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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2503.08774 |
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| _version_ | 1866917087244451840 |
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| author | Carmi, Dean Moreno, Javier Sukholuski, Shimon |
| author_facet | Carmi, Dean Moreno, Javier Sukholuski, Shimon |
| contents | Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and conformal correlators. We derive a position-space dispersion relation for scalar four-point mixed correlation functions in an arbitrary conformal field theory. This formula expresses the correlator in terms of its integrated double discontinuity times a kinematic kernel. The kernel is analytically computed, and expressed in a remarkably simple form as a two-variable Appell function. The dispersion kernel is found by solving a coupled partial differential equation that the kernel obeys. Numerical checks of the dispersion relation are successfully performed for generalized free field correlators. Finally, we show that our position-space dispersion relation is equivalent to a Cauchy-type dispersion relation of the Mellin amplitude of the correlator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08774 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Conformal dispersion relation for mixed correlators Carmi, Dean Moreno, Javier Sukholuski, Shimon High Energy Physics - Theory Dispersion relations are nonperturbative formulas that relate the ultraviolet and infrared behavior of an observable with wide-ranging applications applications in linear response theory, quantum field theory scattering amplitudes, and conformal correlators. We derive a position-space dispersion relation for scalar four-point mixed correlation functions in an arbitrary conformal field theory. This formula expresses the correlator in terms of its integrated double discontinuity times a kinematic kernel. The kernel is analytically computed, and expressed in a remarkably simple form as a two-variable Appell function. The dispersion kernel is found by solving a coupled partial differential equation that the kernel obeys. Numerical checks of the dispersion relation are successfully performed for generalized free field correlators. Finally, we show that our position-space dispersion relation is equivalent to a Cauchy-type dispersion relation of the Mellin amplitude of the correlator. |
| title | Conformal dispersion relation for mixed correlators |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2503.08774 |