Hyperkähler, bi-hypercomplex, generalized hyperkähler structures and T-duality

Kimura, Takeyoshi; Sasaki, Shin; Shiozawa, Kenta

doi:10.1016/j.nuclphysb.2022.115873

Cited by 5 publications

(10 citation statements)

References 34 publications

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“…By applying these conditions to the T-duality transformation rule (9), we obtain the Buscher-like rule from the hyperkähler structure (J a , ω a ) to the bi-hypercomplex structure (J a,± , ω a,± ). See the original paper [14] for details.…”

Section: T-duality Transformation Between Two Different Bi-hypercompl...mentioning

confidence: 99%

“…The metric (10) and the fundamental two-forms (11) give the three complex structures equipped in the Taub-NUT space from the condition J a = −g −1 ω a . The detailed expressions of J a can be found in the original paper [14].…”

Section: T-duality From Kk-vortex To T-fold Geometriesmentioning

confidence: 99%

“…The T-duality transformation (7) along this isometry yields the four-dimensional transverse geometry of the H-monopole (smeared NS5-brane). By using the formulae (9), the bi-hypercomplex structure of the H-monopole can be obtained (see the original paper [14] for details).…”

Section: T-duality From Kk-vortex To T-fold Geometriesmentioning

confidence: 99%

“…We finally discuss the worldsheet instantons on spaces with such non-trivial monodromies by using the Born sigma model. The main results in this contribution are based on the original works [14,15].…”

Section: Introductionmentioning

confidence: 99%

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T-duality relations between hyperkähler and bi-hypercomplex structures

Kimura,

Sasaki,

Shiozawa

2023

J. Phys.: Conf. Ser.

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We investigate the T-duality relations between hyperkähler and bi-hypercomplex structures using the doubled formalism. In generalized geometry, both the hyperkähler and bi-hypercomplex structures are embedded in generalized hyperkähler structures that satisfy the split-bi-quaternion algebra. We write down the analogue of the Buscher rule, which is the T-duality transformation of the hyperkähler and bi-hypercomplex structures. As a practical example, we construct the bi-hypercomplex structure of the 5 2 2 -brane, known as a T-fold, from the hyperkähler structure of the Taub-NUT space using the T-duality transformation. The bi-hypercomplex structures of the T-fold have non-trivial monodromies. This results in the fact that the worldsheet instantons on the T-fold are multi-valued. We comment on the resolution of this issue using the Born sigma model.

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Section: T-duality Transformation Between Two Different Bi-hypercompl...mentioning

confidence: 99%

Section: T-duality From Kk-vortex To T-fold Geometriesmentioning

confidence: 99%

Section: T-duality From Kk-vortex To T-fold Geometriesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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T-duality relations between hyperkähler and bi-hypercomplex structures

Kimura,

Sasaki,

Shiozawa

2023

J. Phys.: Conf. Ser.

Self Cite

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“…This was later extended to include the 5 2 2 obtained via a further T-duality in [20,21]. The generalised complex structures of this duality chain were investigated very recently [22,23].…”

Section: Jhep08(2022)119mentioning

confidence: 99%

Doubled space and extended supersymmetry

Blair

Hulík

Sevrin

et al. 2022

J. High Energ. Phys.

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The doubled formulation of the worldsheet provides a description of string theory in which T-duality is promoted to a manifest symmetry. Here we extend this approach to $$ \mathcal{N} $$ N = (2, 2) superspace providing a doubled formulation for bi-Hermitian/generalised Kähler target spaces. The theory is described by a single function, a doubled-generalised Kähler potential, supplemented with a manifestly $$ \mathcal{N} $$ N = (2, 2) constraint. Several examples serve to illustrate this construction, including a discussion of the $$ \mathcal{N} $$ N = (2, 2) description of T-folds.

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