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Conformal dispersion relations for defects and boundaries
- Source :
- SciPost Phys. 15, 055 (2023)
- Publication Year :
- 2022
-
Abstract
- We derive a dispersion relation for two-point correlation functions in defect conformal field theories. The correlator is expressed as an integral over a (single) discontinuity that is controlled by the bulk channel operator product expansion (OPE). This very simple relation is particularly useful in perturbative settings where the discontinuity is determined by a subset of bulk operators. In particular, we apply it to holographic correlators of two chiral primary operators in $\mathcal{N}= 4$ Super Yang-Mills theory in the presence of a supersymmetric Wilson line. With a very simple computation, we are able to reproduce and extend existing results. We also propose a second relation, which reconstructs the correlator from a double discontinuity, and is controlled by the defect channel OPE. Finally, for the case of codimension-one defects (boundaries and interfaces) we derive a dispersion relation which receives contributions from both OPE channels and we apply it to the boundary correlator in the $O(N)$ critical model. We reproduce the order $\epsilon^2$ result in the $\epsilon$-expansion using as input a finite number of boundary CFT data.<br />Comment: 36 pages, 3 figures
- Subjects :
- High Energy Physics - Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- SciPost Phys. 15, 055 (2023)
- Publication Type :
- Report
- Accession number :
- edsarx.2205.09775
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.21468/SciPostPhys.15.2.055