Abstract
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.
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Gabai, B., Sever, A. & Zhong, Dl. Bootstrap** smooth conformal defects in Chern-Simons-matter theories. J. High Energ. Phys. 2024, 55 (2024). https://doi.org/10.1007/JHEP03(2024)055
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DOI: https://doi.org/10.1007/JHEP03(2024)055