Aspects of Witten diagrams for holographic defects
- 1Theoretical Physics Department, CERN
- 2Department of Mathematics and Physics University of Haifa at Oranim
- 3University of Haifa
Abstract
A bstract : In this paper, we study the conformal block decomposition of Witten diagrams for d -dimensional holographic CFTs in the presence of a p -dimensional conformal defect. The holographic dual in this case contains a probe AdS p +1 brane embedded inside AdS d +1 . In particular, we focus on contact, tree-level exchanges and some one-loop two-point Witten diagrams, which contribute to the two-point function of CFT bulk scalar operators. We also consider a tree-level exchange diagram for a three-point function involving one CFT bulk scalar operator and two scalar operators localized on the defect. Employing the split representation of AdS propagators, adapted to the probe brane setup, we perform the direct channel conformal block decompositions of these diagrams. In the case of tree-level diagrams, we obtain explicit expressions for the OPE coefficients in the direct channel decompositions. For two-point tree-level exchange diagrams, we derive recursion relations for the coefficients in the crossed-channel block expansions and compute the seed coefficients which serve as inputs for these relations. Our explicit results for the block decomposition coefficients for tree-level Witten diagrams are potentially useful for further developing the analytic functional approach to bootstrapping two-point functions of bulk operators in general defect CFTs. We also study the crossing kernel, which encodes the bulk channel partial wave expansion of a defect channel partial wave. Using the bulk channel Lorentzian inversion formula for defect CFTs, we derive closed form expressions for this defect-to-bulk channel crossing kernel for zero-dimensional defects in d = 2, 4 dimensions and surface defects in d = 4, 6 dimensions.
Related
- Combinatorial aspects of holographic quantum secret sharing
- Difference between pair creation and anomaly matching: Nontrivial aspects of invertible symmetries and defects in SU(N) models
- Aspects of holographic timelike entanglement entropy in black hole backgrounds
- Symmetry breaking from conformality loss on holographic Rényi defects
- Surface defects in 𝒩=4 Super Yang-Mills: exact results and holographic bootstrap
BibTeX
@article{carmi2026aspects,
title = {{Aspects of Witten diagrams for holographic defects}},
author = {Dean Carmi and Sudip Ghosh and Trakshu Sharma},
journal = {Journal of High Energy Physics},
year = {2026},
month = oct,
doi = {10.1007/jhep10(2026)240},
url = {https://link.springer.com/article/10.1007/JHEP10(2026)240},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Aspects of Witten diagrams for holographic defects
AU - Dean Carmi
AU - Sudip Ghosh
AU - Trakshu Sharma
PY - 2026
DA - 2026/10/23
JO - Journal of High Energy Physics
DO - 10.1007/jhep10(2026)240
UR - https://link.springer.com/article/10.1007/JHEP10(2026)240
AB - A bstract : In this paper, we study the conformal block decomposition of Witten diagrams for d -dimensional holographic CFTs in the presence of a p -dimensional conformal defect. The holographic dual in this case contains a probe AdS p +1 brane embedded inside AdS d +1 . In particular, we focus on contact, tree-level exchanges and some one-loop two-point Witten diagrams, which contribute to the two-point function of CFT bulk scalar operators. We also consider a tree-level exchange diagram for a three-point function involving one CFT bulk scalar operator and two scalar operators localized on the defect. Employing the split representation of AdS propagators, adapted to the probe brane setup, we perform the direct channel conformal block decompositions of these diagrams. In the case of tree-level diagrams, we obtain explicit expressions for the OPE coefficients in the direct channel decompositions. For two-point tree-level exchange diagrams, we derive recursion relations for the coefficients in the crossed-channel block expansions and compute the seed coefficients which serve as inputs for these relations. Our explicit results for the block decomposition coefficients for tree-level Witten diagrams are potentially useful for further developing the analytic functional approach to bootstrapping two-point functions of bulk operators in general defect CFTs. We also study the crossing kernel, which encodes the bulk channel partial wave expansion of a defect channel partial wave. Using the bulk channel Lorentzian inversion formula for defect CFTs, we derive closed form expressions for this defect-to-bulk channel crossing kernel for zero-dimensional defects in d = 2, 4 dimensions and surface defects in d = 4, 6 dimensions.
SN - 1029-8479
ER -