Complex structure-induced deformations of σ-models

Abstract

Abstract:We describe a deformation of the principal chiral model (with an evendimensional target space G) by a B-field proportional to the Kähler form on the target space. The equations of motion of the deformed model admit a zero-curvature representation. As a simplest example, we consider the case of G = S 1 × S 3 . We also apply a variant of the construction to a deformation of the AdS 3 × S 3 × S 1 (super-)σ-model.

Integrable deformation of ℂPn and generalised Kähler geometry

“…As it turns out, complex projective spaces CP n are the natural setting where to carry out our investigation. They are exemplars of a broader class of algebraic varieties, known as generalised flag manifolds, which have recently benefited, alongside para-complex manifolds, from a surge of interest in the physics literature as they materialise in rich examples [26][27][28][29][30][31].…”

“…(4.8) are adapted to this such that the Killing vectors are simply given by the ∂ φm . We can select the holomorphic (with respect to J ± ) part of σ −1 by acting with a projector 26) such that dq ∧ dp + dQ ∧ dP = σ −1…”

Combining the bi-Yang-Baxter deformation, the Wess-Zumino term and TsT transformations in one integrable σ-model

“…Inverting these relations it is then possible to express the gauge field as 30) and the currents J L ± as…”

Quantum flag manifold $σ$-models and Hermitian Ricci flow

“…Another option is taking an R-matrix induced by a complex structure on the Lie group G with Lie algebra g[42]. In this case (2.7) is the condition of vanishing of the Nijenhuis tensor.…”