Conformal dispersion relations for defects and boundaries

Bianchi, Lorenzo; Bonomi, Davide

doi:10.21468/SciPostPhys.15.2.055

SciPost Physics

Conformal dispersion relations for defects and boundaries

Lorenzo Bianchi, Davide Bonomi

SciPost Phys. 15, 055 (2023) · published 8 August 2023

doi: 10.21468/SciPostPhys.15.2.055
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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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.2.055
TI  - Conformal dispersion relations for defects and boundaries
PY  - 2023/08/08
UR  - https://scipost.org/SciPostPhys.15.2.055
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 2
SP  - 055
A1  - Bianchi, Lorenzo
AU  - Bonomi, Davide
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.15.2.055,
	title={{Conformal dispersion relations for defects and boundaries}},
	author={Lorenzo Bianchi and Davide Bonomi},
	journal={SciPost Phys.},
	volume={15},
	pages={055},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.2.055},
	url={https://scipost.org/10.21468/SciPostPhys.15.2.055},
}

Cited by 9

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¹ ² Lorenzo Bianchi,
³ Davide Bonomi

Funders for the research work leading to this publication

Ministero dell’Istruzione, dell’Università e della Ricerca (MIUR) (through Organization: Ministero dell'Istruzione, dell'Università e della Ricerca / Ministry of Education, Universities and Research [MIUR])
Science and Technology Facilities Council [STFC]