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15
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0answers
280 views

What is the status of Witten's and Vafa's argument that the QCD vacuum energy is a minimum for zero $\theta$ angle?

The argument, which I reproduce here from Ramond's `Journies BSM', is originally by Witten and Vafa in ($\it{Phys}$. $\it{Rev}$. $\it{Lett}$. 53, 535(1984)). The argument is that for $\theta = 0 $ ...
7
votes
0answers
177 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
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0answers
48 views

Ambiguity in Asymptotic Perturbative Series and Instantons

I know there are a number of questions about the asymptoticity of perturbative series and about instantons on StackExchange (e.g. Instantons and Non Perturbative Amplitudes in Gravity from user566, ...
6
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0answers
135 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 ...
4
votes
0answers
84 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 ...
2
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0answers
73 views

Instantons in Witten's supersymmetry and Morse theory

I'm reading Witten's paper on supersymmetry and Morse theory and am confused about the details of the instanton calculation which he uses to define a Morse complex (beginning at page 11 of the pdf) . ...
2
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0answers
43 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 ...
1
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0answers
28 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
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0answers
76 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
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0answers
68 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 ...