Questions tagged [yang-mills-theory]

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Yang-Mills theory with non-compact gauge groups G

Physicists are familiar working with Yang-Mills theory with compact and semi-simple gauge groups $G$ (Lie groups). However, it is not entirely clear the formulation of Yang-Mills theory with non-...
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Existence of Yang-Mills connection

My question is about what we know, in dimension $4$, about the loss of compactness of Yang–Mills connections with $L^2$-bounded curvature. My background is more analytical than geometrical and it is ...
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Standard 2-instantons on the 4-sphere under conformal transformation

It is well-known that there is a standard SU(2) 1-instanton on the 4-sphere and any 1-instanton can be obtained from the standard one by conformal transformation. Is there any explicit (family of) &...
Faniel's user avatar
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Yang-Mills theory v.s. Kaluza–Klein theory: Classical actions

In general Yang-Mills theory [1] seems to be different from the dimensional reduced Kaluza–Klein theory. However, the historical account was that people tried to trace back the origin of non-Abelian ...
wonderich's user avatar
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A question about the book "the geometry and dynamics of magnetic monopoles"

In chapter 2 of the book "The geometry and dynamics of magnetic monopoles", by M.F. Atiyah and N.J. Hitchin (the chapter is called "Geometry of the monopole spaces"), it is written:...
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Do Chern-Simons terms qualitatively alter the behavior of the Yang-Mills gradient flow?

I'm reading about the Yang-Mills heat flow, and I'm curious how adding a Chern-Simons term alters its solutions. This is probably elementary or folklore, but I don't know well enough to say. ...
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What does the Yang-Mills flow and the Yang-Mills QFT tell about each other?

What are some known examples of what the Yang-Mills Quantum Field Theory can tell about solutions to Yang-Mills heat equation? In general, what are some known examples of what the QFT of a Lagrangian ...
Andrew McHugh's user avatar
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Define a (lattice) Yang-Mills theory on $\mathbb{T}^4$ v.s. $\mathbb{R}^4$

Pure Yang-Mills theory (YM) can be easily defined on $\mathbb{T}^4$ on a periodic lattice, using the Wilson lattice gauge theory approach. In reality, we know some of these mathematical results on $\...
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1 vote
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Heat kernel coefficients for Laplacian in instanton background

The heat kernel coefficients $b_{2k}(x,y)$ of the covariant Laplacian in an $SU(2)$ instanton background (for simplicity let's say $q=1$ topological charge, so the 't Hooft solution) on $R^4$ is ...
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Conventions / Normalizations of Yang-Mills Field Theories

Let the spacetime be 4-dimensional. In the usual Maxwell theory of Abelian gauge fields $A$, where field strength $F=dA$ one considers the Maxwell action written as $$ S_{Maxwell}\equiv\int -\frac{...
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