# Linear sigma models and integrable systems

+ 10 like - 0 dislike
52 views

I'm a mathematician who recently became very interested in questions related to mathematical physics but somehow I have already difficulties in penetrating the literature... I'd highly appreciate any help with the following question:

My aim is to relate a certain (equivariant) linear sigma model on a disc (with a non-compact target $\mathbb C$) as constructed in the exciting work of Gerasimov, Lebedev and Oblezin in Archimedean L-factors and Topological Field Theories I, to integrable systems (in the sense of Dubrovin, if you like).

More precisely, I'd like to know if it's possible to express "the" correlation function of an (equivariant) linear sigma model (with non-compact target) as in the above reference in terms of a $\tau$-function of an associated integrable system?

As far as I've understood from the literature, for a large class of related non-linear sigma models (or models like conformal topological field theories) such a translation can be done by translating the field theory (or at least some parts of it) into some Frobenius manifold (as in Dubrovin's approach, e.g., but other approaches are of course also welcome). Unfortunately, so far, I haven't been able to understand how to make things work in the setting of (equivariant) linear sigma models (with non-compact target).

Any help or hints would be highly appreciated!

This post imported from StackExchange Physics at 2014-08-07 15:34 (UCT), posted by SE-user user5831
+1: Sorry I can't help you, but this is a refreshingly good question!

This post imported from StackExchange Physics at 2014-08-07 15:34 (UCT), posted by SE-user Michael Brown
Too bad that we no longer have TP.SE. There such a nice question would have obtained answers pretty quickly. Maybe some people following the research-level tag will finally notice it and can help ...

This post imported from StackExchange Physics at 2014-08-07 15:34 (UCT), posted by SE-user Dilaton
Thank you both very much for your interest, in any case! :)

This post imported from StackExchange Physics at 2014-08-07 15:34 (UCT), posted by SE-user user5831
Thanks for the note, I hope we will soon see an interesting answer here ;-)

This post imported from StackExchange Physics at 2014-08-07 15:34 (UCT), posted by SE-user Dilaton
A very nice high-level physics blog is for example Lumo's TRF, I am there too. If nothing helps, I could ask him there, if he has an answer to the question, he sometimes does it when I ask him :-)

This post imported from StackExchange Physics at 2014-08-07 15:34 (UCT), posted by SE-user Dilaton
 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.