Abstract
Effective field theories (EFT) are strongly constrained by fundamental principles such as unitarity, locality, causality, and Lorentz invariance. In this paper, we consider the EFT of photons (or other U(1) gauge field) and compare different approaches to obtain bounds on its Wilson coefficients. We present an analytic derivation of the implications of unitarity (linear and non-linear positivity bounds) and compare these constraints with the requirement of causal propagation of the photon modes around non-trivial backgrounds generated by external sources. Within this setup, we find that the low energy causality condition can give complementary constraints to our analytic positivity bounds. In other words, simple analytic techniques can give strong constraints on the allowed region of the photon EFT parameters even when the positivity bounds are not numerically optimized.
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Acknowledgments
We would like to thank Calvin Chen, Greg Kaplanek, Aoibheann Margalit and Andrew J. Tolley for useful discussions. The work of MCG, AT and CdR at Imperial is supported by STFC grant ST/T000791/1. VP is funded by the Imperial College President’s Fellowship. SJ is supported by an STFC studentship. CdR is also supported by a Simons Investigator award 690508. The work of AT at final stage is supported in part by the National Natural Science Foundation of China (NSFC) under Grant No. 12147103.
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Carrillo González, M., de Rham, C., Jaitly, S. et al. Positivity-causality competition: a road to ultimate EFT consistency constraints. J. High Energ. Phys. 2024, 146 (2024). https://doi.org/10.1007/JHEP06(2024)146
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DOI: https://doi.org/10.1007/JHEP06(2024)146