https://doi.org/10.1140/epjc/s10052-022-10734-x
Regular Article - Theoretical Physics
Gauge symmetry of linearised Nordström gravity and the dual spin two field theory
1
Physics Faculty, Tomsk State University, Lenin ave. 36, 634050, Tomsk, Russia
2
Departamento de Matemática Aplicada, Universidade Federal do Rio de Janeiro, Av. Athos da Silveira Ramos 149, Centro de Tecnologia, Bloco C, 21941-909, Rio de Janeiro, RJ, Brazil
Received:
29
June
2022
Accepted:
18
August
2022
Published online:
2
September
2022
The field equations are proposed for the third rank tensor field with the hook Young diagram. The equations describe the irreducible spin two massless representation in any 
. The starting point of the construction is the linearised system of Einstein equations which includes the Nordström equation. This equation, being considered irrespectively to the rest of the Einstein system, corresponds to the topological field theory. The general solution is a pure gauge, modulo topological modes which we neglect in this article. We find the sequence of the reducible gauge transformations for the linearised Nordström equation, with the hook tensor being the initial gauge symmetry parameter. By substituting the general solution of the Nordström equation into the rest of the Einstein’s system, we arrive at the field equations for the hook tensor. The degree of freedom number count confirms, it is the spin two theory.
© The Author(s) 2022
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