Twistor sigma models for quaternionic geometry and graviton scattering
We reformulate the twistor construction for hyper- and quaternion-Kähler manifolds, introducing new sigma models that compute scalar potentials for the geometry. These sigma models have the twistor space of the quaternionic manifold as their target and encode finite non-linear perturbations of the f...
| Egile Nagusiak: | , , |
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| Formatua: | Journal article |
| Hizkuntza: | English |
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International Press
2024
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| _version_ | 1826315040984137728 |
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| author | Adamo, T Mason, L Sharma, A |
| author_facet | Adamo, T Mason, L Sharma, A |
| author_sort | Adamo, T |
| collection | OXFORD |
| description | We reformulate the twistor construction for hyper- and quaternion-Kähler manifolds, introducing new sigma models that compute scalar potentials for the geometry. These sigma models have the twistor space of the quaternionic manifold as their target and encode finite non-linear perturbations of the flat structures. In the hyperkähler case our twistor sigma models compute both Plebanski fundamental forms (including the Kähler potential), while in the quaternion-Kähler setting the twistor sigma model computes the Kähler potential for the hyperkähler structure on non-projective twistor space.
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In four-dimensions, one of the models provides the generating functional of tree-level MHV graviton scattering amplitudes; perturbations of the hyperkähler structure corresponding to positive helicity gravitons. The sigma model’s perturbation theory gives rise to a sum of tree diagrams observed previously in the literature, and their summation via a matrix tree theorem gives a firstprinciples derivation of Hodges’ formula for MHV graviton amplitudes directly from general relativity. We generalise the twistor sigma model to higher-degree (defined in the first case with a cosmological constant), giving a new generating principle for the full tree-level graviton S-matrix. |
| first_indexed | 2024-12-09T03:18:44Z |
| format | Journal article |
| id | oxford-uuid:88262c3f-e996-4df7-b43a-55186298a3fb |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-12-09T03:18:44Z |
| publishDate | 2024 |
| publisher | International Press |
| record_format | dspace |
| spelling | oxford-uuid:88262c3f-e996-4df7-b43a-55186298a3fb2024-10-25T16:27:59ZTwistor sigma models for quaternionic geometry and graviton scatteringJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:88262c3f-e996-4df7-b43a-55186298a3fbEnglishSymplectic ElementsInternational Press2024Adamo, TMason, LSharma, AWe reformulate the twistor construction for hyper- and quaternion-Kähler manifolds, introducing new sigma models that compute scalar potentials for the geometry. These sigma models have the twistor space of the quaternionic manifold as their target and encode finite non-linear perturbations of the flat structures. In the hyperkähler case our twistor sigma models compute both Plebanski fundamental forms (including the Kähler potential), while in the quaternion-Kähler setting the twistor sigma model computes the Kähler potential for the hyperkähler structure on non-projective twistor space. <br> In four-dimensions, one of the models provides the generating functional of tree-level MHV graviton scattering amplitudes; perturbations of the hyperkähler structure corresponding to positive helicity gravitons. The sigma model’s perturbation theory gives rise to a sum of tree diagrams observed previously in the literature, and their summation via a matrix tree theorem gives a firstprinciples derivation of Hodges’ formula for MHV graviton amplitudes directly from general relativity. We generalise the twistor sigma model to higher-degree (defined in the first case with a cosmological constant), giving a new generating principle for the full tree-level graviton S-matrix. |
| spellingShingle | Adamo, T Mason, L Sharma, A Twistor sigma models for quaternionic geometry and graviton scattering |
| title | Twistor sigma models for quaternionic geometry and graviton scattering |
| title_full | Twistor sigma models for quaternionic geometry and graviton scattering |
| title_fullStr | Twistor sigma models for quaternionic geometry and graviton scattering |
| title_full_unstemmed | Twistor sigma models for quaternionic geometry and graviton scattering |
| title_short | Twistor sigma models for quaternionic geometry and graviton scattering |
| title_sort | twistor sigma models for quaternionic geometry and graviton scattering |
| work_keys_str_mv | AT adamot twistorsigmamodelsforquaternionicgeometryandgravitonscattering AT masonl twistorsigmamodelsforquaternionicgeometryandgravitonscattering AT sharmaa twistorsigmamodelsforquaternionicgeometryandgravitonscattering |