2014/01/31 by P. Salgado, Patricio Salgado, Richard J. Szabo +1 · 1 citation
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Coset #Cosmology and Gravitation Theories #Gauge group #Gauge theory #Group (periodic table) #Invariant (physics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Nonlinear system #Physics #Poincaré conjecture #Poincaré group #Quantum mechanics #Scalar field #Sigma model #String theory #Supergravity #Supersymmetry #Topology (electrical circuits) #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.1103/physrevd.89.084077
published as Phys. Rev. D 89, 084077 Published 30 April 2014 · 22 pages; v2: minor corrections, references added; v3: analysis involving Maxwell algebra expanded, references added; v4: referencing fixed; Final version to be published in Physical Review D
arxiv created 2014/04/14 · openalex publication_date 2014/04/30 · arxiv updated 2014/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We show that Poincar'e-invariant topological gravity in even dimensions can be formulated as a transgression field theory in one higher dimension whose gauge connections are associated to linear and nonlinear realizations of the Poincar'e group ISO(d\ensuremath-1,1). The resulting theory is a gauged Wess-Zumino-Witten (WZW) model whereby the transition functions relating gauge fields live in the coset \fracISO(d\ensuremath-1,1)SO(d\ensuremath-1,1). The coordinate parametrizing the coset space is identified with the scalar field in the adjoint representation of the gauge group of the even-dimensional topological gravity theory. The supersymmetric extension leads to topological supergravity in two dimensions starting from a transgression field theory which is invariant under the supersymmetric extension of the Poincar'e group in three dimensions. We also apply this construction to a three-dimensional Chern-Simons theory of gravity which is invariant under the Maxwell algebra and obtain the corresponding WZW model.