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3
votes
1answer
70 views

Ward identity prohibits mass of photon

On wikipedia one can read the following statement: The photon and gluon do not get a mass through renormalization because gauge symmetry protects them from getting a mass. This is a consequence of ...
3
votes
0answers
63 views

A Question about Wave-Function Renormalization Factor in SQCD

Here, I have a question about the one-loop computation of the wave-function renormalization factor in SQCD. According to Seiberg duality, the following electric $\mathrm{SQCD}_{e}$ \begin{gather} ...
5
votes
2answers
123 views

Why don't we add Wilson loops to the SM Lagrangian?

As the title says: why don't we add Wilson loops to common Lagrangians such as the Standard Model? They're gauge invariant and (correct me if I'm wrong, not sure on that) are renormalizable. Suppose ...
2
votes
1answer
75 views

Reference for proof of renormalizability

I have been trying to truly understand the renormalizability of quantum (i.e., without anomalies) gauge theories (after which I will focus on the case with spontaneous symmetry breaking). The problem ...
0
votes
1answer
57 views

Why is the relation $M_W=M_Z\cos\theta_W$ true only at tree-level?

In Glashow-Weinberg-Salam electroweak theory, the relation $$M_W=M_Z\cos\theta_W\tag{1}$$ is said to be remain true only at the tree-level; it receives corrections from the loop diagrams. See here. ...
7
votes
2answers
132 views

Why does the divergence of a QFT's coupling constant under RG flow trivialize the theory if it occurs in the UV but not in the IR?

When you first learn quantum field theory, at some point you calculate the beta function (to leading order) for a renormalizable coupling constant of some theory like $\varphi^4$ theory, Yukawa theory,...
3
votes
1answer
236 views

Beta function in the Standard Model

In Srednicki's textbook "Quantum Field Theory", Problem 89.4 asks us to compute the leading terms in the beta function for each of the three gauge couplings of the Standard Model. These gauge ...
1
vote
1answer
112 views

Interactions terms among vector fields in Lagrangian

In the QED Lagrangian we have terms that look like $\partial_{\nu} A_{\mu}$ and $J_{\nu} A_{\mu}$. We cannot have $A_{\mu} A^{\mu}$ as its coefficient would give a mass term, and for the photon we ...
14
votes
1answer
843 views

Gauge invariance is just a redundancy. Why is massive abelian gauge field renormalizable but massive non-abelian gauge field nonrenormalizable?

For example, Kaku's QFT pp. 214-215: Massive vector theory with non-Abelian group is non-renormalizable. Massive vector Abelian theory is renormalizable. I heard about the following arguments,...
1
vote
1answer
190 views

Anti-ghost translation invariance$.$

The Faddeev-Popov gauge-fixed Yang-Mills Lagrangian is invariant under $$ \bar c\to\bar c+\chi $$ for any odd constant $\chi$. What is the physical interpretation of this invariance? What does this ...
5
votes
1answer
116 views

Obstruction in calculating $\mathcal{Z}_{\mathcal{N}=1}$ SYM partition function

Seiberg and Witten and Nekrasov managed to completely find the exact partition function of the $\mathcal{N}=2$ SYM theory on $\mathbb{R}^4$. As in $\mathcal{N}=2$ in $\mathcal{N}=1$ the NSZV (Novikov-...
4
votes
1answer
316 views

Gauge invariance or global invariance, which one makes theory renormalizable?

We know that gauge theory is renormalizable, due to the Ward-Takahashi identity (for non-Abelian theory, it is Slavnov-Taylor identity), which reflects the conserved current of gauge symmetry. But ...
7
votes
1answer
166 views

How does gauge invariance protect the SM gauge boson masses in SUSY from divergent radiative corrections?

The W and Z gauge bosons receive radiative corrections in loop from the heavy SUSY scalars. There is an argument using gauge invariance which explains how the masses remains protected. I am not able ...
0
votes
1answer
705 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 ...
1
vote
0answers
196 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? Based ...
0
votes
1answer
52 views

Charge loop corrections

Let's assume some theory in which there is some gauge group (spontaneously broken) field $B$ and fermion field $b$ which isn't charged under this group, and this statement must hold for each order of ...
0
votes
1answer
285 views

Why 5D gauge theory is non-renormalizable?

My question is following "Why 5D gauge theory is non-renormalizable?" Here I treat $5D$ supersymmetric gauge theories. Also I heard Non-renormalizablity of $5D$ gauge theories implies the ...
2
votes
0answers
170 views

Evaluation of the anomalous dimensions of fields in SUSY $SU(5)$

The general formula for the anomalous dimension can be found in Martin΄s review article (hep-ph/9709356), on page 62 relation (6.5.4). In the case of $SU(5)$ and especially in the paper of Kobayashi, ...
8
votes
2answers
970 views

Gauge choice after Spontaneous Symmetry Breaking

After the spontaneous breakdown of local symmetry in presence of gauge fields (Higgs Mechanism), we can always choose a gauge where the Goldstone bosons are eaten up by the gauge field (also called ...
6
votes
1answer
500 views

Why do we need to prove the gauge invariance of QED (or all of the gauge theories) on the Feynman diagrams language?

Let's have the QED lagrangian. It has explicit gauge invariance, so, by the naive thinking, all of the EM processes must satisfy the property of gauge invariance. So why do we need to recheck of gauge ...
11
votes
1answer
753 views

Why does local gauge invariance suggest renormalizability?

I'm reading Gauge Field Theories: An Introduction with Applications by Mike Guidry and this particular remark is not obvious to me: A tempting avenue is suggested by the QED paradigm, for if a ...
8
votes
1answer
587 views

Anomalous Dimensions of Gauge Interactions

Peskin and Schroeder mention a few times that the anomalous dimension of a gauge interaction operator is zero. The justification for this is that the charge operator shouldn't get modified under ...
13
votes
1answer
2k views

How does the Ward-Takahashi Identity imply that non-transverse photons are unphysical in QED?

Peskin and Schroeder say that the Ward Identity of QED proves that non-transverse photon polarizations can be consistently ignored, but I'm confused about the details. Setup One starts by ...
13
votes
2answers
4k 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 ...