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arXiv · 2509.04578

Do null defects dream of conformal symmetry?

Rajeev S. Erramilli·Justin Kulp·Fedor K. Popov
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Abstract

We initiate the study of null line defects in Lorentzian conformal field theories in various dimensions. We show that null lines geometrically preserve a larger set of conformal isometries than their timelike and spacelike counterparts, explain a connection to non-relativistic systems, and constrain correlation functions using conformal Ward identities. We argue that having conformal symmetry, and especially maximal conformal symmetry, is extremely constraining -- nearly trivializing systems. We consider the (3+1)d scalar pinning field and null Wilson line examples in depth, compare their results to ultraboosted limits of timelike and spacelike systems, and argue that shockwave-type solutions are generic. A number of physical consistency conditions compel us to consider defect correlators as distributions on a restricted subspace of Schwartz test functions. Consequently, we provide a resolution to the longstanding problem of ultraboosted limits of gauge potentials in classical electromagnetism. We briefly analyze semi-infinite sources for the scalar in ($4-\epsilon$)-dimensions, consider solutions on the Lorentzian cylinder, and introduce the ''perfect null polygon'' which emerges for compatibility between Gauss' law and ultraboosted limits.

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Rajeev S. Erramilli, Justin Kulp, Fedor K. Popov. 2025-09-04. Do null defects dream of conformal symmetry?. https://arxiv.org/abs/2509.04578

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