2016/03/29 by Rakibur Rahman, Massimo Taronna · 1 citation
Mathematics · Physics and Astronomy · #Abelian group #Advanced Operator Algebra Research #Algebra over a field #Black Holes and Theoretical Physics #Consistency (knowledge bases) #Manifold (fluid mechanics) #Massless particle #Quantum Chromodynamics and Particle Interactions #String theory #Symmetric tensor #TRACE (psycholinguistics) #Tensor (intrinsic definition) #Tensor field #hep-th
paper · pdf · doi:10.1142/9789813144101_0020
typos corrected, references added; contributed to the proceedings of the "International Workshop on Higher Spin Gauge Theories", Singapore 4-6 November 2015
arxiv created 2016/03/29 · openalex created_date 2016/06/24 · openalex publication_date 2016/10/27 · arxiv updated 2016/11/23 · openalex updated_date 2026/08/05
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.