The Stack Overflow podcast is back! Listen to an interview with our new CEO.

Questions tagged [instantons]

An instanton (pseudoparticle) is a classical solution to the equations of motion, usually of Yang-Mills theory, with a finite, non-zero action, on a Euclidean spacetime. Instantons normally dominate the path integral of Y-M theory and determine its quantum tunneling behavior. May use for merons and other topological field-theoretic configurations.

Filter by
Sorted by
Tagged with
1
vote
1answer
44 views

Are there winding-number vacua in Weinberg-Salam (Or are they a gauge artifact)?

In pure SU(2) Yang-Mills the vacua van be grouped in homotopy classes labeled by their winding number. Instantons connect these giving rise to the theta-vacuum. I’m studying the SU(2) sphaleron in ...
0
votes
0answers
36 views

Why do quarks flip chirality when exchanging an instanton?

Quarks are elementary particles, part of the SM. There are a lot of different questions and answers on this site about chirality, I did not find a really good description, so I will use this wiki ...
2
votes
0answers
45 views

What exactly do the zero-modes of the instanton mean?

I am studying instantons in quantum mechanics. My question is regarding the the zero mode of the fluctuation determinant that we get because the solution for the instanton breaks time translation ...
3
votes
1answer
79 views

Equilibrium points of bounce/instanton solution after Wick's rotation

In Coleman's paper Fate of the false vacuum: Semiclassical theory while working out the exponential coefficient for tunneling probability through a potential barrier, he studies the problem with Wick'...
1
vote
0answers
22 views

Supersymmetric Quantum Mechanics and the Localization Theorem

I am working through Tachikawa's review on instanton counting arXiv:1412/7121, and in his treatment of Atiyah's localization theorem (see section 3.1.3), he mentions the following equations: $$\text{...
4
votes
0answers
47 views

Why does the Holst term not affect gravitational dynamics?

The general first-order Palatini action in four dimensions is given by $$S[e,\omega]=\frac{1}{2\kappa}\int_{\mathcal{M}} F_{IJ}[\omega]\wedge\left(\star+\frac{1}{\gamma}\right)\left(e^I\wedge e^J\...
1
vote
0answers
39 views

Implications of Instanton Corrections (to Degenerate Vacuua) for Spontaneous Symmetry Breaking

We consider that if the classical vacuua of a theory are degenerate then each of them can be non-invariant under one or more of the symmetries of the Lagrangian. We can choose one of the vacuua and ...
3
votes
0answers
45 views

Instantons, renormalization, and the Schwinger Model

Instantons in QCD contribute to the up, down, and strange quark masses (see, e.g., Georgi and McArthur (1981) or Kaplan and Manohar (1986)). Some papers claim that this contribution is equivalent to ...
1
vote
1answer
58 views

Winding number in 4D & $SU(2)$ group

In the book Quantum field theory by Mark Srednicki (chapter 93, pages 575-576) in order to compute winding number, $n$, in a 4-dimensional space with coordinates $x = (x_1, x_2, x_3, x_4)$ and such ...
1
vote
0answers
24 views

A question on 't Hooft's paper “Computation of the quantum effects due to a four-dimensional pseudo-particle”

In the avove paper 't Hooft considers the following (rotation invarinat) operators on the Euclidean space $\mathbb{R}^4$: \begin{eqnarray} \mathcal{M}_0=-\left(\frac{\partial}{\partial r}\right)^2-\...
1
vote
0answers
28 views

Quantum Fluctuation Contribution in the Path Integral of a Meta-stable Potential

In Wen XiaoGang's QFT of Many-Body Systems Sect 2.4.2, He studied the decay of a Meta-stable state via path integral method. The real-time potential is A state at $x=-a$ decays to $x=\infty$. The ...
3
votes
1answer
71 views

Are theta vacua topologically protected?

In discussions of Yang-Mills instantons it is often stated that one should sum in the path integral over all contributions of fluctuations around all the topologically distinct vacua labelled by ...
3
votes
1answer
110 views

Are Instantons Massless?

That is, are the only field configurations which give a non-zero winding number ones in which the Fourier transform includes a factor like $\theta(k^0)\hat{D}\delta(k^2)$, where $\hat{D}$ is some ...
2
votes
0answers
49 views

How does the instanton break the $U(1)_A$ symmetry in QCD?

The $U(1)_A$ symmetry in QCD is anomalous. Its supposed to be broken by the instantons. Can anyone physically describe how does that happen?
4
votes
0answers
55 views

Reference on instantons in gauge theories

Is there a reasonably detailed and systematic exposition of the theory of instantons in non-abelian gauge theories?
0
votes
0answers
33 views

What is the difference between real and complex instantons (mathemtically, and their physical significance), and connection to Wick rotation

I am struggling to understand the difference and physical significance between real and complex instantons- I think these are also sometimes called ghost instantons? There are also anti-instantons. ...
3
votes
0answers
107 views

What is the 't Hooft determinant?

