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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeMay 4th 2020
• (edited May 4th 2020)

starting something, for the moment mainly to give a home to relation between 5d Maxwell theory and self-dual 3-forms in 6d – section

• CommentRowNumber2.
• CommentAuthorUrs
• CommentTimeMay 4th 2020

added a section “Relation between 5d Maxwell theory and massive vector mesons in 4d” (here) spelling out a key step in

(but not the full construction there, and also using some other assumptions, as I have highlighted in the text – maybe more later)

• CommentRowNumber3.
• CommentAuthorUrs
• CommentTimeMay 6th 2020
• (edited May 6th 2020)

I am starting a subsection “Relation to massive vector mesosns in 4d – The Sakai-Sugimoto model” (here), following Sutcliffe.

So far I have added a (somewhat lengthy) proof (here) that the 5d vacuum Maxwell equations on the Sakai-Sugimoto spacetime

$g \;\coloneqq\; H^{+1} \, \eta_{\mu \nu} d x^\mu \otimes d x^\nu + H^{-1} d z \otimes d z$

with

$H(\{x^\mu\}, z) \;\coloneqq\; H(z) \;\coloneqq\; \left( 1 + \frac{z^2}{L^2} \right)^{2/3}$

are equivalent to the following massive 4d wave equation:

\begin{aligned} & \star d \star d A \;=\; 0 \\ \Leftrightarrow \;\;\; & \eta^{\mu \nu}\partial_\mu \partial_\nu A \;+\; H^{1/2} \partial_z \left( H^{3/2} \partial_z A \right) \;=\; 0 \end{aligned}

This statement is sort of in the references cited, but in a somewhat roundabout manner. I wanted to write out an explicit statement and proof.

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