The gauge-theory tag has no wiki summary.
41
votes
4answers
3k views
Gauge symmetry is not a symmetry?
I have read before in one of Seiberg's articles something like, that gauge symmetry is not a symmetry but a redundancy in our description, by introducing fake degrees of freedom to facilitate ...
22
votes
0answers
398 views
On the Coulomb branch of N=2 supersymmetric gauge theory
The chiral ring of the Coulomb branch of a 4d N=2 supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the Casimirs are ...
15
votes
1answer
131 views
Models of higher Chern-Simons type
It has long been clear that (the action functional of) Chern-Simons theory has various higher analogs and variations of interest. This includes of course traditional higher dimensional Chern-Simons ...
15
votes
0answers
106 views
Systematic approach to deriving equations of collective field theory to any order
The collective field theory (see nLab for a list of main historical references) which came up as a generalization of the Bohm-Pines method in treating plasma oscillations are often used in the study ...
14
votes
3answers
207 views
Which exact solutions of the classical Yang-Mills equations are known?
I'm interested in the pure gauge (no matter fields) case on Minkowski spacetime with simple gauge groups.
It would be nice if someone can find a review article discussing all such solutions
EDIT: I ...
13
votes
1answer
94 views
realization of: CFT generating fuction = AdS partition function
An important aspect of the AdS/CFT correspondence is the recipe to compute correlation functions of a boundary operator $\mathcal{O} $ in terms of the supergravity fields in the interior of the ...
13
votes
2answers
2k views
Is there a T-dual of Witten's twistor topological string theory?
In late 2003, Edward Witten released a paper that revived the interest in Roger Penrose's twistors among particle physicists. The scattering amplitudes of gluons in $N=4$ gauge theory in four ...
12
votes
2answers
149 views
Topological twists of SUSY gauge theory
Consider $N=4$ super-symmetric gauge theory in 4 dimensions with gauge group $G$. As is explained in the beginning of the paper of Kapustin and Witten on geometric Langlands, this
theory has 3 ...
12
votes
1answer
155 views
What is a “free” non-Abelian Yang-Mill's theory?
I hope this question will not be closed down as something completely trivial!
I did not think about this question till in recent past I came across papers which seemed to write down pretty much ...
11
votes
1answer
66 views
Are possible gauge fields in a Lagrangian theory always determined by the structure of the charged degrees of freedom?
An elementary example to explain what I mean. Consider introducing a classical point particle with a Lagrangian $L(\mathbf{q} ,\dot{\mathbf{q}}, t)$. The most general gauge transformation is $L ...
11
votes
2answers
142 views
Gauge invariance for electromagnetic potential observables in test function form
This is a reference request for a relationship in quantum field theory between the electromagnetic potential and the electromagnetic field when they are presented in test function form. $U(1)$ gauge ...
10
votes
1answer
143 views
Chern-Simons theory
In Witten's paper on QFT and the Jones polynomial, he quantizes the Chern-Simons Lagrangian on
$\Sigma\times \mathbb{R}^1$ for two case: (1) $\Sigma$ has no marked points (i.e., no Wilson loops) and ...
10
votes
1answer
131 views
Normalization of the Chern-Simons level in $SO(N)$ gauge theory
In a 3d SU(N) gauge theory with action $\frac{k}{4\pi} \int \mathrm{Tr} (A \wedge dA + \frac{2}{3} A \wedge A \wedge A)$, where the generators are normalized to $\mathrm{Tr}(T^a ...
10
votes
2answers
348 views
Gauge invariance and diffeomorphism invariance in Chern-Simons theory
I have studied Chern-Simons (CS) theory somewhat and I am puzzled by the question of how diff. and gauge invariance in CS theory are related, e.g. in $SU(2)$ CS theory. In particular, I would like to ...
9
votes
4answers
550 views
Nonlinear optics as gauge theory
the widely used approach to nonlinear optics is a Taylor expansion of the dielectric displacement field $\mathbf{D} = \epsilon_0\cdot\mathbf{E} + \mathbf{P}$ in a Fourier representation of the ...
9
votes
1answer
30 views
Dual Pairs in Four Dimensions
Following the conversation here, I am wondering if anyone knows of an example of dual pair with 4-dimensional N=1 SUSY which relates a non-Abelian gauge theory on one side to a theory with a ...
