22
votes
1answer
1k views

What does it mean that there is no mathematical proof for confinement?

I see this all the time* that there still doesn't exist a mathematical proof for confinement. What does this really mean and how would a sketch of a proof look like? What I mean by that second ...
0
votes
2answers
131 views

Reasons for choosing $SU(3)$ as the color group vs. $SO(4)$

What are the reasons that $SU(3)$ is used for QCD? Why wouldn't the simpler & smaller group $SO(4)$ make a better candidate?
7
votes
1answer
73 views

Large-$N$ Yang Mills

I've bumped into the study of the $SU(N)$ theory in the large-$N$ limit. I'm wondering in which way the study of this Yang-Mills theory, can give contribution to QCD with gauge group $SU(3)$, i.e. ...
3
votes
1answer
119 views

Are “confinement” and “asymptotic freedom” two sides of the same coin?

On Wikipedia it says that the two peculiar properties of quantum chromodynamics (QCD) are: confinement and asymptotic freedom. Asymptotic freedom is the idea that at low energies we cannot use ...
1
vote
2answers
128 views

Fermion field structure in non-abelian gauge theories

I am trying to understand the structure of the fermions in non-abelian gauge theories. Disclaimer: my question might be very trivial (I suspect the answer could simply be "a change of basis"), but I ...
2
votes
1answer
159 views

Glueball mass in non-abelian Yang Mills theory

How can the glueball mass be calculated in Yang Mills theory?
4
votes
1answer
534 views

Wilson loops and gauge invariant operators (Part 2)

These questions are sort of a continuation of this previous question. I would like to know of the proof/reference to the fact that in a pure gauge theory Wilson loops are all the possible gauge ...
10
votes
0answers
265 views

Gauge invariant but not gauge covariant regularization

I'm not sure if someone's already asked this before, but I was wondering, in field theory, when we say that a certain field is gauge invariant but not gauge covariant, what does this mean? In ...
7
votes
1answer
236 views

Reference for the ${\cal N}=3$ Chern-Simons Lagrangian at general $N_c$, $N_f$

I was wondering if someone could give me a reference where someone has explicitly written the Lagrangian for ${\cal N}=3$ $SU(N_c)$ Chern-Simons theory coupled to $N_f$ fundamental hypermultiplets. ...
6
votes
4answers
961 views

What's the distinctions between Yang-Mills theory and QCD?

So Yang-Mills theory is a non-abelian gauge theory, and we used a lot in QCD calculation. But what are the distinctions between Yang-Mills theory and QCD? And distinctions between supersymmetric ...
5
votes
1answer
443 views

A certain gluon scattering amplitude

I am stuck with this process of calculating the tree-level scattering amplitude of two positive helicity (+) gluons of momentum say $p_1$ and $p_2$ scattering into two gluons of negative (-) helicity ...
7
votes
1answer
34 views

Low-energy gluodynamics as a string

Does anyone know of a (most likely heuristic) derivation of the use of the string sigma model action to model the soft gluonic interactions between color charges? I'm familiar with the classic ...
7
votes
1answer
110 views

Some more questions about the BCFW reduction

This question is a continuation of this previous question of mine and I am continuing with the same notation. One claims that one can actually split this $n$-gluon amplitude such that there is just ...
4
votes
1answer
167 views

Colour decomposition of $n-$gluon tree amplitude

I have here a $SU(N_c)$ Yang-Mill's theory and let the index $i$, label the $n$-gluons, and $\{k_i, \lambda_i, a_i\}$ be its momenta, helicity and colour index and $\cal{A}_n^{tree/1-loop}(\{k_i, ...
10
votes
1answer
351 views

Derivation of the effective potential between a quark and an anti-quark

Typically in particle physics books (not in QFT books!) I have often seen this statement that the potential between a heavy quark and its anti-quark can be "empirically" represented as $V(r) = ...
1
vote
0answers
130 views

Is the axial gauge with a $\xi$ term useful in Yang-Mills theory?

i) Do people use axial gauge with a $\xi$ term? When $\xi\neq 0$, ghosts do not decouple, but maybe it's still useful? ii) Is it proved that the term $\frac 1 {2\xi}(n.A)^2$ in the Lagrangian does ...