constructions, and we conclude with a discussion of Galileons and DBI-Galileons in the context of UV-completability vs. the Swampland.

Supersymmetric Massive Gravity

“…Here we see how to evade the no-go theorem of [123]. In the absence of the SU(4) global tensor structures the above analysis gives the same result but without the Levi-Civita symbols, and so the unique N = 4 compatible amplitude at six-derivative order is proportional to s + t + u = 0.…”

“…Unfortunately, there is actually a subtle difference between the assumptions made in [123] and the present analysis, and the no-go theorem does not apply in this case. To see this we will explicitly construct the most general form of the superamplitude (6.2).…”

“…Following the logic of section 4.2, an easier approach to studying higher-multiplicity interactions may be to first construct a massless supersymmetric model describing the decoupling limit. The problem of constraining models of a supersymmetric Galileon has been considered [118][119][120][121][122][123], and we might hope to make use of these results to constrain supersymmetric massive gravity. Of particular interest, [123] recently proved an interesting no-go theorem for Galileons in N = 4 supersymmetric models.…”

“…The problem of constraining models of a supersymmetric Galileon has been considered [118][119][120][121][122][123], and we might hope to make use of these results to constrain supersymmetric massive gravity. Of particular interest, [123] recently proved an interesting no-go theorem for Galileons in N = 4 supersymmetric models. Below we will re-derive this result in detail and discuss why it does not lead to any constraints on an N = 4 supersymmetric model of massive gravity.…”

“…Therefore the above quartic Galileon amplitude must be valid in that case also with the modification that we must set α 3 = −1/2 to satisfy the cubic constraints derived in section 3.2. The no-go theorem of [123] is the claim that the amplitude (6.5) cannot be obtained from an N = 4 supersymmetric model if the Galileon φ is a combination of scalars in a massless vector multiplet. This would seem to be consistent with a maximally R-symmetric model of N = 4 massive gravity only if the prefactor in the above expression vanishes, giving α 4 = 9/64.…”