Shadow Celestial Operator Product Expansions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909610541056000 |
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| author | Himwich, Elizabeth Pate, Monica |
| author_facet | Himwich, Elizabeth Pate, Monica |
| contents | The linearized massless wave equation in four-dimensional asymptotically flat spacetimes is known to admit two families of solutions that transform in highest-weight representations of the Lorentz group ${\rm SL}(2, \mathbb{C})$. The two families are related to each other by a two-dimensional shadow transformation. The scattering states of one family are constructed from standard momentum eigenstates by a Mellin transformation with respect to energy. Their operator product expansion (OPE) is directly related to collinear limits of momentum space amplitudes. The scattering states of the other family are a priori non-local on the celestial sphere and lack a standard notion of OPE. Such states appear naturally in the context of asymptotic symmetries, but their properties as operators remain largely unexplored. Here we initiate a study, to be continued in a forthcoming companion paper, of a definition of an OPE for shadow operators. We present a useful technical ingredient: the transformation of the OPE coefficients associated to collinear limits under a shadow. Our results can be used to find the coefficients of all three-point functions involving any combination of celestial and shadow primaries. An OPE block is used to account for the contribution from a primary together with its global conformal descendants, all of which contribute when deriving the shadowed OPE coefficients. Applications involving $U(1)$ currents and stress tensors as well as a chiral current algebra of soft gluons are discussed. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_09499 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Shadow Celestial Operator Product Expansions Himwich, Elizabeth Pate, Monica High Energy Physics - Theory The linearized massless wave equation in four-dimensional asymptotically flat spacetimes is known to admit two families of solutions that transform in highest-weight representations of the Lorentz group ${\rm SL}(2, \mathbb{C})$. The two families are related to each other by a two-dimensional shadow transformation. The scattering states of one family are constructed from standard momentum eigenstates by a Mellin transformation with respect to energy. Their operator product expansion (OPE) is directly related to collinear limits of momentum space amplitudes. The scattering states of the other family are a priori non-local on the celestial sphere and lack a standard notion of OPE. Such states appear naturally in the context of asymptotic symmetries, but their properties as operators remain largely unexplored. Here we initiate a study, to be continued in a forthcoming companion paper, of a definition of an OPE for shadow operators. We present a useful technical ingredient: the transformation of the OPE coefficients associated to collinear limits under a shadow. Our results can be used to find the coefficients of all three-point functions involving any combination of celestial and shadow primaries. An OPE block is used to account for the contribution from a primary together with its global conformal descendants, all of which contribute when deriving the shadowed OPE coefficients. Applications involving $U(1)$ currents and stress tensors as well as a chiral current algebra of soft gluons are discussed. |
| title | Shadow Celestial Operator Product Expansions |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2505.09499 |