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arXiv:2609.04035

Cusped Defects: Cusp Operator Expansion, Conformal Properties and Bootstrap Applications

Lorenzo Bianchi, Andrea Cavaglià, A. David Gutiérrez, Stefanos Robert Kousvos, Marco Meineri

Published Sep 3, 2026• 0 citations
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Abstract

We analyze general properties of cusped defect lines embedded in generic conformal field theories (CFTs). We prove that suitably defined cusp scaling operators transform like primary operators under general conformal transformations. We show that, via the cusp operator expansion (COE), defects of general shape can be expanded in a basis of cusped defects. These findings are checked and exemplified in the case of the localized magnetic field defect. Finally, we derive analytic constraints on dynamical cusp data by making use of a crossing equation, and discuss possible numerical bootstrap applications of our results.

DOI
10.48550/arxiv.2609.04035

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We analyze general properties of cusped defect lines embedded in generic conformal field theories (CFTs). We prove that suitably defined cusp scaling operators transform like primary operators under general conformal transformations. We show that, via the cusp operator expansion (COE), defects of general shape can be expanded in a basis of cusped defects. These findings are checked and exemplified in the case of the localized magnetic field defect. Finally, we derive analytic constraints on dynamical cusp data by making use of a crossing equation, and discuss possible numerical bootstrap applications of our results.
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We consider conformal boundaries and defects in Euclidean conformal field theory (CFT) at finite temperature and infinite volume. We distinguish defects that wrap the thermal circle and defects that are localised at a point on it. In both set-ups, and for any dimension and co-dimension, we classify bulk one-point functions of scalar, vector and spin-2 primaries. We relate the low-temperature expansion of bulk scalar one-point functions to zero-temperature defect CFT data and new finite-temperature data of defect primaries. For localised defects, we derive one-point bootstrap sum rules using periodicity and the defect operator expansion. We consider several examples in free bulk CFTs: unitary and non-unitary boundary CFTs, a wrapping monodromy defect, and a localised magnetic line. We determine thermal defect CFT data in all examples. For defects wrapping the thermal circle, we compute thermodynamic observables. For localised defects, we observe a Hurwitz zeta function decomposition of one-point functions suggestive of an underlying dispersion relation.
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