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| 001 | 434677 | ||
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| 100 | 1 | _ | |a Coman-Lohi, Ioana |0 P:(DE-H253)PIP1021430 |b 0 |e Corresponding author |
| 245 | _ | _ | |a Toda Conformal Blocks, Quantum Groups, and Flat Connections |
| 260 | _ | _ | |a Heidelberg |c 2019 |b Springer |
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| 520 | _ | _ | |a This paper investigates the relations between the Toda conformal field theories,quantum group theory and the quantisation of moduli spaces of flat connections.We use the free field representation of theW-algebras to define natural bases for spacesof conformal blocks of the Toda conformal field theory associated to the Lie algebrasl3 on the three-punctured sphere with representations of generic type associated to thethree punctures. The operator-valued monodromies of degenerate fields can be used todescribe the quantisation of the moduli spaces of flat SL(3)-connections. It is shown thatthe matrix elements of the monodromies can be expressed as Laurent polynomials ofmore elementary operatorswhich have a simple definition in the free field representation.These operators are identified as quantised counterparts of natural higher rank analogsof the Fenchel–Nielsen coordinates from Teichmüller theory. Possible applications tothe study of the non-Lagrangian SUSY field theories are briefly outlined. |
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