Abstract
We build on the results of [1] for generalised frame fields on generalised quotient spaces and study integrable deformations for ℂPn. In particular we show how, when the target space of the Principal Chiral Model is a complex projective space, a two-parameter deformation can be introduced in principle. The second parameter can however be removed via a diffeomorphism, which we construct explicitly, in accordance with the results stemming from a thorough integrability analysis we carry out. We also elucidate how the deformed target space can be seen as an instance of generalised Kähler, or equivalently bi-Hermitian, geometry. In this respect, we find the generic form of the pure spinors for ℂPn and the explicit expression for the generalised Kähler potential for n = 1, 2.
Highlights
Is not an isometry group) but obey a modified on-shell conservation law that is noncommutative with respect to a “dual” algebra g [4, 5]
In particular we show how, when the target space of the Principal Chiral Model is a complex projective space, a two-parameter deformation can be introduced in principle
If the coset space G/H is an Hermitian and Poisson homogenous space (i.e. H is a coistropic subgroup) we demonstrate that the deformed target space geometry is generalised Kahler [32, 33]
Summary
The generalised coset construction which we will present was originally motivated by closed string world sheet theories with Poisson-Lie symmetry. From this perspective one can readily extract conventional target space geometric data even though the underlying algebraic structure is rather obscured. To expose this structure it is helpful to adopt a Hamiltonian approach called the E-model [8] — introduced in section 2.2 — and construct the corresponding Poisson brackets
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