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arXiv:2403.18691 · Physical Review Letters

Defect Conformal Field Theory from Sachdev-Ye-Kitaev Interactions

Yang Ge, Shao-Kai Jian

Published Dec 24, 2024• 4 citations
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Abstract

The coupling between defects and extended critical degrees of freedom gives rise to the intriguing theory known as defect conformal field theory (CFT). In this work, we introduce a novel family of boundary and interface CFTs by coupling N Majorana chains with SYK_{q} interactions at the defect. Our analysis reveals that the interaction with q=2 constitutes a new marginal defect. Employing a versatile saddle-point method, we compute unique entanglement characterizations, including the g function and effective central charge, of the defect CFT. Furthermore, we analytically evaluate the transmission coefficient using CFT techniques. Surprisingly, the transmission coefficient deviates from the universal relation with the effective central charge across the defect at the large N limit, suggesting that our defect CFT extends beyond all known examples of Gaussian defect CFT.

DOI
10.1103/physrevlett.133.266503

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The coupling between defects and extended critical degrees of freedom gives rise to the intriguing theory known as defect conformal field theory (CFT). In this work, we introduce a novel family of boundary and interface CFTs by coupling N Majorana chains with SYK_{q} interactions at the defect. Our analysis reveals that the interaction with q=2 constitutes a new marginal defect. Employing a versatile saddle-point method, we compute unique entanglement characterizations, including the g function and effective central charge, of the defect CFT. Furthermore, we analytically evaluate the transmission coefficient using CFT techniques. Surprisingly, the transmission coefficient deviates from the universal relation with the effective central charge across the defect at the large N limit, suggesting that our defect CFT extends beyond all known examples of Gaussian defect CFT.
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We consider the structure of current and stress tensor two-point functions in conformal field theory with a boundary. The main result of this paper is a relation between a boundary central charge and the coefficient of a displacement operator correlation function in the boundary limit. The boundary central charge under consideration is the coefficient of the product of the extrinsic curvature and the Weyl curvature in the conformal anomaly. Along the way, we describe several auxiliary results. Three of the more notable are as follows: (1) we give the bulk and boundary conformal blocks for the current two-point function; (2) we show that the structure of these current and stress tensor two-point functions is essentially universal for all free theories; (3) we introduce a class of interacting conformal field theories with boundary degrees of freedom, where the interactions are confined to the boundary. The most interesting example we consider can be thought of as the infrared fixed point of graphene. This particular interacting conformal model in four dimensions provides a counterexample of a previously conjectured relation between a boundary central charge and a bulk central charge. The model also demonstrates that the boundary central charge can change in response to marginal deformations.
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