Causality constraints on nonlinear supersymmetry. (arXiv:2206.13451v3 [hep-th] UPDATED)
<a href="http://arxiv.org/find/hep-th/1/au:+Bonnefoy_Q/0/1/0/all/0/1">Quentin Bonnefoy</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Casagrande_G/0/1/0/all/0/1">Gabriele Casagrande</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Dudas_E/0/1/0/all/0/1">Emilian Dudas</a>
It is well-known that gravitino propagation in standard supergravities is
free of any causality problems. However, two issues related to gravitino
propagation were recently uncovered in specific supergravities with nonlinear
supersymmetry. One of them concerns potential acausality/superluminality,
whereas the second one arises from the vanishing of the sound speed at specific
points during inflation. The former is famously related to positivity
constraints on specific EFT operators, derived from dispersion relations on the
energy-growing part of scattering amplitudes, and indeed we show that
subluminality constraints for the gravitino are related via the equivalence
theorem to positivity bounds in low-energy goldstino actions. However, the
former are stronger, in the sense that they apply to functions of the scalar
fields not only in the ground state, but for any field values such as those
scanned by time-dependent solutions, unlike bounds derived from $2to 2$
scattering amplitudes in the vacuum. We also argue that nontrivial causality
constraints arise only in the case where nonlinear supersymmetry in the matter
sector is encoded into superfield constraints which do not seem to arise from
microscopic two-derivative lagrangians, in particular for the orthogonal
constraint used to build minimal models of inflation in supergravity. This
allows us to propose simple alternatives which maintain the minimality of the
spectra and are causal in all points of the theory parameter space. We also
discuss minimal supergravity models of inflation along these lines.
It is well-known that gravitino propagation in standard supergravities is
free of any causality problems. However, two issues related to gravitino
propagation were recently uncovered in specific supergravities with nonlinear
supersymmetry. One of them concerns potential acausality/superluminality,
whereas the second one arises from the vanishing of the sound speed at specific
points during inflation. The former is famously related to positivity
constraints on specific EFT operators, derived from dispersion relations on the
energy-growing part of scattering amplitudes, and indeed we show that
subluminality constraints for the gravitino are related via the equivalence
theorem to positivity bounds in low-energy goldstino actions. However, the
former are stronger, in the sense that they apply to functions of the scalar
fields not only in the ground state, but for any field values such as those
scanned by time-dependent solutions, unlike bounds derived from $2to 2$
scattering amplitudes in the vacuum. We also argue that nontrivial causality
constraints arise only in the case where nonlinear supersymmetry in the matter
sector is encoded into superfield constraints which do not seem to arise from
microscopic two-derivative lagrangians, in particular for the orthogonal
constraint used to build minimal models of inflation in supergravity. This
allows us to propose simple alternatives which maintain the minimality of the
spectra and are causal in all points of the theory parameter space. We also
discuss minimal supergravity models of inflation along these lines.
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