9
votes
1answer
723 views
Diff(M) as a gauge group and local observables in theories with gravity
In a gauge theory like QED a gauge transformation transforms one mathematical representation of a physical system to another mathematical representation of the same system, where the two mathematical ...
9
votes
1answer
426 views
Discrete gauge theories
I'm trying to understand a particular case of gauge theories, namely discrete spaces on which a group G can act transitively, with a gauge group H which is discrete as well.
From what I've already ...
9
votes
0answers
224 views
How can two time theories be compactified to 3+1 without any Kaluza-Klein remnants
I have recently been looking into the two-time theories and the implied concepts.
For me this seems slightly hard to grasp.
How can I see the basic concept in this theory in a fundamental way based ...
8
votes
2answers
130 views
Is ghost-number a physical reality/observable?
One perspective is to say that one introduced the ghost fields into the Lagrangian to be able to write the gauge transformation determinant as a path-integral. Hence I was tempted to think of them as ...
8
votes
4answers
332 views
To which extent is general relativity a gauge theory?
In quantum mechanics, we know that a change of frame -- a gauge transform -- leaves the probability of an outcome measurement invariant (well, the square modulus of the wave-function, i.e. the ...
8
votes
1answer
318 views
argument about fallacy of diff(M) being a gauge group for general relativity
I want to outline a solid argument (or bulletpoints) to show how weak is the idea of diff(M) being the gauge group of general relativity.
basically i have these points that in my view are very solid ...
7
votes
4answers
663 views
How many fundamental forces could there be?
We’re told that ‘all forces are gauge forces’. The process seems to start with the Lagrangian corresponding to a particle-type, then the application of a local gauge symmetry leading to the emergence ...
7
votes
2answers
201 views
Is there a meaning to the E,B analogues of other gauge fields?
From the gauge field $A_\mu$ and the QED lagrangian we can derive maxwell's equations in terms of electric and magnetic fields. Are there any situations where similar derivations using the other gauge ...
7
votes
1answer
253 views
Diffeomorphisms, Isometries And General Relativity
Apologies if this question is too naive, but it strikes at the heart of something that's been bothering me for a while.
Under a diffeomorphism $\phi$ we can push forward an arbitrary tensor field $F$ ...
7
votes
0answers
189 views
How to determine if an emergent gauge theory is deconfined or not?
2+1D lattice gauge theory can emerge in a spin system through fractionalization. Usually if the gauge structure is broken down to $\mathbb{Z}_N$, it is believed that the fractionalized spinons are ...
6
votes
2answers
173 views
How to prove quantum N=4 Super-Yang-Mills is superconformal?
I'm especially interested in elegant illuminating proofs which don't involve a lot of straightforward technical computations
Also, does a non-perturbative proof exist?
6
votes
2answers
285 views
Wilson/Polyakov loops in Weinberg's QFT books
I wanted to know if the discussion on Wilson loops and Polyakov loops (and their relationship to confinement and asymptotic freedom) is present in the three volumes of Weinberg's QFT books but in some ...
6
votes
4answers
587 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 ...
6
votes
5answers
1k views
proof of gauge invariance for quantum 1D ring
This is a question on gauge invariance in quantum mechanics. I do some simple math on a 1D wave-function with periodic boundary conditions, and get that gauge invariance is violated. What am I doing ...
6
votes
1answer
247 views
Why is color conserved in QCD?
According to Noether's theorem, global invariance under $SU(N)$ leads to $N^2-1$ conserved charges. But in QCD gluons are not conserved; color is. There are N colors, not $N^2-1$ colors. Am I ...
6
votes
1answer
400 views
Modes of a QFT and irreducible representation of the gauge group
This is in reference to the calculation in section 3.3 starting page 20 of this paper.
I came across an argument which seems to say that the "constraint of Gauss's law" enforces gauge theory on ...
6
votes
1answer
130 views
How can a massless boson (Gluon) mediate the short range Strong Force?
I thought massless particles were mediators for long range forces such as electromagnetism and gravitation. How can the massless gluon mediate the short range strong force?
6
votes
2answers
197 views
Chern-Simons degrees of freedom
I'm currently reading the paper http://arxiv.org/abs/hep-th/9405171 by Banados. I am just getting acquainted with the details of Chern-Simons theory, and I'm hoping that someone can explain/elaborate ...