The 't Hooft vertex/determinant is somehow generated by instantons and is responsible for the generation of mass gap in pseudo-Goldstone bosons, such as an axion. For example, the complex Peccei-...
1
vote
0answers
17 views

Is there any connection between instantons and surface-interacting polymers?

Excluded volume polymers interacting with a penetrable hypersurface of variable dimension is a very interesting system to study critical behavior via perturbative renormalization. Since a penetrable ...
1
vote
0answers
21 views

Checking modularity-like transformation property

Assume $M$ is a 4 manifold. Let $Z_v$ be partition function of fixed magnetic flux $v$ with all instanton configuration summed over where $v\in H^2(M,Z/nZ)$. $\tau$ denotes complex parameter on upper ...
1
vote
1answer
88 views

Isn't there a unique vacuum of the Yang-Mills quantum theory?

The theta vacua$^1$ of a Yang-Mills quantum theory are given by $$|\theta\rangle=\sum\limits_{n=-\infty}^{\infty}e^{in\theta}|n\rangle.$$ In Srednicki's Quantum Field Theory, he claims that the ...
1
vote
1answer
111 views

What does $B+L$ anomaly have to do with a phase redefinition of the left-handed quark field?

According to this answer, the reason why $SU(2)_L$ weak theory does not have a theta vacuum is because any theta term can be reabsorbed with a phase redefinition of the left-handed quark field. ...
3
votes
1answer
130 views

How many connected components are there in the vacuum manifold of $\phi^4$ theory?

Consider the following theory in $1+1$ dimensions $$\mathcal L = \frac12(\partial\phi)^2 - \frac\lambda4 (\phi^2 - v^2)^2 \,,$$ which exhibits a $\mathbb Z_2 = \{0,1\}$ symmetry, $\phi \to -\phi$, ...
1
vote
0answers
99 views

Does Coleman-de Luccia instanton approach a Hawking-Moss instanton?

Suppose a Coleman-de Luccia instanton terminates in the basin with the true vacuum between the top of the potential barrier and the field value with potential energy equal to the potential energy of ...
2
votes
0answers
62 views

Multi-instanton contribution to path integral

Briefly, I would like to have a reference to a clear detailed exposition of the computation of the multi-instanton contribution to the path integral while computing the energy levels splitting of the ...
4
votes
1answer
112 views

What is the relationship between the JNR instantons and the BPST instanton?

The JNR instantons are related to the t'Hooft ansatz, and take the form \begin{equation} A=\sigma_{\mu\nu}\frac{\partial_\nu \rho}{\rho}dx^\mu, \end{equation} where $\rho$ takes the form \begin{...
11
votes
1answer
244 views

Why not regard all large gauge transformations as genuine ones?

A large gauge transformation is a gauge transformation that is not connected to the identity. When quantizing a gauge theory, we must take configurations related by ordinary gauge transformations to ...
5
votes
1answer
99 views

What justifies compactifying space and spacetime, in the context of instantons?

When studying Yang-Mills instantons, there are two instances where one compactifies a space. When classifying vacuum states, one demands $A_\mu(\mathbf{x})$ to become a constant as $\mathbf{x} \to \...
3
votes
1answer
130 views

Vacuum Stability

I am studying one of the paper of Sidney Coleman, "Fate of the False Vacuum. II. First quantum corrections". Just before eq. (2.18) he says "Because of time translation invariance, this equation ...
3
votes
1answer
120 views

Simple explanation of the QCD VEV in terms of instantons

I've heard that instantons in QCD generate quark bilinear condensate $\langle \bar{q}_{L}q_{R}\rangle$ which is responsible for spontaneous symmetry breaking. Is there any clear and simple way to ...
3
votes
0answers
77 views

Comparison between $U(1)$, $SU(N)$ and $SO(N)$ instantons

I am interested in knowing the details of the comparison between $U(1)$, $SU(N)$ and $SO(N)$ instantons for their gauge theories in 4 spacetime dimensions., in terms of: Chern class (1st, 2nd), and ...
3
votes
1answer
152 views

Does the ABJ anomaly for the Abelian gauge field have a topological argument?

We known that the ABJ anomaly for non-abelian gauge fields with gauge group containing $SU(2)$ as a subgroup has a topological argument from the Euclidean path integral. Through studying the Euclidean ...
2
votes
0answers
109 views

Validity of the thin wall approximation

Inspired by the question How can I understand the tunneling problem by Euclidean path integral where the quadratic fluctuation has a negative eigenvalue?, I decided to come back to the first paper by ...
3
votes
0answers
55 views

Instanton Counting (Tachikawa's Review) and “Hilbert Space”

I'm reading this review on instanton counting. I cannot understand in section 3 how supersymmetric Hilbert spaces come about. For instance in section 3.1.1, covering the supersymmetric particle on $\...
4
votes
0answers
126 views

Instanton contributions in quantum gravity

Suppose a low-energetic System, i.e. a System, where the presence of "classical" gravitational fields can be assumed to be Zero. Classically we would have e.g. the ordinary Minkowski metric or more ...
3
votes
1answer
104 views

Which vacuum is the Universe really in?

