For targets
For targets
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For targets
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Chern-Simons-
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for targets
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topological AdS7/CFT6-sector
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Topological Yang-Mills theory is a gauge theory topological quantum field theory .
For $X$ a 4-dimensional smooth manifold, $\mathfrak{g}$ a Lie algebra with Lie group $G$ and $\langle-,-\rangle \in W(\mathfrak{g})$ a binary invariant polynomial on $\mathfrak{g}$, topological Yang-Mills theory is the quantum field theory defined by the action functional
on the groupoid of $G$-principal bundles with connection on a bundle that sends a connecton $\nabla$ to the integral of the curvature 4-form $\langle F_\nabla \wedge F_\nabla \rangle$ of the corresponding Chern-Simons circle 3-bundle:
The ordinary kinetic term of Yang-Mills theory differs from this by the fact that the Hodge star operator appears $\langle F_\nabla \wedge \star F_\nabla \rangle$. In full Yang-Mills theory both terms appear.
The topological Yang-Mills action also appears in the generalized Chern-Simons theory given by a Chern-Simons element in a Lie 2-algebra, where it is coupled to BF-theory. See Chern-Simons element for details.
A general account emphasizing the relation to Chern-Simons theory is
The relation to Chern-Simons theory on the boundary in an ambient string theoretic context is indicated in section 2 (starting around p. 21) of
Last revised on September 21, 2016 at 14:41:25. See the history of this page for a list of all contributions to it.