Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories
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| Format: | Preprint |
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2023
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| _version_ | 1866910416578281472 |
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| author | Gabai, Barak Sever, Amit Zhong, De-liang |
| author_facet | Gabai, Barak Sever, Amit Zhong, De-liang |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17132 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories Gabai, Barak Sever, Amit Zhong, De-liang High Energy Physics - Theory 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. |
| title | Bootstrapping Smooth Conformal Defects in Chern-Simons-Matter Theories |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2312.17132 |