Geometry of Special Galileon

Abstract

Theory known as Special Galileon has recently attracted considerable interest due to its peculiar properties. It has been shown that it represents an extremal member of the set of effective field theories with enhanced soft limit. This property makes its tree-level S-matrix fully on-shell reconstructible and representable by means of the Cachazo-He-Yuan representation. The enhanced soft limit is a consequence of new hidden symmetry of the Special Galileon action, however, until now, the origin of this peculiar symmetry has remained unclear. In this paper we interpret this symmetry as a special transformation of the coset space $GAL(D,1)/SO(1,D-1)$ and show, that there exists a three-parametric family of invariant Galileon actions. The latter family is closed under duality which appears as a natural generalization of the above mentioned symmetry. We also present a geometric construction of the Special Galileon action using $D$-dimensional brane propagating in $2D$-dimensional flat pseudo-riemannian space. Within such framework, the Special Galileon symmetry emerges as an $U(1,D-1)$ symmetry of the target space, which can be treated as a $D$-dimensional Kähler manifold. Such a treatment allows for classification of the higher order invariant Lagrangians needed as counterterms on the quantum level. We also briefly comment on relation between such higher order Lagrangians and the Lagrangians invariant with respect to the polynomial shift symmetry.

42 pages, 8 figures

References in corpus (15)

• Resummation of Massive Gravity
• Generalized Galileons: All scalar models whose curved background extensions maintain second-order field equations and stress tensors
• DBI and the Galileon reunited
• Effective Field Theories from Soft Limits
• Multi-field galileons and higher co-dimension branes
• A Periodic Table of Effective Field Theories
• Symmetries for Galileons and DBI scalars on curved space
• Non-Renormalization and Naturalness in a Class of Scalar-Tensor Theories
• Galileons as Wess-Zumino Terms
• Generalized Galileon Duality
• Nonlinear realizations of symmetries and unphysical Goldstone bosons
• Unification of Galileon Dualities
• Goldstones with Extended Shift Symmetries
• Inequivalence of Coset Constructions for Spacetime Symmetries
• Quantum Corrections in Galileons from Matter Loops

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• Nonrelativistic effective field theories with enhanced symmetries and soft behavior
• Gauged Galileons
• Shift Symmetries for p-Forms and Mixed Symmetry Fields on (A)dS