Abstract
Four point tree-level local S-matrices form a module over ring of polynomials of Mandelstam invariants s, t and u. The module of local analytic S-matrices can be encoded in terms of a partition function which is enumerated using plethystic techniques. In this paper, we enumerate the plethystic contribution to local four point photon, graviton and gluon multi-particle partition functions that encode parity violating 2 → 2 scattering. We generalise the counting problem solved in [1, 2] to project out parity violating sectors, a subtle task in even dimensions [3]. We explicitly enumerate the parity odd contributions to the multi-letter partition function for gauge fields, gravitons and gluons and evaluate the resulting parity violating partition functions in D = 4, 6. We also perform a large D analysis to show that parity violating local interactions do not contribute to four particle scattering in higher dimensions (D ≥ 8). Our computations and observations for photons, gravitons and gluons agree with the transformation properties of these S-matrices previously conjectured in [1, 2]
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Chowdhury, S.D. Counting parity-violating local S-matrices. J. High Energ. Phys. 2023, 109 (2023). https://doi.org/10.1007/JHEP04(2023)109
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DOI: https://doi.org/10.1007/JHEP04(2023)109