An algebraic classification of exceptional EFTs

Roest, Diederik; Stefanyszyn, David; Werkman, Pelle

doi:10.1007/jhep08(2019)081

Cited by 31 publications

(63 citation statements)

References 97 publications

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“…Effective field theories for a massless vector field in flat space do not exhibit enhanced single soft limits [15]. Similar results were obtained by studying the algebras that such shift symmetries would imply [16][17][18][19][20]. However, in de Sitter (dS) and anti-de Sitter (AdS) space there is a richer variety of possible single-field theories with shift symmetries [21].…”

Section: Introductionsupporting

confidence: 66%

Shift-symmetric spin-1 theories

Bonifacio

Hinterbichler

Johnson

et al. 2019

J. High Energ. Phys.

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We study interacting massive spin-1 theories in de Sitter (dS) and anti-de Sitter (AdS) space that possess shift symmetries parametrized by (A)dS Killing vectors. We show how they emerge from the massless limit of massive spin-2 theories on (A)dS space. In the case of massive gravity, the corresponding spin-1 theory realizes a symmetry breaking pattern that takes two copies of the (A)dS isometry group down to a diagonal subgroup. By taking the flat space limit of this theory, we find a new symmetry of the decoupling limit of massive gravity in flat space. This symmetry acts on the vector modes, is parametrized by an antisymmetric tensor, and fixes the nonlinear structure of the scalar-vector sector of the decoupling limit.

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Section: Introductionsupporting

confidence: 66%

Shift-symmetric spin-1 theories

Bonifacio

Hinterbichler

Johnson

et al. 2019

J. High Energ. Phys.

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“…and there is no allowed region of parameter space (c.f. (40)), at least for a single massive spin-2 EFT whose Abelian gauge symmetry is broken in the NDA power counting (2). Interestingly, the same is not true for the non-Abelian symmetry (i.e.…”

Section: Positivity and The Nature Of Uv Completionmentioning

confidence: 98%

UV constraints on massive spinning particles: lessons from the gravitino

Melville

Roest

Stefanyszyn

2020

J. High Energ. Phys.

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Self-interacting massive particles with spin ≥ 1 unavoidably violate unitarity; the question is at what scale. For spin-1 the strong coupling scale (at which perturbative unitarity is lost) cannot be raised by any finite tuning of the interactions, while for spin-2 there exists a special tuning of the Wilson coefficients which can raise this scale (and enjoys numerous special properties such as ghost-freedom). Here, we fill in the missing piece by describing how the self-interactions of a massive spin-3/2 field, or "massive gravitino", become strongly coupled at high energies. We show that while several different structures appear in the leading order potential, the strong coupling scale cannot be raised (in the absence of additional fields). At the level of the off-shell Lagrangian, it is always the non-linear symmetries of the longitudinal Stückelberg mode that dictate the strong coupling, and we show that in general it is only possible to parametrically raise the strong coupling scale if Wess-Zumino structures exist for these symmetries. We complement this off-shell approach with a first analysis of positivity bounds for a massive spin-3/2 particle, showing that any potential self-interaction which contributes to an on-shell 2-to-2 elastic process at tree level must vanish if this low-energy theory is to have a standard UV completion. We identify the mixing between the longitudinal mode and the transverse modes as the main obstacle to positivity, and clarify how the non-Abelian nature of non-linear (dRGT) massive gravity allows it to satisfy positivity where all known spin ≥ 3/2 Abelian theories fail. Our results imply that a massive gravitino cannot appear alone in a controlled EFT-it must be accompanied by other particles, e.g. as part of a supermultiplet. Together with the spin-1 and spin-2 cases, we suggest features which will persist in even higher spin massive theories.In this paper we fill in the gap between spin-1 and spin-2 by studying the EFT of a massive, self-interacting spin-3/2 field [6], which we shall refer to as a "massive gravitino" (although we are not considering supermultiplets). Such particles appear in many areas of physics-e.g. as QCD resonances, in supergravity and string theoryhowever a detailed study of their possible self-interactions is, until now, absent from the literature. We will approach the massive gravitino EFT from two complementary perspectives: an off-shell analysis of the strong coupling scales appearing in the Lagrangian (signalling when new physics must become important), and an on-shell analysis of the positivity properties of scattering amplitudes (revealing whether this new physics can be consistent with standard QFT axioms), drawing various parallels with the spin-1 and spin-2 cases as we proceed. By completing the catalogue of massive fields with spins ≤ 2, we will draw some general conclusions/conjectures for arbitrary spin.On the strong coupling side, if we assume a simple EFT power counting (naive dimensional analysis, or NDA [7,8]) in which the gauge invariant...

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“…From further Jacobi identities, we can again conclude that the generator content of the inverse Higgs tree at order n coincides with the Lorentz representations at nth order in a Taylor expansion of a spin-s field. [76,79] This is of course very reminiscent of the symmetry transformations (2.90) we examined in section 2.5. We will argue below that precisely these symmetry transformations result from the coset construction for a scalar essential Goldstone.…”

Section: Extended Shift Symmetries and Ihcsmentioning

confidence: 73%

“…[54] [141] As we will see, these conditions enable us to classify all possible non-linear symmetry algebras that can be realized on a particular choice of Goldstone fields, under minimal assumptions. [76] [77] [78] [79] We will cover the coset construction for space-time symmetries in detail in section 3.2, but leave the explanation of the EFT classification for the following chapter.…”

Section: Chaptermentioning

confidence: 99%