| Autor: |
Gover, A. Rod, Peterson, Lawrence J., Sleigh, Callum |
| Předmět: |
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| Zdroj: |
Communications in Contemporary Mathematics; Mar2024, Vol. 26 Issue 2, p1-27, 27p |
| Abstrakt: |
We define a conformally invariant action on gauge connections on a closed pseudo-Riemannian manifold M of dimension 6. At leading order this is quadratic in the gauge connection. The Euler–Lagrange equations of , with respect to variation of the gauge connection, provide a higher-order conformally invariant analogue of the (source-free) Yang–Mills equations. For any gauge connection A on M , we define (A) by first defining a Lagrangian density associated to A. This is not conformally invariant but has a conformal transformation analogous to a Q -curvature. Integrating this density provides the conformally invariant action. In the special case that we apply to the conformal Cartan-tractor connection, the functional gradient recovers the natural conformal curvature invariant called the Fefferman–Graham obstruction tensor. So in this case, the Euler–Lagrange equations are exactly the "obstruction-flat" condition for 6-manifolds. This extends known results for 4-dimensional pseudo-Riemannian manifolds where the Bach tensor is recovered in the Yang–Mills equations of the Cartan-tractor connection. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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