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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Non-inertial frames in Lagrangian mechanics?

Building on this Phys.SE post I am interested in how non-inertial frames can be considered in Lagrangian mechanics. My understanding is that changing the reference frame causes a transformation of the ...
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190 views
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Is there some no-go theorem for $D=9$ Kaluza Klein QCD+EM?

While QCD is a typical product of AdS/CFT and some other research trends in extra dimensions, I have never found in the literature an example producing the non-chiral part of the standard model, ...
2
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49 views
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Question about the Georgi-Glashow model and the VEV of the scalar field

Consider the Georgi-Glashow model, an $SU(2)$ gauge theory with a real scalar in the adjoint (thus a 3-vector in the colour space) $\phi$. The Lagrangian is $$ L = -\frac{1}{4g^2} F_{\mu \nu}^{\, a} ...
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1answer
34 views

Coupling an electric charge to a gauge field. How is it done in this setup?

In page 9 of Tachikawa's N=2 susy dynamics for pedestrians it says that an electric particle with charge $n$ in the first quantised setup (in what sense first quantised?), Wick rotated to Euclidean ...
4
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96 views

Charged CFT observables and AdS/CFT

I have a simple question regarding the holographic dictionary when mapping operators on the CFT side to those in AdS. One piece of the dictionary is that a global symmetry maps onto a gauge symmetry ...
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1answer
59 views

Is EM interpreted in a principal or vector bundle?

I've read in a few places that EM is a $U(1)$-principal bundle; but is this correct? Isn't it rather an associated vector bundle using the adjoint representation of $U(1)$?
2
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64 views

Massive Gauge Bosons without Higgs Effect

In a possible theory like our Standard model but without a Higgs i.e.: $$ \mathcal{L}=i\bar{\Psi}_f\gamma_\mu D^\mu\Psi_f-\text{Tr}[G^b_{\mu\nu}G^{b\,\mu\nu}] $$ where $b,f$ run over the typical ...
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1answer
77 views

Consequences of local and global anomaly

Are the physical consequences of anomalies associated with a local symmetry is different from that of a global symmetry? If yes, why? We have global anomaly in the standard model but not local ...
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1answer
41 views

Dimensional reduction of SUSY theories

I know that if one reduces 10 dimensional $\mathcal{N}=1$ SYM theory to 4 dimensions one gets $\mathcal{N}=4$ SYM. There are other examples also. I have two related questions regarding this fact. ...
2
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1answer
32 views

Gluon have colour-anticolour; what about weak bosons?

Gluons can be red-antiblue, or green-antired, etc. What about weak interaction bosons? (Say before symmetry breaking, to make matters simpler.) Is there a similar "weak charge" structure of ...
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65 views

How are quadruple gluon vertices related to $SU(2)$ and $SU(3)$?

I once read that the non-commutativity of the Lie Groups $SU(2)$ and $SU(3)$ is the reason that the weak and strong interactions have Feynman diagrams with quadruple vertices, where four gauge bosons ...
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261 views

How do gauge boson interact with elementary particles?

We know that gauge bosons are the force carriers of fundamental interactions, but how do the gauge bosons themselves interact with particles?
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1answer
65 views

Why must superpartners have the same gauge quantum numbers?

The title leaves it quite clear, why must superpartners have the same gauge quantum numbers?
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57 views

How does the Higgs field relate to the Yang-Mills fields and gauge theories in general?

I asked this in astronomy How does the Higgs field relate to the Yang-Mills fields and gauge theories in general? but they suggested I ask it here. It is very confusing. Is there an easy ...
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34 views

Effect of orbifolding on gauge fields

A paper by Lalak et al, entitled "Soliton Solutions of M-theory on an orbifold", considers the brane solutions of 11 dimensional supergravity on a space of the form $R^{10} \times S^1/\mathbb{Z}_2$. ...
2
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79 views

Mathematician learning theoretical physics [duplicate]

EDIT: I was aware of the supposed duplicate. But I'm interested in a clear and focused path through the basics to advanced theoretical physics such as string theory - a path that avoids studying ...
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1answer
32 views

How to check if some term in the Lagrangian involving gauge bosons is gauge invariant without explicit computations?

Normally (for fermions and scalars) we can simply use the decomposition of tensor products of gauge group representations to find invariant terms that we can write into the Lagrangian. For example ...
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1answer
56 views

Gauge freedom in tetrad

I asked the question in the MathOverflow, but didn't get any response. I thought maybe better luck here. I'm reading the following paper about Petrov type D space times called "Type D vacuum ...
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1answer
34 views

Do gauge bosons really transform according to the adjoint representation of the gauge group?

