Questions tagged [yang-mills-theory]
The yang-mills-theory tag has no usage guidance.
17
questions
-5
votes
0
answers
33
views
What is wrong with these solutions? Yang-Mills problem in R4? [closed]
My question would be what is wrong with these solutions of the Yang-Mills problem?
https://arxiv.org/pdf/2203.14279.pdf
https://link.springer.com/content/pdf/10.1134/S1061920820010033.pdf
https://www....
- 1
2
votes
1
answer
412
views
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:...
CommunityBot
- 1
1
vote
0
answers
123
views
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 ...
- 996
7
votes
0
answers
313
views
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 ...
- 33.9k
5
votes
0
answers
101
views
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) &...
- 653
2
votes
0
answers
242
views
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.
...
- 5,879
2
votes
0
answers
208
views
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 ...
- 641
19
votes
2
answers
869
views
A non-Abelian de Rham complex?
This question is inspired by this physics stack exchange post, which is recent and has not received an answer yet, nontheless I feel that there is a better way to ask this question here with a larger ...
- 3,984
1
vote
1
answer
368
views
Yang-Mills over surfaces
For a principal bundle $(P,\nabla)\to M$ over a Riemann surface with fiber $G$, the Yang-Mills equation is $\nabla *F=0$, where $*F$ is dual of the curvature with respect to a fixed metric on the ...
- 21.5k
5
votes
0
answers
376
views
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 ...
- 10.3k
10
votes
0
answers
1k
views
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-...
- 10.3k
2
votes
0
answers
213
views
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 $\...
- 10.3k
7
votes
1
answer
553
views
Implications of gauge symmetry breaking on the spectral side of geometric Langlands?
Let $G$ be a complex reductive algebraic group and $X$ be a smooth compact complex curve. It's easy to see that the space of vacua in B-twisted $N=4$ SUSY Yang--Mills theory is $\mathfrak{h}^*[2]/W$ (...
1
vote
0
answers
527
views
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{...
- 10.3k
23
votes
3
answers
2k
views
What are the applications of the Atiyah-Bott Yang Mills paper?
I recently finished a seminar going through Atiyah and Bott's paper ''The Yang-Mills Equations over Riemann surfaces''. The ideas going into the proof were surprising and very beautiful to me.
...
- 19.2k
8
votes
1
answer
306
views
Deformation-Obstruction Theory of YM Instantons
In Donaldson-Kronhiemer Section 4.2.5. (local models of the moduli space of YM instantons) they first get local models of the moduli space $M$ inside the space of all connections modulo gauge $\...
- 34k
11
votes
3
answers
3k
views
About Simon Donaldson's book on four dimensional manifold
Recently I'm reading Donaldson's Geometry of four manifolds. It seems to me that the book requires a lot for background. Additionally, the proof in the book is too sketchy without too much detail. I ...
- 714