There ate two types of vacuum of the Standard model-the vacuum of the Higgs potential and that of the vacuum of the Yang-Mills fields labelled by the Chern-Simons number. See the figure 5 here. The ...
1
vote
1answer
61 views

Quark pair superconductor: Even parity is favorred than odd parity

It seems that the quark pair superconductor can be odd or even parity pairing respect to the parity $P$. Say that the even parity has the form: $$ \langle\psi C \gamma^5 \psi\rangle $$ the odd ...
2
votes
0answers
205 views

Gauged Linear Sigma Model (GLSM) with target space $E^8$ gauge group

I just read a few reviews (and also Witten's original paper http://arxiv.org/abs/hep-th/9301042) about the GLSM (Gauged Linear Sigma Model) in (2,2) and (0,2) formulations. I have several natural ...
5
votes
1answer
181 views

Experimentally distinguishing between topologically inequivalent physical states in gauge theory

In gauge theory, physical states are often said to be characterized by equivalence classes of gauge field configurations that differ by gauge transformations. But according to Large and small gauge ...
2
votes
1answer
308 views

Is it the chiral anomaly which is solely responsible for having instanton effects (and therefore, the $\theta-$term) in the QCD action?

$\textbf{Fact 1}$ In principle, the QCD Lagrangian should contain a Lorentz invariant, gauge invariant, dimension-4 term $\sim\theta \text{Tr}[F^{\mu\nu}\tilde{F}_{\mu\nu}]$. This term, however, is ...
2
votes
2answers
311 views

Finding classical action in tunneling problem

In QM: I am trying to show that the minimum action for a classical path going between two potential wells (centered at $\pm L$) in a dbl-well potential is $$S_{classical} = \int_{-L}^{L} dx' \sqrt{...
0
votes
1answer
71 views

Non-Perturbative effects QCD and the Standard Model?

I read in an article that the Standard Model leaves unanswered questions about the non-perturbative effects of the QCD. I have basic knowledge about the perturbative and non-perturbative QCD. Could ...
1
vote
0answers
106 views

Reference request for semiclassical approximations for Schwinger-Keldysh path integrals

Can some one provide some resources for understanding semi-classical approximations for Schwinger-Keldysh path integrals. Is there any discussion about instanton (and multi-instanton) (for even single ...
5
votes
0answers
335 views

Physical origin of Nekrasov Partition Function

I've seen a few papers [1,2,3,4] which defined Nekrasov Partition Function as (in particular [2,3,4]) \begin{equation} Z(\mathbf{a}, \epsilon_1,\epsilon_2,\Lambda) := \sum_{n = 0}^\infty \Lambda^n\...
1
vote
1answer
78 views

Resources for self-dual solutions to Maxwell's equation on Euclidean or pseudo-Euclidean space

I am attempting to understand a question posed to me by an acquaintance, who asked me if I could refer him to literature on "self-dual solutions to Maxwell's equations on Euclidean space, or pseudo-...
3
votes
0answers
134 views

Are Instantons Quantum or Classical?

I'm talking specifically about instantons on four-manifolds, but my confusion here is probably of a more general nature. So I'd also appreciate less specific answers! Okay, so I know that in physics,...
6
votes
1answer
173 views

Peculiarities of non-Abelian gauge groups: self-coupling and topology

There are two striking aspects of non-Abelian gauge groups (compared to their Abelian cousins): (1) The pure gauge parts of non-Abelian Lagrangians contain self-interaction terms that are trilinear ...
4
votes
0answers
88 views

What happens when there are different classical trajectories before and after Wick rotation? [duplicate]

Recently I read the path integral of double well tunnelling. I am puzzled about the Wick rotation calculation. For example, I choose potential like $V(x)=(x^2-1)^2$ and Lagragian $L= \frac{1}{2} \dot ...
2
votes
0answers
132 views

A proof of Gel'fand-Yaglom theorem

I am trying to understand the Gel'fand-Yaglom theorem. The Gel'fand-Yaglom theorem is the following. Let us consider the eigenvalue problem of the operator $-\partial^2+W(t)$ with the eigenfunctions ...
13
votes
2answers
919 views

How to understand “analytical continuation” in the context of instantons?

Since this is a subtle and interesting question to me. I will give a rather detailed description. I hope you can keep reading it and find it interesting too. For simplicity, in the following I will ...
1
vote
1answer
189 views

Why true -> true vacuum instantons (tunneling) not possible in QFT?

According to Tanedo in his text 't Hooft and $\eta$'ail (see paragraph 2.6), unlike the case in QM, true->true vacuum tunneling in QFT is prohibited. They do explain the reason, but I still do not ...