Abstract
We show that in D=4 AdS, s≥3/2 partially massless (PM) fermions retain the duality invariances of their flat space massless counterparts. They have tuned ratios m2/M2≠0 that turn them into sums of effectively massless unconstrained helicity ±(s,⋯,32) excitations, shorn of the lowest (non-dual) helicity ±12-rung and — more generally — of succeeding higher rung as well. Each helicity mode is separately duality invariant, like its flat space counterpart.
Highlights
IntroductionS = 3/2 is the basic, and long known, example of a dual invariant s = 3/2 tuned system [4]: In order to obtain the cosmological, necessarily AdS extension of SUGRA, one must add a mass term ∼ mψmσ mnψn to its massless action, with the tuning m ∼
We address, and complete the answer to, the question whether/how free m = 0 spin ≥ 1 systems can retain their known universal (D = 4) flat space duality invariance [1] when embedded in (A)dS, rather than flat, backgrounds
We show that in D = 4 AdS, s ≥ 3/2 partially massless (PM) fermions retain the duality invariances of their flat space massless counterparts
Summary
S = 3/2 is the basic, and long known, example of a dual invariant s = 3/2 tuned system [4]: In order to obtain the cosmological, necessarily AdS extension of SUGRA, one must add a mass term ∼ mψmσ mnψn to its massless action, with the tuning m ∼ The effect of this change is to restore the flat space commutativity, [∂μ, ∂ν ] = 0 → [Dμ, Dν ] = 0, thereby restoring the flat space invariance of the model under local spinor transformations, under δψμ = Dμα(x), and so again removing the lowest, helicity 1/2, excitation [5]. The governing variables are the transverse-traceless and γi -traceless spinor-spatial tensors ψitjT··T· , the PM invariance [3] always removes the lowest, here helicity 1/2, leaving an effectively massless (upon, legally, field redefining) array of helicities ±(s + 1/2, . . . , 3/2), each separately duality invariant, but at the above AdS point
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