# Generalized spin connection and dreibein in higher spin gravity

+ 1 like - 0 dislike
102 views

I am studying higher spin gravity and I would like to know the mathematical and physical meaning of generalized spin connection and generalized dreibein that appear in this theory. It is well known that there are important connections between higher spin theories and string theory. For this reason I am wondering if the generalized spin connection is related or not to the parallel transport of extended objects (strings, membranes, etc.) on compact manifolds. Is there also a relation with Hitchin's generalized geometry?

This post imported from StackExchange MathOverflow at 2015-03-10 13:03 (UTC), posted by SE-user Gian
retagged Mar 10, 2015

+ 2 like - 0 dislike

Higher spin symmetries can be interpreted as generalized symmetries of free field differential equations. "Generalized symmetries" means here symmetries generated by differential operators of order larger than one. (Amusingly, some mathematicians call such symmetries "higher symmetries" and this dates back from before the link with higher spin theories was recognized.) In a suitable sense, the higher spin fields are gauging these generalized symmetries.

A general discussion of this fact appears in Bekaert's paper

http://arxiv.org/abs/0807.4223

I showed in

http://arxiv.org/abs/1402.4486

Section 4.2 how the family of higher spin Lie algebras in 3-dimension (usually called ${\rm hs}(\lambda)$) can be recovered from the generalized symmetries of the Klein-Gordon equation on AdS3, with the parameter $\lambda$ being related to the mass term.

Good references on generalized symmetries include the book Application of Lie groups to differential equations by Olver and Symmetries and conservation laws for differential equations of mathematical physics by Krasilshchik and Vinogradov.

This post imported from StackExchange MathOverflow at 2015-03-10 13:03 (UTC), posted by SE-user Samuel Monnier
answered Jan 31, 2015 by (60 points)

 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): Email me at this address if my answer is selected or commented on: 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$\hbar$ysicsOve$\varnothing$flowThen 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.