TY - JOUR
T1 - Quantum holographic surface anomalies
AU - Drukker, Nadav
AU - Shahpo, Omar
AU - Trépanier, Maxime
N1 - Funding Information:
We are grateful to C R Graham, F Hübner, L Pando Zayas, G Papadopoulos, R Sinha, A Tseytlin and E Witten for helpful discussions, and especially A Tseytlin his many helpful comments on a preliminary version of this paper. ND would like to thank EPFL, CERN and DESY for their hospitality in the course of this work. ND’s research is supported by the Science Technology & Facilities council under the Grants ST/P000258/1 and ST/X000753/1. OS’s research is funded by the Engineering & Physical Sciences Research Council under Grant Number EP/W524025/1. MT gratefully acknowledges the support from the Institute for Theoretical and Mathematical Physics (ITMP, Moscow) where this project began, and the Perimeter Institute where part of this project was realised. MT’s research is funded by the Engineering & Physical Sciences Research Council under the Grant EP/W522429/1.
Publisher Copyright:
© 2024 The Author(s). Published by IOP Publishing Ltd.
PY - 2024/2/23
Y1 - 2024/2/23
N2 - Expectation values of surface operators suffer from logarithmic divergences reflecting a conformal anomaly. In a holographic setting, where surface operators can be computed by a minimal surface in AdS, the leading contribution to the anomaly comes from a divergence in the classical action (or area) of the minimal surface. We study the subleading correction to it due to quantum fluctuations of the minimal surface. In the same way that the divergence in the area does not require a global solution but only a near-boundary analysis, the same holds for the quantum corrections. We study the asymptotic form of the fluctuation determinant and show how to use the heat kernel to calculate the quantum anomaly. In the case of M2-branes describing surface operators in the N=(2,0) theory in 6d, our calculation of the one-loop determinant reproduces expressions for the anomaly that have been found by less direct methods.
AB - Expectation values of surface operators suffer from logarithmic divergences reflecting a conformal anomaly. In a holographic setting, where surface operators can be computed by a minimal surface in AdS, the leading contribution to the anomaly comes from a divergence in the classical action (or area) of the minimal surface. We study the subleading correction to it due to quantum fluctuations of the minimal surface. In the same way that the divergence in the area does not require a global solution but only a near-boundary analysis, the same holds for the quantum corrections. We study the asymptotic form of the fluctuation determinant and show how to use the heat kernel to calculate the quantum anomaly. In the case of M2-branes describing surface operators in the N=(2,0) theory in 6d, our calculation of the one-loop determinant reproduces expressions for the anomaly that have been found by less direct methods.
UR - https://arxiv.org/abs/2311.14797
UR - http://www.scopus.com/inward/record.url?scp=85187289161&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/ad2296
DO - 10.1088/1751-8121/ad2296
M3 - Article
SN - 1751-8113
VL - 57
JO - Journal Of Physics A-Mathematical And Theoretical
JF - Journal Of Physics A-Mathematical And Theoretical
IS - 8
M1 - 085402
ER -