Integrable deformation of $\mathbb{CP}^n$ and generalised Kähler geometry

Demulder, Saskia; Hassler, Falk; Piccinini, Giacomo; Thompson, Daniel C.

doi:10.1007/JHEP10(2020)086

Integrable deformation of $\mathbb{CP}^n$ and generalised Kähler geometry

Saskia Demulder
(
- Munich, Max Planck Inst.
)
,
Falk Hassler
(
- Texas A-M
)
,
Giacomo Piccinini
(
- Swansea U.
)
,
Daniel C. Thompson
(
- Swansea U. and
- Intl. Solvay Inst., Brussels and
- Vrije U., Brussels
)

Feb 25, 2020

29 pages

Published in:

JHEP 10 (2020) 086

Published: Oct 14, 2020

e-Print:

2002.11144 [hep-th]

DOI:

10.1007/JHEP10(2020)086

View in:

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Abstract: (Springer)

We build on the results of [1] for generalised frame fields on generalised quotient spaces and study integrable deformations for ℂP

^{n}

. 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 ℂP

^{n}

and the explicit expression for the generalised Kähler potential for n = 1, 2.

Note:

25 pages

Integrable Field Theories
Sigma Models
Differential and Algebraic Geometry
String Duality
potential: Kaehler
model: chiral
deformation
integrability
geometry
diffeomorphism

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Integrable deformation of CPn\mathbb{CP}^nCPn and generalised Kähler geometry

Citations per year

Integrable deformation of $\mathbb{CP}^n$ and generalised Kähler geometry