All Questions
25
questions
6
votes
1
answer
2k
views
What is the current status (October 2021) of the Yang-Mills existence and mass gap problem?
One of the famous "millennium prize problems" is the "Yang–Mills existence and mass gap" problem, which in its official description by E. Witten and A. Jaffe has the following form:...
- 1,540
2
votes
1
answer
377
views
Magnetic monopoles in an $SU(2)$ gauge theory
I had heard from a professor saying that "Polyakov and ’tHooft discover the magnetic monopoles in $SU(2)$ gauge theory with scalar fields [Georgi-Glashow model]." And he cited two references:...
- 4,336
4
votes
1
answer
151
views
Mass terms in the SUSY gauged linear sigma model
Okay, I have a very basic question about the SUSY gauged linear sigma model which is driving me crazy. I am following Chapter $15$ of Mirror Symmetry by Hori et al. I am considering the SUSY gauged ...
- 577
1
vote
0
answers
281
views
Instantons in Minkowski spacetime? or only valid in Euclidean spacetime?
In the usual description of the instanton of nonabelian gauge theory in $D=4$ spacetime, we always (or just usually?) choose the $D=4$ Euclidean spacetime see for example https://en.wikipedia.org/wiki/...
- 4,336
7
votes
0
answers
212
views
Where do theta terms live?
Consider a gauge theory with group $G$. The canonical kinetic term for the gauge field is $F\wedge\star F$ and, depending on the dimensionality of spacetime, there are other allowed terms, such as ...
2
votes
0
answers
154
views
Exotic perturbative anomaly captured only by higher-loop Feynman graphs, but not by any 1-loop Feynman graph?
My question: Are there any perturbative anomaly captured by higher-loop but not by captured at the 1-loop Feynman graph (say, not enough)?
We are familiar with the text book example of a ...
- 4,336
6
votes
1
answer
206
views
What classifies gaugings?
Gauging a global symmetry $G$ introduces several free parameters to the theory. For example,
In $d=4$, gauging a simple and simply-connected Lie group introduces a coupling constant and a theta term, ...
7
votes
0
answers
108
views
Can you do gauge theories over topological groups?
Quantum gauge theories involve (functional) integration over a Lie group. Is there any meaningful generalisation to (non-manifold) topological groups?
Consider for example the Whitehead tower
$$
\...
14
votes
1
answer
2k
views
How to identify higher-form symmetries?
A $q$-form symmetry is a symmetry that naturally acts on objects whose support is a $q$-dimensional surface (ref.1). For example, what we usually call a "regular" symmetry, is actually a $0$-form ...
3
votes
0
answers
151
views
Which of the Wightman axioms are not incorporated by four dimensional quantum Yang-Mills?
I am trying to understand the quantum Yang-Mills existence problem but the best I have seen so far is the statement that there is no known interacting relativist field theory in four dimensions which ...
- 17.8k
8
votes
1
answer
813
views
Do higher homotopy groups play any role in gauge theory?
As is more-or-less well-known, the magnetic monopoles of a gauge theory are classified by the first homotopy group of the gauge group, $\pi_1(G)$ (cf. Lubkin (1963)). The second homotopy group is ...
5
votes
1
answer
227
views
U(1) Dirac string moved to the SU(2) or SO(3) gauge theory
Dirac string describes the string connecting the U(1) magnetic monopole to the U(1) anti-magnetic monopole in the U(1) gauge theory.
Since U(1) is a subgroup of SU(2) and SO(3), we may embed the U(1) ...
- 4,336
7
votes
1
answer
712
views
The Hilbert space of Chern-Simons on a torus, part one$.$
There is a key result in 2+1 dimensional Chern-Simons theory, which was first discussed in ref.1.: the Hilbert space of the theory, when quantised on $T^2\times\mathbb R$, is isomorphic to
$$
\frac{\...
7
votes
1
answer
589
views
When is a Wess-Zumino term well-defined?
According to wikipedia, a Wess-Zumino term is well-defined when the Lie group (target space) $G$ is compact and simply connected, because that implies that $\pi_2(G)$ is trivial. But there are Lie ...
12
votes
1
answer
2k
views
Fields are sections of a bundle associated to a $\mathrm{SO}(1,3)$-bundle or to a gauge group bundle?
In Quantum Field Theory particles are associated to unitary representations of the Poincare group and fields are classified according to the irreducible representations of the Lorentz group.
In the ...
- 36.4k