7
votes
1answer
75 views

Connection beween infinite gauge symmetries and UV finiteness

In e.g., http://arxiv.org/abs/arXiv:0712.3526 the author claims: Since the massless higher-spin field theories involve infinite-dimensional gauge symmetries, one expects that such theories may be ...
1
vote
0answers
54 views

Global anomaly for discrete groups

We know that: a global anomaly is a type of anomaly: in this particular case, it is a quantum effect that invalidates a large gauge transformations that would otherwise be preserved in the ...
3
votes
0answers
90 views

Large gauge transformations for higher p-form gauge fields

Question: What is the large gauge transformations for higher p-form gauge field on a spatial d-dimensional torus $T^d$ or a generic (compact) manifold $M$? for p=1,2,3, etc or any other integers. Is ...
2
votes
1answer
111 views

How to get a $\mathcal{N}=2$ SuperYang-Mills Lagrangian from a quiver

How can one write down the $\mathcal{N}=2$ SuperYang-Mills Lagrangian given a quiver graph? For concreteness consider the quiver $$(2)-(4)-[6]$$ where the node $(2)$ corresponds to a $U(2)$ factor ...
1
vote
0answers
41 views

Degeneracy and the unitarity of a gauge theory with a non-compact gauge group

The topological ground state degeneracy(g.s.d.) provides useful information for a topological field theory(TQFT), such as this post shows some example. To count g.s.d., it seems to be equivalent to ...
3
votes
2answers
223 views

Why does the $\pi$-flux state have time-reversal symmetry?

It's known that the $\pi$-flux state of the antiferromagnetic Heisenberg model on the square lattice is an important concept. The $\pi$-flux state is described by the (simplified) mean-field ...
2
votes
0answers
39 views

What's the necessary and sufficient condition for gauge equivalence in the projective construction?

The definition of gauge equivalence and notations used here is the same as those in my previous question. As we know, the condition $\chi_{ij}'=G_i\chi_{ij}G_j^\dagger$(where $G_i\in SU(2)$) is a ...
2
votes
0answers
77 views

Some questions on the Wilson loop in the projective construction?

Based on the previous question and the comment in it, imagine two different mean-field Hamiltonians $H=\sum(\psi_i^\dagger\chi_{ij}\psi_j+H.c.)$ and $H'=\sum(\psi_i^\dagger\chi_{ij}'\psi_j+H.c.)$, we ...
2
votes
1answer
166 views

Does the low-energy gauge structure depend on the choice of $SU(2)$ gauge freedom?

The starting point and notations used here are presented in Two puzzles on the Projective Symmetry Group(PSG)?. As we know, Invariant Gauge Group(IGG) is a normal subgroup of Projective Symmetry ...
2
votes
2answers
183 views

Two puzzles on the Projective Symmetry Group(PSG)?

Recently I'm studying PSG and I felt very puzzled about two statements appeared in Wen's paper. To present the questions clearly, imagine that we use the Shwinger-fermion ...
9
votes
1answer
246 views

Anomalies for not-on-site discrete gauge symmetries

If a symmetry group $G$ (let's say finite for simplicity) acts on a lattice theory by acting only on the vertex variables, I will call it ultralocal. Any ultralocal symmetry can be gauged. However, in ...
9
votes
1answer
440 views

Large and small gauge transformations?

I've a questions about the difference between small and large gauge transformations (a small gauge transformation tends to the identity at spatial infinity, whereas the large transformations don't). ...
6
votes
1answer
170 views

Proof that we can always find a gauge transformation such that $A_0=0$?

I'm trying to follow Coleman's proof from his lectures "Aspects of Symmetry" on page 200-201. He proofs it is always possible to work in the temporal gauge for a general Yang-Mills-Higgs theory. I ...
6
votes
2answers
735 views

The phrase “Trace Anomaly” seems to be used in two different ways. What's the relation between the two?

I've seen the phrase "Trace Anomaly" refer to two seemingly different concepts, though I assume they must be related in some way I'm not seeing. The first way I've seen it used is in the manner, for ...
5
votes
1answer
88 views

4D instantons and the moduli space of N=2 on R^3 x S^1

I am reading the paper arXiv:0807.4723 by Gaiotto, Moore, and Neitzke on wall-crossing. I would like to understand whether if the Darboux coordinates in the mutually non-local case contain the ...
2
votes
1answer
131 views

How to justify matter-field interaction for non-gauge-invariant Hamiltonian?

I'm wondering how can one formally justify the electromagnetic response of a system which does not verify local U(1) gauge invariance. A good example of what I would like to consider is given by the ...
6
votes
1answer
161 views

Background Gauge Condition In Moduli Space

I'm really confused on the background gauge condition for the moduli space of BPS-monopoles: \begin{equation} D_i \delta A_i + e [\phi , \delta \phi]=0 \end{equation} I can see that this conditions ...
2
votes
1answer
40 views

Time Evolution of a Manifold Embedding

Given a smooth manifold $\mathcal{M}$ with a simplicial complex embedding $\mathsf{S}$, what specific tools or methods can be used to give an analysis of the time evolution of the manifold given some ...
2
votes
2answers
166 views

Gauge invariant scalar potentials

If $\Phi$ is a multi-component scalar field which is transforming in some representation of a gauge group say $G$ then how general a proof can one give to argue that the potential can only be a ...
4
votes
1answer
331 views

Gauge invariance and the form of the Rarita-Schwinger action

in Weinberg Vol. I section 5.9 (in particular p. 251 and surrounding discussion), it is explained that the smallest-dimension field operator for a massless particle of spin-1 takes the form of a field ...
6
votes
2answers
129 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 ...
6
votes
1answer
89 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: ...
12
votes
1answer
373 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 ...
30
votes
0answers
925 views

On the Coulomb branch of N=2 supersymmetric gauge theory

The chiral ring of the Coulomb branch of a 4D $\mathcal N=2$ supersymmetric gauge theory is given by the Casimirs of the vector multiplet scalars, and they don't have non-trivial relations; the ...
5
votes
2answers
129 views

Is the distinction between the Poincaré group and other internal symmetry groups artificial?

For instance, given a theory and a formulation thereof in terms of a principal bundle with a Lie group $G$ as its fiber and spacetime as its base manifold, would a principle bundle with the Poincaré ...
5
votes
1answer
75 views

What does Gribov's last paper tell about coloured states?

In the first days of July 1997, after a long driving effort, crossing all of Europe to come to a meeting in Peñiscola, Vladimir Gribov fell fatally sick and he passed away one month later. His paper ...
13
votes
2answers
291 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 ...
8
votes
2answers
319 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?
19
votes
4answers
532 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
184 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 ...
12
votes
2answers
320 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 ...
11
votes
2answers
290 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 ...
25
votes
0answers
214 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 ...
9
votes
1answer
47 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 ...
17
votes
1answer
252 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 ...
12
votes
1answer
150 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 ...
58
votes
4answers
5k 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 ...
15
votes
1answer
1k 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 ...
21
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 ...