Multi-spin soft bootstrap and scalar-vector Galileon

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In this work, higher-derivative corrections of the non-linear sigma model of both even and odd intrinsic-parity sectors are systematically studied, focusing on ordered amplitudes of flavor scalars in massless limit. It should correspond to a theory known as chiral perturbation theory (ChPT) without external sources and with only single-trace operators. We briefly overview its formal development and apply new S-matrix methods to its amplitude constructions. The bottom-up analysis of the tree-level amplitudes of different orders and multiplicities focuses on the formal structure of general ChPT. Possible theoretical simplifications based on the Kleiss-Kuijf and Bern-Carrasco-Johansson relations are presented. Finally, in the same context, the comparison with the so-called Z-function, which is connected with string theory, is also discussed.

Section: Jhep12(2021)140mentioning

confidence: 99%

The ChPT: top-down and bottom-up

Kampf

2021

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“…Also the theories which couple photons (or massless vector particles) to Goldstone bosons can be reconstructible from their soft limits. This is the case for the Special scalarvector Galileon and its generalizations discussed recently in [38]. In this theory, which is a single-ρ theory with ρ = 2, the enhanced Adler zero condition for the soft scalars is combined with the generalized soft theorem for the soft photons.…”

Section: Jhep10(2021)101mentioning

confidence: 95%

“…This applies e.g. to the case of exceptional scalar field theories (the nonlinear sigma model (NLSM), the DBI scalar, the Special Galileon), vector theories (Born-Infeld electrodynamics) or scalar-vector theories (the Special scalar-vector Galileon [38]), all of which can be uniquely reconstructed from the corresponding soft limits [33]. Some of these theories were discovered first just by constructing their tree-level amplitudes and only then identified with a particular Lagrangian.…”

Section: Introductionmentioning

confidence: 99%

Extended DBI and its generalizations from graded soft theorems

Kampf

Novotný

Vasko

2021

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We analyze a theory known as extended DBI, which interpolates between DBI and the U(N) × U(N)/U(N) non-linear sigma model and represents a nontrivial example of theories with mixed power counting. We discuss symmetries of the action and their geometrical origin; the special case of SU(2) extended DBI theory is treated in great detail. The revealed symmetries lead to a new type of graded soft theorem that allows us to prove on-shell constructibility of the tree-level S-matrix. It turns out that the on-shell constructibility of the full extended DBI remains valid, even if its DBI sub-theory is modified in such a way to preserve its own on-shell constructibility. We thus propose a slight generalization of the DBI sub-theory, which we call 2-scale DBI theory. Gluing it back to the rest of the extended DBI theory gives a new set of on-shell reconstructible theories — the 2-scale extended DBI theory and its descendants. The uniqueness of the parent theory is confirmed by the bottom-up approach that uses on-shell amplitude methods exclusively.

“…The principal idea then is to redefine F ns (z) so that the contribution from the pole at infinity still vanishes, and use subleading terms from soft theorems to determine additional poles from F ns (z) in the contour integral (4.31). Soft theorems encoding information beyond the soft scaling of scattering amplitudes can be used as input in soft bootstrap techniques to extend the exploration of the EFT landscape [26,58], but this is beyond the scope of the present work.…”

Section: Jhep03(2022)086mentioning

confidence: 99%

“…Apart from analyzing the properties of already known theories, the novel on-shell recursion relations for EFTs have been utilized to further explore the landscape of EFTs with enhanced symmetries and soft limits [21,22,24,25]. Very recently, the same philosophy was also applied to EFTs with universal albeit not necessarily vanishing soft behavior of the S-matrix [26]. The combination of on-shell recursion relations and soft theorems has developed into a full-fledged soft bootstrap program [22].…”

Section: Introductionmentioning

confidence: 99%

Nonrelativistic effective field theories with enhanced symmetries and soft behavior

Mojahed

Brauner

2022

We systematically explore the landscape of nonrelativistic effective field theories with a local S-matrix and enhanced symmetries and soft behavior. The exploration is carried out using both conventional quantum field theory methods based on symmetry arguments, and recently developed on-shell recursion relations. We show that, in contrary to relativistic theories, enhancement of the soft limit of scattering amplitudes in nonrelativistic theories is generally not a byproduct of symmetry alone, but requires additional low-energy data. Sufficient conditions for enhanced scattering amplitudes can be derived by combining symmetries and dispersion relations of the scattered particles. This has direct consequences for the infrared dynamics that different types of nonrelativistic Nambu-Goldstone bosons can exhibit. We then use a bottom-up soft bootstrap approach to narrow down the landscape of nonrelativistic effective field theories that possess a consistent low-energy S-matrix. We recover two exceptional theories of a complex Schrödinger-type scalar, namely the ℂP1 nonlinear sigma model and the Schrödinger-Dirac-Born-Infeld theory. Moreover, we use soft recursion to prove a no-go theorem ruling out the existence of other exceptional Schrödinger-type theories. We also prove that all exceptional theories of a single real scalar with a linear dispersion relation are necessarily Lorentz-invariant. Soft recursion allows us to obtain some further general bounds on the landscape of nonrelativistic effective theories with enhanced soft limits. Finally, we present a novel theory of a complex scalar with a technically natural quartic dispersion relation. Altogether, our work represents the first step of a program to extend the developments in the study of scattering amplitudes to theories without Lorentz invariance.