Bootstrapping smooth conformal defects in Chern-Simons-matter theories

Barak Gabai, Amit Sever, De Liang Zhong*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large N holographic theories, these fundamental observables are dual to the open-string partition function in AdS. In this paper, we develop a bootstrap method for studying them and apply it to conformal line defects in Chern-Simons matter theories. In these cases, the line bootstrap is based on three minimal assumptions — conformal invariance of the line defect, large N factorization, and the spectrum of the two lowest-lying operators at the end of the line. On the basis of these assumptions, we solve the one-dimensional CFT on the line and systematically compute the defect expectation value in an expansion around the straight line. We find that the conformal symmetry of a straight defect is insufficient to fix the answer. Instead, imposing the conformal symmetry of the defect along an arbitrary curved line leads to a functional bootstrap constraint. The solution to this constraint is found to be unique.

Original languageEnglish
Article number55
JournalJournal of High Energy Physics
Issue number3
StatePublished - Mar 2024


FundersFunder number
Simons Collaboration Grants on the Non-Perturbative Bootstrap
Israel Science Foundation1197/20
U.S. Department of EnergyDE-SC0007870
Royal SocietyURF/R1/221310


    • Chern-Simons Theories
    • Field Theories in Higher Dimensions
    • Scale and Conformal Symmetries
    • Wilson, ’t Hooft and Polyakov loops


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