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Yang-Mills connections and sigma-models on quantum Heisenberg manifolds | | Stine Marie Berge
; Sooran Kang
; Franz Luef
; | | Date: |
27 Mar 2022 | | Abstract: | We associate to a spectral triple of a quantum Heisenberg manifold an energy
functional on the set of projections, following the approach of
Mathai-Rosenberg to non-linear sigma models. We derive a lower bound for this
energy functional that depends on the topological charge of the projection
which depends on the curvature of a compatible connection. A detailed study of
this lower bound is given for the Kang projection in quantum Heisenberg
manifolds. These results display an intriguing interplay between non-linear
sigma models and Yang-Mills theory on quantum Heisenberg manifolds, unlike in
the well-studied case of noncommutative tori. | | Source: | arXiv, 2203.14279 | | Services: | Forum | Review | PDF | Favorites | |
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