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# (26.07.) Plurality of effective actions: Quasi-Poisson case

### Jan Vysoký (TU Prague)

#### 12.07.2018 at 16:15

In 1995 Klimčík and Ševera proposed a new kind of duality for two-dimensional sigma models

targeted in two mutually dual Poisson-Lie groups. On the level of corresponding low-energy

effective actions, one has to find the correct formulas for dilaton fields. This can be done either by

careful analysis of the associated path integral densities or (rather surprisingly) using the Levi-

Civita connections on Courant algebroids. A Manin pair is formed by a quadratic Lie algebra and its

Lagrangian subalgebra. Whenever it integrates to a Lie group D and its subgroup G, one obtains a

quasi-Poisson structure on G and a quasi-Poisson action of G on the coset space S = D/G. One

can build an effective theory targeted on S. However, there can be several such subgroups G.

Using the language of Courant algebroids, we prove the following: starting with a certain data on

the quadratic Lie algebra, one can construct fields on all possible target spaces S satisfying the

respective equations of motion.

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