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arXiv · 2312.17132

Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories

Barak Gabai·Amit Sever·De-liang Zhong
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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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Barak Gabai, Amit Sever, De-liang Zhong. 2023-12-28. Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories. https://doi.org/10.1007/jhep03(2024)055

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