Two point functions in defect CFTs

Christopher P. Herzog; Abhay Shrestha

doi:10.1007/JHEP04(2021)226

Two point functions in defect CFTs

Christopher P. Herzog, Abhay Shrestha^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

20 Citations (Scopus)

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Abstract

This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝ^p× (ℝ^q/ℤ₂) and a free four dimensional Maxwell theory on a wedge.

Original language	English
Article number	226
Number of pages	35
Journal	Journal of High Energy Physics
Volume	2021
Issue number	4
Early online date	22 Apr 2021
DOIs	https://doi.org/10.1007/JHEP04(2021)226
Publication status	Published - Apr 2021

Keywords

Boundary Quantum Field Theory
Conformal Field Theory

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10.1007/JHEP04(2021)226

Two point functions_HERZOG_Accepted 14 Mar 2021_GOLD_VoRAccepted author manuscript, 543 KBLicence: CC BY

Cite this

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AB - This paper is designed to be a practical tool for constructing and investigating two-point correlation functions in defect conformal field theory, directly in physical space, between any two bulk primaries or between a bulk primary and a defect primary, with arbitrary spin. Although geometrically elegant and ultimately a more powerful approach, the embedding space formalism gets rather cumbersome when dealing with mixed symmetry tensors, especially in the projection to physical space. The results in this paper provide an alternative method for studying two-point correlation functions for a generic d-dimensional conformal field theory with a flat p-dimensional defect and d − p = q co-dimensions. We tabulate some examples of correlation functions involving a conserved current, an energy momentum tensor and a Maxwell field strength, while analysing the constraints arising from conservation and the equations of motion. A method for obtaining bulk-to-defect correlators is also explained. Some explicit examples are considered: free scalar theory on ℝp× (ℝq/ℤ2) and a free four dimensional Maxwell theory on a wedge.

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Two point functions in defect CFTs

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