Geometry of Multiflavor Galileon-Like Theories

Abstract

We use Lie-algebraic arguments to classify Lorentz-invariant theories of massless interacting scalars that feature coordinate-dependent redundant symmetries of the Galileon type. We show that such theories are determined, up to a set of low-energy effective couplings, by specifying an affine representation of the Lie algebra of physical, non-redundant internal symmetries and an invariant metric on its target space. This creates an infinite catalog of theories relevant for both cosmology and high-energy physics thanks to their special properties such as enhanced scaling of scattering amplitudes in the soft limit.Dedicated to Jiří Hošek on the occasion of his 75 th birthday.

An algebraic classification of exceptional EFTs

“…The Jacobi identity (P, P, G) imposes [P, K] ∝ D + M for the vector inessential K of the dilaton D. This means that K necessarily generates a type of special conformal transformation. Because the case Z max = 1 without the dilaton was considered in [10,11], we will focus on what changes when the dilaton is included. We define our generators as follows: the scalar generator D is the dilaton.…”

“…Recently, much effort has been devoted to classifying EFTs using both on-shell methods [1] (constructing amplitudes using minimal assumptions, see e.g. [2][3][4][5][6][7][8][9] and references therein), and Lie-algebras (classifying the algebras that dictate the structure of these amplitudes [10][11][12]). Both approaches are completely insensitive to the Lagrangian basis for the Goldstone self-interactions and hence avoid Lagrangian redundancies associated with non-linear field redefinitions.…”

“…Given that these symmetries have to form a consistent Lie-algebra with the Poincaré symmetries and the U(1), a Lie-algebraic classification is also a very efficient way of examining the existence of these special EFTs and indeed those consisting of other irreducible representations of the Lorentz group. This approach is complementary to the amplitudes one and has been explored for scalars in [10,11] and Abelian gauge vectors in [12]. Our primary aim in this paper is to outline an algorithm to efficiently derive all possible algebras which can be non-linearly realised on a given set of Goldstone fields of any spin under three assumptions:…”

An algebraic classification of exceptional EFTs. Part II. Supersymmetry

“…One can therefore ask which Lie-algebras are consistent within the framework of the coset construction for non-linear realisations [19][20][21] augmented with the crucial inverse Higgs phenomenon 3 [22]. For scalar EFTs Lie-algebraic approaches have been presented in [23,24] while in [25] these methods were used to prove that a gauge vector cannot be a Goldstone mode of a spontaneously broken space-time symmetry without introducing new degrees of freedom. This implies that the Born-Infeld (BI) vector is not special from the perspective of non-linear symmetries and enhanced soft limits (the same result was found in [8] where it was shown that the BI vector has a vanishing soft weight).Recently, we presented an algorithm for an exhaustive classification of the possible algebras which can be non-linearly realised on a set of Goldstone modes with linearly realised Poincaré symmetries 4 and canonical propagators in [26].…”

“…This algebra also appeared in[24] and let us note that it is not clear if there exists a sensible realisation where both scalars have canonical kinetic terms. However, we will see in a moment that even if this theory existed, it cannot be supersymmetrised.…”