Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

177 submissions , 139 unreviewed
4,336 questions , 1,662 unanswered
5,101 answers , 21,661 comments
1,470 users with positive rep
642 active unimported users
More ...

  A proof for physicists of Proposition 5.5 in "Foundations of Differential Geometry Vol 1" by Kobayashi and Nomizu

+ 3 like - 0 dislike
120 views

Please consider the proposition

My questions are : 

1.  How to give a proof for physicists of this proposition?

2.  What could be a physical application of this proposition?

asked Mar 22 in Mathematics by juancho (1,105 points) [ revision history ]
retagged Mar 24 by juancho

1 Answer

+ 1 like - 0 dislike

A possible application of the the proposition 5.5  in physics occurs in the case of the Kapustin-Witten equation:

In this case  $\phi$ is a tensorial 1-form of type  $ad G$ and $d_{A} \phi$  is given by the proposition 5.5.

It is conjectured that the coefficients of the Jones polynomial of a knot can be computed by counting solutions of the KW equations on a half-space in $R^4$ with the generalized Nahm pole boundary conditions. 

The Jones polynomial is a Laurent series $J \left( q \right) =\sum _ na_{{n}}{q}^{n} $,  and the conjecture is that $a_ n$  is an algebraic count of the number of solutions of the KW equations with second Chern class   equal to $n$.

Reference :  https://arxiv.org/pdf/1712.00835.pdf

answered Mar 23 by juancho (1,105 points) [ revision history ]
edited Mar 24 by juancho

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$y$\varnothing$icsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
To avoid this verification in future, please log in or register.




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...