3D Conformal Field Theory in Twistor Space
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866910845197352960 |
|---|---|
| author | Bala, Aswini Jain, Sachin S., Dhruva K. Mazumdar, Deep Singh, Vibhor |
| author_facet | Bala, Aswini Jain, Sachin S., Dhruva K. Mazumdar, Deep Singh, Vibhor |
| contents | The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity operators apart from the conformal generators play an important role in fixing their functional form. The equations take the form of first order Euler equations which in addition to the usual solutions that are polynomials, also possess weak solutions which are distributional in nature. All of these play an important role in our analysis. For instance, in the case of three point functions, the distributional solutions are indeed the ones realized by the CFT correlators. We also extend our analysis to parity odd Wightman functions which take an interesting form in twistor space. We verify our results by systematically analyzing the corresponding Wightman functions in momentum space and spinor helicity variables and matching with the twistor results via a half-Fourier transform. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | 3D Conformal Field Theory in Twistor Space Bala, Aswini Jain, Sachin S., Dhruva K. Mazumdar, Deep Singh, Vibhor High Energy Physics - Theory Mathematical Physics The aim of this paper is to study three dimensional Lorentzian conformal field theories in twistor space. We formulate the conformal Ward identities and solve for two and three point Lorentzian Wightman functions. We found that the Helicity operators apart from the conformal generators play an important role in fixing their functional form. The equations take the form of first order Euler equations which in addition to the usual solutions that are polynomials, also possess weak solutions which are distributional in nature. All of these play an important role in our analysis. For instance, in the case of three point functions, the distributional solutions are indeed the ones realized by the CFT correlators. We also extend our analysis to parity odd Wightman functions which take an interesting form in twistor space. We verify our results by systematically analyzing the corresponding Wightman functions in momentum space and spinor helicity variables and matching with the twistor results via a half-Fourier transform. |
| title | 3D Conformal Field Theory in Twistor Space |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2502.18562 |