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# High Energy Physics - Theory

# Title: Variational cohomology and topological solitons in Yang-Mills-Chern-Simons theories

(Submitted on 4 Mar 2021 (v1), last revised 16 Nov 2021 (this version, v4))

Abstract: We study a set of cohomology classes which emerge in the cohomological formulations of the calculus of variations as obstructions to the existence of (global) solutions of the Euler-Lagrange equations of Chern-Simons gauge theories in higher dimensions $2p+1 > 3$. It seems to be quite common to assume that such obstructions always vanish, at least in the cases of interest in theoretical physics. This is not so: for Yang-Mills-Chern-Simons theories in odd dimensions $> 5$ we find a non trivial obstruction which leads to a quite strong non existence theorem for topological solitons/instantons. Applied to holographic QCD this reveals then a possible mathematical inconsistency. For solitons in the important Sakai-Sugimoto model this inconsistency takes the form that their $\mathfrak{u}_1$-component cannot decay sufficiently fast to "extend to infinity" like the $\mathfrak{su}_n$-component.

## Submission history

From: Ekkehart Winterroth [view email]**[v1]**Thu, 4 Mar 2021 13:53:11 GMT (37kb)

**[v2]**Tue, 14 Sep 2021 17:03:15 GMT (52kb)

**[v3]**Mon, 11 Oct 2021 13:15:30 GMT (55kb)

**[v4]**Tue, 16 Nov 2021 15:14:06 GMT (34kb)

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