Its commonly said that gauge bosons transform according to the adjoint representation of the corresponding gauge group. For example, for $SU(2)$ the gauge bosons live in the adjoint $3$ dimensional ...
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1answer
88 views

How to write the Lagrangian in terms of a projection

We know that $$ L=\frac{1}{2}\left(\partial_{\mu} A_{\nu} \partial^{\mu} A^{\nu}-\partial_{\mu} A_{\nu} \partial^{\nu} A^{\mu}\right) $$ But how do we write the Lagrangian in the following way: ...
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42 views

Extension of vector field and fluid velocity

I've been studying locomotion at low Reynolds number with gauge theories reading this paper and on pages 567 and 568 we find the explanation on how to compute the field strength tensor. For simplicity ...
3
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1answer
114 views

Observation of gauge in artificial magnetic fields

In the ultracold atom community, an "artificial gauge field" or "artificial magnetic field" is a spatially varying hopping phase somehow engineered into the system, so that atoms hopping around an ...
4
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107 views

Why the field strength tensor for locomotion at low Reynolds number may be written like that?

I've been studying locomotion at low Reynolds number for some time now and it has been a quite tough problem. I've already asked two questions about the problem here, and now there is this question ...
3
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85 views

Field strength tensor for locomotion at low Reynolds number

Recently I've been studying locomotion at low Reynolds number. I already asked here about the computation of the gauge potential. Now I have a more objective question, which arose when reading the ...
2
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1answer
97 views

Why is the electromagnetic four-potential $A_{\mu}$ not an observable?

Why within classical field-theory the electromagnetic four-potential (usually $A_{\mu}$) not an observable? In classical mechanics we don't have problems with energy measurements and in quantum ...
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1answer
114 views

Is my understanding of Gauge Symmetries correct?

I'm currently working on a project about Symmetry Breaking for my physics bachelor. Right now I'm trying to understand Gauge Symmetries (although I guess it's not much of a symmetry). And I've been ...
2
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58 views

AdS/CFT-duality: How does the $U(1)$ decouple form the $U(N)$?

A stack of N coincident D3-branes on its world-volume describe, at the lowest order in $\alpha'$ and in absence of non-trivial background fields, a supersymmetric $U(N)$ gauge theory as explained in ...
2
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1answer
54 views

Are the pion fields in chiral perturbation theory complex or real fields?

The chiral perturbation theory Lagrangian is written $$\mathcal{L}_2=\frac{f_{\pi}^2}{4}Tr(D_{\mu}U^{\dagger}D^{\mu}U)$$ where $$U=e^{i\sqrt{2}\Phi/f}$$ and $$\Phi= \begin{pmatrix} ...
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1answer
79 views

Are all elementary interactions arising from a gauge theory?

The standard model of particle physics is based on the gauge group $U(1) \times SU(2) \times SU(3)$ and describes all well-known physical interactions but with exception that gravity isn't involved. ...
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1answer
39 views

Transformations of electroweak gauge field $W_\mu$ under $U(1)_{e.m.}$

As the vector boson field $W_\mu$ is, together with $Z^0$, the gauge field for the Standard electroweak model, I know it transforms as a connection under the $SU(2)\times U(1)_Y$ group. But, when this ...
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2answers
61 views

The notion of fixing a gauge

I don't understand the notion of gauge fixing; can we choose any gauge or are there some restrictions? For example why can we choose $\nabla\phi = 0$ here: Determine the Electric field using ...
4
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1answer
60 views

Why is $U(1)$ special when defining global charges?

For gauge groups like $SU(2)$ and $SU(3)$ etc. we know that observable states such as mesons or baryons must be charge neutral. However, for a $U(1)$ gauge group we can have charged initial states in ...
2
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1answer
57 views

Origin of integral of field strength tensor in path-ordered exponential in gauge field theory

When studying some gauge theories approach to problems in Mechanics, I've found the following integral $$P\exp\left[\oint A \ dt\right]=1+\dfrac{1}{2}\oint_{\partial ...
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1answer
86 views

Are gauge theories always renormalizable?

