$N=(2,2)$ superfields and geometry revisited
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916448312492032 |
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| author | Hull, Chris Zabzine, Maxim |
| author_facet | Hull, Chris Zabzine, Maxim |
| contents | We take a fresh look at the relation between generalised Kähler geometry and $N=(2,2)$ supersymmetric sigma models in two dimensions formulated in terms of $(2,2)$ superfields. Dual formulations in terms of different kinds of superfield are combined to give a formulation with a doubled target space and both the original superfield and the dual superfield. For Kähler geometry, we show that this doubled geometry is Donaldson's deformation of the holomorphic cotangent bundle of the original Kähler manifold. This doubled formulation gives an elegant geometric reformulation of the equations of motion. We interpret the equations of motion as the intersection of two Lagrangian submanifolds (or of a Lagrangian submanifold with an isotropic one) in the infinite dimensional symplectic supermanifold which is the analogue of phase space. We then consider further extensions of this formalism, including one in which the geometry is quadrupled, and discuss their geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19079 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $N=(2,2)$ superfields and geometry revisited Hull, Chris Zabzine, Maxim High Energy Physics - Theory Differential Geometry Symplectic Geometry We take a fresh look at the relation between generalised Kähler geometry and $N=(2,2)$ supersymmetric sigma models in two dimensions formulated in terms of $(2,2)$ superfields. Dual formulations in terms of different kinds of superfield are combined to give a formulation with a doubled target space and both the original superfield and the dual superfield. For Kähler geometry, we show that this doubled geometry is Donaldson's deformation of the holomorphic cotangent bundle of the original Kähler manifold. This doubled formulation gives an elegant geometric reformulation of the equations of motion. We interpret the equations of motion as the intersection of two Lagrangian submanifolds (or of a Lagrangian submanifold with an isotropic one) in the infinite dimensional symplectic supermanifold which is the analogue of phase space. We then consider further extensions of this formalism, including one in which the geometry is quadrupled, and discuss their geometry. |
| title | $N=(2,2)$ superfields and geometry revisited |
| topic | High Energy Physics - Theory Differential Geometry Symplectic Geometry |
| url | https://arxiv.org/abs/2404.19079 |