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6
votes
1answer
182 views

Invariance of supersymmetric Yang-Mills theory under supersymmetry

I was following Brink, Scherk and Schwartz, "Supersymmetric Yang-Mills theories". The variation of the Lagrangian w.r.t a supersymmetry transformation can be reduced to $$ \delta L = -igf_{a b c} ...
3
votes
1answer
95 views

Einstein-Yang-Mills Connections

I am playing around with coupling a classical $SU(2)$ Yang-Mills theory to Einstein's equations. Assuming spherical symmetry, the $SU(2)$ connection can be written \begin{equation} A = ...
0
votes
1answer
19 views

Vector potential in gauge transformation

While applying Gauge transformation, $\psi\prime = U \psi$ , where $ U= e^{i q \lambda(x)}$ , transformation law for "Vector Potential" comes out to be : $$ A_{\mu}\prime= ...
13
votes
0answers
381 views

What is Motivic mathematics and how is it used in physics?

In a few videos I've seen where he discusses the new approach to calculating the super Yang Mills scattering amplitudes, Nima Arkani-Hamed sometimes alludes to the use of Motivic methods as being ...
9
votes
0answers
302 views

Gauge invariant but not gauge covariant regularization

I'm not sure if someone's already asked this before, but I was wondering, in field theory, when we say that a certain field is gauge invariant but not gauge covariant, what does this mean? In ...
6
votes
0answers
132 views

Questions regarding $D=4 $ ${\cal N}=4$ supersymmetric Yang-Mills

I have some questions regarding the $D=4 $ ${\cal N}=4$ super-Yang-Mills theory (the one with a really long action which can be acquired by compactifying the 10-dimensional ${\cal N}=1$ theory). I ...
5
votes
0answers
132 views

(coordinates) Invariance/Covariance of Chern-Simons theory and Yang-Mills theory

It is known that 3D Chern-Simons(C-S) theory has no explicit metric involving in the Lagrangian density: $$ A \wedge dA + (2/3) A \wedge A \wedge A $$ while the 4D Yang-Mills(Y-M) theory has the ...
5
votes
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 ...
4
votes
0answers
183 views

Gauge Invariance of Yang Mills Lagrangian

I am trying to show the invariance of the following Yang Mills Lagrangian: $$L= -\frac{1}{4} F^a_{\mu \nu} F_a^{\mu\nu} + J_a^\mu A_\mu^a$$ under the following gauge transformation ($\theta$ being a ...
3
votes
0answers
142 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? ...
3
votes
0answers
140 views

SU(2) critical point and volume dependence

I am doing multi-dimensional plots of $\beta_j$ for SU(2) for infinite volume to understand the flow behavior and I was wondering, before I go too much further, if anyone knew off the top of their ...
2
votes
0answers
62 views

Why is QCD hard to solve if I know the beta functions?

Why is it still hard to solve QCD if we know the beta functions of the coupling? Aren't only the loops causing problems? And am I not able to write every possible interaction exact at tree-level with ...
2
votes
0answers
49 views

How to show isotropy of $SU(2)$ Yang Mills stress energy tensor?

When I vary the action of the YM Lagrangian density $$L = -\frac{1}{4} F^a_{\mu \nu}F^{\mu \nu}_a + J_a^\mu A^a_\mu$$ with respect to the metric, I obtain: $$T_{\mu \nu} = \frac{-2}{\sqrt{|g|}} ...
2
votes
0answers
144 views

From Berry's phase to artificial Gauge potential

How a nonzero geometric phase in a loop is used to generate artificial gauge potentials? If possible, can you also tell how to generate the non-abelian artificial gauge potentials.
1
vote
0answers
14 views

Are correlators constructed out of Wilson loops singular in pure Yang-Mills?

If I have some gauge invariant function of two Wilson loops (such as $\left<\text{Tr}W_1 \text{Tr}W_2\right>$) does the expectation value diverge when the loops coincide the same way ...
1
vote
0answers
58 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 ...
1
vote
0answers
69 views

Intro to Super Yang Mills theory

I'm looking to start learning Super Yang Mills theory. Currently I have studied Peskin and Schroeder up to the Renormalization Group, but don't know supersymmetry yet. I know some Conformal Field ...
1
vote
0answers
85 views

Field renormalization of scalar Yang-Mills

In most books, one can find the field renormalization $Z_3$ in Yang-Mills with fermionic matter in the fundamental. In the $\overline{MS}$ scheme, tt is given by $$ Z_3 = 1 + \frac{g^2}{16\pi^2 ...
1
vote
0answers
52 views

Is there a well-defined partition function of 4d Yang-Mills?

So I've looked everywhere to find a resource on 4 dimensional Yang-Mills partition functions, but have only managed to find examples using supersymmetry. Is there a resource describing the partition ...
1
vote
0answers
56 views

What makes Lattice Yang-Mills hard?

I've been reading up on non-perturbative Yang-Mills, and have found the following equation: $$Z[\gamma, g^2, G]=\int \! \prod e^{-S}\mathrm{d}U_i$$ Now I don't know much about computational physics, ...
1
vote
0answers
63 views

Calculation of the Poisson bracket of a (Classical) Yang-Mills generator

This question might be too technical or minute, but I believe someone can give me the right advise. What I want to calculate is a Poisson bracket algebra of classical YM gauge generators, ...
1
vote
0answers
50 views

On self-duality of N=4 super Yang Mills theories

I am looking at S-duality a bit, and was wondering if anyone had the answer to the following question. It is known that the supersymmetric Yang-Mills theory in 4 space dimensions is self-dual with ...
1
vote
0answers
104 views

Perturbative vs. non-perturbative approaches to a well-defined Yang-Mills theory in 4 dimensions

Another question regarding the Yang-Mills Existence and Mass Gap problem (http://www.claymath.org/sites/default/files/yangmills.pdf). Does the problem require that the "construction" of a four ...
1
vote
0answers
166 views

Yang-Mills Coulomb Gauge

My Question is how to explicitly move into the "Coulomb gauge" in Yang-Mills theory. Using the answer provided by QMechanic, one can move into the "temporal gauge" for Yang-Mills fields: Gauge fixing ...
1
vote
0answers
146 views

Is the axial gauge with a $\xi$ term useful in Yang-Mills theory?

i) Do people use axial gauge with a $\xi$ term? When $\xi\neq 0$, ghosts do not decouple, but maybe it's still useful? ii) Is it proved that the term $\frac 1 {2\xi}(n.A)^2$ in the Lagrangian does ...
0
votes
0answers
61 views

Taking squares or square roots of differential forms?

Reading the recent paper Loop Integrands from the Riemann Sphere by Yvonne Geyer, Lionel Mason, Ricardo Monteiro and Piotr Tourkine I noticed that the authors occasionally seem to take squares and ...
0
votes
0answers
52 views

Is it true that particles propagate on geodesics in Yang-Mills theory?

I mean free particles. Sorry for the inaccurate wording, I'm new in this field of physics.
0
votes
0answers
93 views

What is the current situation of the Yang-Mills existence problem?

What is the current situation of the Yang-Mills existence and mass gap problem? And who are the physicists and mathematicians working in this nowaday?