Speaking of quantum field theories. Is one of the following implications correct? gauge theory (gauge invariant) => renormalizable renormalizable => gauge theory (gauge invariant) If yes do you ...
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76 views

Branes at the conifold

Consider $N$ $D3$-branes at the singularity of the conifold. This particular example can be viewed as a $AdS_{5} \times T^{1,1}$ in the near horizon limit, where the Einstein manifold has isometry ...
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43 views

Why gauge field should be vanishing on horizon?

When considering an AdS spacetime including a black hole, matter field and gauge field, the value of temporal component $A_t$ of the gauge potential $A_\mu$ on horizon always is set be zero, even the ...
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69 views

Counting Degrees of Freedom in Field Theories

I'm somewhat unsure about how we go about counting degrees of freedom in CFT, and in QFT. Often people talk about field theories as having 'infinite degrees of freedom'. My understanding of this is ...
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0answers
33 views

Changing variables in a Lagrangian to obtain mass terms of gauge fields [closed]

Context: In a excercise, consider a SU(2) gauge theory. The Lagrangian of the theory contains the three gauge fields and some scalar matter fields: $\phi_1 , \phi_2$ form a SU(2) doublet (fundamental ...
3
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133 views

Geometric interpretation of quantum Yang-Mills field

In most books\articles review geometric interpretation of classical Yang-Mills field in terms of principal bundle, connections...etc. What are geometric interpretation of quantum Yang-Mills field? ...
2
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1answer
210 views

Reduction of Nambu Goto action to true degrees of freedom

First consider the particle $$S=m\int\sqrt{-\dot{X}^2}d\tau$$ if you choose the static gauge $\tau=X^0$ and replace it in the action you get $$=m\int\sqrt{1-\dot{X}^j\dot{X}^j}d\tau$$ So now, you ...
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2answers
90 views

Why don't we take this term $D_{\mu}D_{\nu}F^{\mu\nu}$ in Lagrangians?

Why don't we take $$D_{\mu}D_{\nu}F^{\mu\nu}$$ in Lagrangians?
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55 views

Are mass terms forbidden in the Lagrangian because of parity violation or because fermions live in a complex representation?

Normally one argues that we can't write down Lorentz AND gauge invariant mass terms, because of parity violation, i.e. l-chiral and r-chiral fields transform differently. This means that mass terms ...
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0answers
28 views

Covariant derivative of Noether current [closed]

I am working with a non-abelian gauge gauge theory that has one gauge field and a complex scalar field. I am supposed to prove that \begin{equation} (D_\mu j^\mu)^a=0, \end{equation} where ...
1
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1answer
77 views

Is gauge invariance essential to a theory be renormalizable?

Let's consider a model of New Physics in which all operator have dimension smaller than four, but which breaks explicitly $SU(2)_L$ gauge symmetry. Is this model necessarily renormalizable? ...
2
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1answer
87 views

Showing closure of the SUSY algebra of a free abelian gauge multiplet

Given the complete supersymmetric lagrangian of a free abelian gauge multiplet $$ \mathcal{L} = -\frac{1}{4} F_{\mu\nu} F^{\mu\nu} + i \bar{\lambda} \bar{\sigma}^\mu \partial_\mu \lambda + \frac{1}{2} ...
3
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0answers
124 views

Effective field theories and gauge anomalies cancellation

Lets assume some theory which concludes sets of generations of fermions (lets call them $A$ and $B$). Fermions $A$ have some gauge group $G_{A}$ (for example, SM), while fermions $B$ are charged under ...
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2answers
73 views

Why gauge fields are traceless Hermitian?

So I've had a read of this, and I'm still not convinced as to why gauge fields are traceless and Hermitian. I follow the article fine, it's just the section that says "don't worry about this ...
1
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1answer
71 views

Commutator of Gauge Covariant derivatives

What is the physical meaning of $$ [D_{\mu}, D_{\nu}] ~\propto~ F_{\mu, \nu}, $$ where $D_{\mu}$ is the gauge covariant derivative and $F_{\mu,\nu}$ is the field strength? Is it just a definition? ...
3
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1answer
78 views

Why is the gauge potential $A_{\mu}$ in the Lie algebra of the gauge group $G$?

If we have a general gauge group whose action is $$ \Phi(x) \rightarrow g(x)\Phi(x), $$ with $g\in G$. Then introducing the gauge covariant derivative $$ D_{\mu}\Phi(x) = ...
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22 views

Wu experiment and masses of neutrino

Wu experiment have shown that there are only left-handed neutrinos (and right-handed antineutrinos) take part in weak interactions. My question is about the significance of this experiment in a ...