TY - JOUR

T1 - BPS surface operators and calibrations

AU - Drukker, Nadav

AU - Trépanier, Maxime

N1 - Funding Information:
We are grateful to J Maldacena, M Martone, D Panov and especially M Probst for helpful discussions. N D would like to thank l’École Polytechnique Fédérale de Lausanne, the Simons Center for Geometry and Physics, Stony Brook and the KITP, Santa Barbara for their hospitality in the course of this work. N D’s research is supported by the Science Technology & Facilities council under the Grants ST/T000759/1 and ST/P000258/1 and by the National Science Foundation under Grant No. NSF PHY-1748958. M T gratefully acknowledges the support from the Institute for Theoretical and Mathematical Physics (ITMP, Moscow) where this project began, and Université Laval, the Simons Center for Geometry and Physics, Stony Brook and New York University where parts of this project were realised. M T’s research is funded by the Engineering & Physical Sciences Research Council under the Grant EP/W522429/1. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research and Innovation.
Publisher Copyright:
© 2023 The Author(s). Published by IOP Publishing Ltd.

PY - 2023/4/28

Y1 - 2023/4/28

N2 - We present here a careful study of the holographic duals of BPS surface operators in the 6d theory. Several different classes of surface operators have been recently identified and each class has a specific calibration form—a 3-form in A d S 7 × S 4 whose pullback to the M2-brane world-volume is equal to the volume form. In all but one class, the appropriate forms are exact, so the action of the M2-brane is easily expressed in terms of boundary data, which is the geometry of the surface. Specifically, for surfaces of vanishing anomaly, it is proportional to the integral of the square of the extrinsic curvature. This can be extended to the case of surfaces with anomalies, by taking the ratio of two surfaces with the same anomaly. This gives a slew of new expectation values at large N in this theory. For one specific class of surface operators, which are Lagrangian submanifolds of R 4 ⊂ R 6 , the structure is far richer and we find that the M2-branes are special Lagrangian submanifold of an appropriate six-dimensional almost Calabi-Yau submanifold of A d S 7 × S 4 . This allows for an elegant treatment of many such examples.

AB - We present here a careful study of the holographic duals of BPS surface operators in the 6d theory. Several different classes of surface operators have been recently identified and each class has a specific calibration form—a 3-form in A d S 7 × S 4 whose pullback to the M2-brane world-volume is equal to the volume form. In all but one class, the appropriate forms are exact, so the action of the M2-brane is easily expressed in terms of boundary data, which is the geometry of the surface. Specifically, for surfaces of vanishing anomaly, it is proportional to the integral of the square of the extrinsic curvature. This can be extended to the case of surfaces with anomalies, by taking the ratio of two surfaces with the same anomaly. This gives a slew of new expectation values at large N in this theory. For one specific class of surface operators, which are Lagrangian submanifolds of R 4 ⊂ R 6 , the structure is far richer and we find that the M2-branes are special Lagrangian submanifold of an appropriate six-dimensional almost Calabi-Yau submanifold of A d S 7 × S 4 . This allows for an elegant treatment of many such examples.

UR - http://www.scopus.com/inward/record.url?scp=85152551686&partnerID=8YFLogxK

U2 - 10.1088/1751-8121/acc771

DO - 10.1088/1751-8121/acc771

M3 - Article

SN - 1751-8113

VL - 56

JO - Journal Of Physics A-Mathematical And Theoretical

JF - Journal Of Physics A-Mathematical And Theoretical

IS - 17

M1 - 175403

ER -