Tensor Galileons and Gravity

Abstract

The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian $p$-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to $p$-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

24 pages; v2: references added, minor clarifications

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• Higher Derivative Field Theories: Degeneracy Conditions and Classes
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• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded mechanics: the classical theory
• ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$-graded mechanics: the quantization
• The Graded Differential Geometry of Mixed Symmetry Tensors
• Pseudo-Linear Spin-2 Interactions
• Classifying Galileon $p$-form theories
• Gauged Galileons
• Relation between standard and exotic duals of differential forms
• A unified approach to standard and exotic dualizations through graded geometry
• Duality and higher Buscher rules in p-form gauge theory and linearized gravity
• Impossible Symmetries and Conformal Gravity
• A different kind of four dimensional brane for string theory
• Tensor Galileons as Lovelock theories
• Instances of Higher Geometry in Field Theory
• Graded Geometry and Tensor Gauge Theories