Questions tagged [yang-mills-theory]

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3
votes
0answers
177 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 ...
9
votes
0answers
347 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-...
2
votes
0answers
153 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 $\...
1
vote
0answers
143 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{...
7
votes
1answer
369 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 $\mathfrak{h}^*[2]/W$ (...
20
votes
3answers
975 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. ...
8
votes
1answer
196 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 $\...
7
votes
3answers
1k 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 ...