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11
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0answers
324 views

Does the existence of instantons imply non-trivial cohomology of spacetime?

Gauge theories are considered to live on $G$-principal bundles $P$ over the spacetime $\Sigma$. For convenience, the usual text often either compactify $\Sigma$ or assume it is already compact. An ...
7
votes
0answers
244 views

Instantons and Borel Resummation

As explained in Weinberg's The Quantum Theory of Fields, Volume 2, Chapter 20.7 Renormalons, instantons are a known source of poles in the Borel transform of the perturbative series. These poles are ...
6
votes
0answers
165 views

What is the rate of B violation expected in the standard model during high energy collisions?

In a recent question Can colliders detect B violation? I asked about detecting B violation in collisions. Here I am interested in the theory aspect. (I asked both questions originally in the same ...
5
votes
0answers
157 views

Could sphaleron-induced proton decay also cause vacuum decay?

I will say right away that I don't mean standard-model sphalerons, I mean the sphalerons of some extension of the standard model. The reason to even think about this is last year's paper by Frampton ...
4
votes
0answers
67 views

Why is the Taub-NUT instanton singular at $\theta=\pi$?

Consider the following metric $$ds^2=V(dx+4m(1-\cos\theta)d\phi)^2+\frac{1}{V}(dr+r^2d\theta^2+r^2\sin^2\theta{}d\phi^2),$$ where $$V=1+\frac{4m}{r}.$$ That is the Taub-NUT instanton. I have been ...
2
votes
0answers
86 views

Why instantons can not cause confinement in 4d?

I am reading Aspects of Symmetry by Sidney Coleman. More specifically I am trying to learn about instantons, and I would like some clarifications. In chapter 7, section 4. he derives confinement in ...
2
votes
0answers
49 views

't Hooft many instanton solutions

I'm study 't Hooft many instanton solutions of self-duality equation. In this method $A^a_\mu=-\bar{\eta}^{a}_{\mu\nu}\partial^\nu \ln{\Phi}$. After substitution in self-duality equation I've proven ...
1
vote
0answers
16 views

Few questions about SM baryogenesis

SM provides baryogenesis via leptogenesis due to anomalies and sphaleron processes. I have a few questions on it. How exactly the anomalies in lepton and baryon currents provide convertation of ...
1
vote
0answers
42 views

Instantons and confinement

Do instantons tell us something about behavior of QCD when lowering an energies? I.e., is it possible that instantons provide confinement? Are there some calculations which tell us that instantons ...
1
vote
0answers
29 views

manipulations with SU(N) Nekrasov partition function

Think of a Young tableau $R$ as collection of rows $y_1 \geq ... \geq y_d > y_{d+1}=0$ and all others zero, with $\ell(Y):= \sum_j y_j$ and for a box $s=(i,j)\in R$ we have $a_Y(s):=y_i-j$ and ...
1
vote
0answers
41 views

Proof for the Mass gap of non-chiral Luttinger liquids with a Cosine potential

Similar to this post, I believe in condensed matter, people know the mass-gap statement for non-chiral Luttinger liquids with large $g \cos(\beta_{}^{} \cdot\phi_{})$ potential. This is the ...
1
vote
0answers
93 views

Quantum tunneling in a time dependent potential

I wonder if I could use the technique for finding the tunneling rate given by $$ \Gamma=2 \Im[ F]$$ where $F$ is the free energy in case of time dependent potentials? Relevant to the previous ...
1
vote
0answers
73 views

An Equality in The Calculus of Many Instantons

I am reading the review on instantons. When I tried to derive formula (2.27) on page 17, I always get the different coefficient of $gF_{mn}$ term. My calculation is just directly expanding the first ...
0
votes
0answers
53 views

Knotted solutions of Maxwell's equations in flat vacuum - do they really exist?

The paper http://arxiv.org/abs/1502.01382 claims that such solutions exist and that a number of specialists know them since a long time. Is this paper correct? Jackson's text on electrodynamics does ...
0
votes
0answers
38 views

Bound states and extensive field configurations

What are extensive field configurations in QFT (instantons, monopoles etc.)? What is the difference in description of their contribution in path integral value or in $n$-point operator functions ...