Linear sigma models and integrable systems

Question

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

Comments

+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

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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

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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

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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

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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

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That would be great, of course! ;)

This post imported from StackExchange Physics at 2014-08-07 15:34 (UCT), posted by SE-user user5831

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I did ask Lumo, he said is a very serious (meaning great ;-)...) question but he does not know the answer or how to answer it ... :-/

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

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Thanks a lot in any case for your help!!! :) I hope that I will be able to convince some of the experts on this to help me out here. The answer to the question seems to be positive though, but so far I haven't seen/received any details... ;)

This post imported from StackExchange Physics at 2014-08-07 15:34 (UCT), posted by SE-user user5831

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It is a shame that such questions do not find answers here, maybe the only thing that could help is this

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