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#### Comments on Higher-Spin Fields in Nontrivial Backgrounds

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1603.03050.pdf

(Preprint), 245KB

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##### Citation

Rahman, R., & Taronna, M. (2017). Comments on Higher-Spin Fields in Nontrivial
Backgrounds. In L. Brink (*Higher Spin Gauge Theories*
(pp. 381-390). Singapur: World Scientific.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002A-C18A-8

##### Abstract

We consider the free propagation of totally symmetric massive bosonic fields

in nontrivial backgrounds. The mutual compatibility of the dynamical equations

and constraints in flat space amounts to the existence of an Abelian algebra

formed by the d'Alembertian, divergence and trace operators. The latter, along

with the symmetrized gradient, symmetrized metric and spin operators, actually

generate a bigger non-Abelian algebra, which we refer to as the "consistency"

algebra. We argue that in nontrivial backgrounds, it is some deformed version

of this algebra that governs the consistency of the system. This can be

motivated, for example, from the theory of charged open strings in a background

gauge field, where the Virasoro algebra ensures consistent propagation. For a

gravitational background, we outline a systematic procedure of deforming the

generators of the consistency algebra in order that their commutators close. We

find that equal-radii AdSp X Sq manifolds, for arbitrary p and q, admit

consistent propagation of massive and massless fields, with deformations that

include no higher-derivative terms but are non-analytic in the curvature. We

argue that analyticity of the deformations for a generic manifold may call for

the inclusion of mixed-symmetry tensor fields like in String Theory.

in nontrivial backgrounds. The mutual compatibility of the dynamical equations

and constraints in flat space amounts to the existence of an Abelian algebra

formed by the d'Alembertian, divergence and trace operators. The latter, along

with the symmetrized gradient, symmetrized metric and spin operators, actually

generate a bigger non-Abelian algebra, which we refer to as the "consistency"

algebra. We argue that in nontrivial backgrounds, it is some deformed version

of this algebra that governs the consistency of the system. This can be

motivated, for example, from the theory of charged open strings in a background

gauge field, where the Virasoro algebra ensures consistent propagation. For a

gravitational background, we outline a systematic procedure of deforming the

generators of the consistency algebra in order that their commutators close. We

find that equal-radii AdSp X Sq manifolds, for arbitrary p and q, admit

consistent propagation of massive and massless fields, with deformations that

include no higher-derivative terms but are non-analytic in the curvature. We

argue that analyticity of the deformations for a generic manifold may call for

the inclusion of mixed-symmetry tensor fields like in String Theory.