A gauge theory has internal degrees of freedom that do not affect the foretold physical outcomes of the theory. The theory has a Lie group of *continuous symmetries* of these internal degrees of freedom, *i.e.* the predicted physics under any transformation in this group on the degrees of freedom. ...

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198 views

Quantum master equation in the Batalin-Vilkovisky formalism

I am reading the Section 15.9 of Weinberg's book "The Quantum Theory of Fields, vol. 2". Under a shift $\delta\Psi[\chi]$ in $\Psi[\chi]$, we have $$ \begin{split} \delta ...
3
votes
1answer
197 views

Four-gauge-boson vertex in non-Abelian gauge theories

In Peskin & Schroeder's book page 524, the following diagram is calculated for the gauge boson self-energy in order $g^2$: In dimensional regularization, its contribution is given by ...
3
votes
2answers
529 views

What is the ontological status of Faddeev Popov ghosts?

We all know Faddeev-Popov ghosts are needed in manifestly Lorentz covariant nonabelian quantum gauge theories. We also all know they decouple from the rest of matter asymptotically, although they ...
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0answers
100 views

Is there a critical order of the Abelian gauge theory in (2+1)D

In (2+1)D spacetime, it is known that the $U(1)$ gauge theory is always confined (according to Polyakov), while the $\mathbb{Z}_2$ gauge theory can support a deconfined phase. Now consider a generic ...
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2answers
1k 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 ...
3
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1answer
243 views

Using the covariant derivative to find force between 't Hooft-Polyakov magnetic monopoles

I am reading this research paper authored by NS Manton on the Force between 't Hooft-Polyakov monopoles. I have a doubt in equation 3.6 and 3.7. We assume the gauge field for a slowly accelerating ...
3
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0answers
61 views

Holomorphic coupling as a source for gaugino condensation

On the top of page 23 of hep-th/03061119, it is pointed out that treating the holomorphic gauge coupling $\tau$ as a background (spurion) superfield allows one to think of its $F$-term, $F_\tau$ as ...
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2answers
419 views

primary constraints for constrained Hamiltonian systems

I would be most thankful if you could help me clarify the setting of primary constraints for constrained Hamiltonian systems. I am reading "Classical and quantum dynamics of constrained Hamiltonian ...
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2answers
652 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 ...
1
vote
1answer
375 views

Are string theories gauge theories?

The wikipedia page for String Theory lists SO(32) and E8×E8 as group symmetries of some of the string theory types, and the page on E8 says: E8×E8 is the gauge group of one of the two types of ...
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1answer
129 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 ...
3
votes
0answers
72 views

Does the ensemble of effective Lagrangians in the String theory landscape mostly include gauge theories?

String theory false vacua can be described by effective Lagrangians at low energy. Is there generally a correspondence between these effective Lagrangians and SU(N) gauge theories? Or do the effective ...
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1answer
1k 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?
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80 views

The consistency conditions of constrained Hamiltonian systems

I am studying the Hamiltonian description of a constrained system. There are some questions puzzled me for days, which I have been stuck on it. From the lagrangian, we can obtain the primary ...
7
votes
1answer
536 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 ...
3
votes
1answer
241 views

Moose Models (Purpose, Examples)

A problem set for my QFT class is titled "Moose Models" and deals with the moose model for a gauge symmetry of $U(1)\times U(1)$. I was wondering if I could get an explanation of what a Moose Model ...
3
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0answers
264 views

Weak isospin and types of weak charge

My understanding is that QCD has three color charges that are conserved as a result of global SU(3) invariance. What about SU(2) weak? Does it have two types of charges? What I'm getting at is: U(1) ...
5
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0answers
72 views

axial and vector resonances in composite higgs models

Is there a reason to believe that the axial resonances be heavier than the vector resonances in the composite higgs models? For instance, in http://arxiv.org/abs/0808.2071, to have zero tree level ...
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vote
1answer
231 views

Interaction potential analysis from $\phi^4$ model

In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by $$S=\int d^d\! x ...
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0answers
98 views

sigma model on $S^1 \times S^3$

In arXiv:1207.3497 - 4D partition function on $S^1 \times S^3$ and 2D Yang-Mills with nonzero area, Yuji Tachikawa explains the partition function for an 4d $\mathcal{N}=2$ sigma model on $S^3 \times ...
3
votes
1answer
334 views

The theory of strings stretching between intersecting D-branes

I am trying to understand various aspects of intersecting D-branes in terms of the gauge theories on the worldvolume of the D-branes. One thing I'd like to understand is the worldvolume action for ...
7
votes
0answers
144 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 ...
2
votes
1answer
47 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 ...
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votes
2answers
2k views

What is the difference between a photon and a phonon?

More specifically, how does a wave-particle duality differ from a quasiparticle/collective excitation? What makes a photon a gauge boson and a phonon a Nambu–Goldstone boson?
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2answers
271 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
476 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 ...
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1answer
113 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
499 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 ...
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0answers
62 views

Do Boundary Conditions depend on spin connections for gauge fields?

In the article arXiv:1206.5642, which talks about gauge fields in conical spacetime, I came across the statement in footnote 4 that the boundary conditions on the gauge field depend on the spin ...
5
votes
0answers
141 views

Master Field Large N limit

I would like to ask a question about the so-called ''Master Field''. As far as I understand, this represents a classical configuration in the large n limit (saddle point solution) but there is no ...
2
votes
1answer
196 views

Construction of the supersymmetric Faraday tensor

When I first learned gauge theories in my introductory quantum field theory course, I was taught that the Faraday (field-strength) tensor can be constructed by computing the commutator of the ...
8
votes
2answers
509 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 ...
9
votes
2answers
333 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 ...
13
votes
1answer
258 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 ...
5
votes
3answers
323 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 ...
17
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1answer
323 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 ...
10
votes
1answer
408 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 ...
9
votes
1answer
57 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 ...
1
vote
1answer
251 views

observable quantities are gauge invariant?

I have a simply question, that is whether spatial velocity is gauge invariant. It is seems that under a infinitesimal coordinate transformation the velocity is just transform as other vectors, and it ...
4
votes
1answer
1k views

Local and Global Symmetries

Could somebody point me in the direction of a mathematically rigorous definition local symmetries and global symmetries for a given (classical) field theory? Heuristically I know that global ...
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votes
0answers
52 views

Good Books on Gauge Theory [duplicate]

Possible Duplicate: Comprehensive book on group theory for physicists? I'm having a hard time trying to get my head around the fundamentals of gauge theory. I've taken classes in QFT and ...
6
votes
2answers
1k 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 ...
8
votes
2answers
154 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 ...
1
vote
1answer
196 views

In a gauge theory, are two states related by a global phase transformation identified?

In a gauge theory (non-abelian for this question), I am told that two states $|\psi\rangle$ and $|\phi\rangle$ are to be identified if they are related by a gauge transformation $U(x)$ ...
8
votes
1answer
904 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 $F$ ...
3
votes
4answers
1k views

First class and second class constraints

Hello I am working on a project that involves the constraints. I checkout the paper of Dirac about the constraints as well as some other resources. But still confuse about the first class and second ...
5
votes
1answer
80 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 ...
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2answers
435 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
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2answers
346 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 ...
8
votes
1answer
432 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 ...