6
votes
1answer
106 views
What is the meaning of non-compactness in the context of $U(1)$ in gauge theories?
In John Preskill's review of monopoles he states
Nowadays, we have another way of understanding why electric charge is
quantized. Charge is quantized if the electromagnetic U(l)em gauge
group ...
6
votes
1answer
76 views
Do instantons support quantum bound states?
When one quantizes a scalar in the 1+1 dimensions in the kink background of a double well potential, one finds a spectrum that includes: (1) a zero mode corresponding to the classical particle ...
6
votes
1answer
180 views
Introduction to Gauge Symmetries: Good, Bad or Ugly?
I'm trying to come up with a good (as in intuitive and not 'too wrong') definition of a gauge symmetry.
This is what I have right now:
A dynamical symmetry is a (differentiable) group of ...
6
votes
1answer
43 views
How does a geodesic equation on an n-manifold deal with singularities?
My general premise is that I want to investigate the transformations between two distinct sets of vertices on n-dimensional manifolds and then find applications to theoretical physics by:
...
6
votes
2answers
306 views
Lagrangians combining terms with 1 and 2 derivatives
How are field theory Langrangians treated when some terms have 2 derivatives but others have only 1? Because the number of derivatives in a Lagrangian term is more easily even than odd, the ...
6
votes
0answers
96 views
How to perform contour integral in Nekrasov's formula
My question is technical. It is about instanton counting calculation (see this paper).
The partition function of SU(N) gauge theory with $N_f$ fundamental multiplets in k instanton background is ...
5
votes
3answers
355 views
Gauge fixing choice for the gauge field $A_0$
In many situations, I have seen that the the author makes a gauge choice $A_0=0$, e.g. Manton in his paper on the force between the 't Hooft Polyakov monopole.
Please can you provide me a ...
5
votes
2answers
475 views
Decomposition of a vectorial field in free-curl and free-divergence fields
Is it always possible to do that decomposition? I'm asking it because Helmholtz theorem says a field on $\mathbb{R}^3$ that vanishes at infinity ($r\to \infty$) can be decomposed univocally into a ...
5
votes
2answers
196 views
Why is the Yang-Mills gauge group assumed compact and semi-simple?
What is the motivation for including the compactness and semi-simplicity assumptions on the groups that one gauges to obtain Yang-Mills theories? I'd think that these hypotheses lead to physically ...
5
votes
2answers
230 views
Geometrical significance of gauge invariance of the QED Lagrangian
The QED Lagrangian is invariant under
$\psi(x) \to e^{i\alpha(x)} \psi (x)$, $A_{\mu} \to A_{\mu}- \frac{1}{e}\partial_{\mu}\alpha(x)$. What is the geometric significance of this result? Also why is ...
5
votes
6answers
526 views
Interaction ranges in the Standard Model - Electrodynamics vs QCD
as you might know, the Standard Model of physics can be seen as a $U(1)\times SU(2)\times SU(3)$ gauge theory where each symmetry group accounts for different force fields.
The behaviour for the ...
5
votes
2answers
84 views
Torsion and gauge invariant EM kinetic term
Everytime I hear about adding torsion to GR, something struggles me: how do you create a kinetic term for the electromagnetic field that is still gauge-invariant? One of the consequences of torsion is ...
5
votes
3answers
245 views
Could general relativity and gauge theories in principle be covered in one course?
It's always nice to point out the structural similarieties between (semi-)Riemannian geometry and gauge field theories alla Classical yang Mills theories. Nevertheless, I feel the relation between the ...
5
votes
2answers
318 views
Winding number in the topology of magnetic monopoles
I am reading on magnetic monopoles from a variety of sources, eg. the Jeff Harvey lectures.. It talks about something called the winding $N$, which is used to calculate the magnetic flux. I searched ...
5
votes
1answer
329 views
Faddeev-Popov ghost propagator in canonical quantization
Obtaining the propagator for the Faddeev-Popov (FP) ghosts from the path integral language is straightforward. It is simply
$$\langle T(c(x) \bar c(y))\rangle~=~\int\frac{d^4 p}{(2\pi)^4}\frac{i ...
5
votes
2answers
267 views
Why do we like gauge potentials so much?
Today I read articles and texts about Dirac monopoles and I have been wondering about the insistence on gauge potentials. Why do they seem (or why are they) so important to create a theory about ...
