TY - JOUR

T1 - Broken Global Symmetries and Defect Conformal Manifolds

AU - Drukker, Nadav

AU - Kong, Ziwen

AU - Sakkas, Georgios

N1 - Funding Information:
We are indebted to G. Bliard, S. Giombi, N. Gromov, C. Herzog, Z. Komargodski, C. Meneghelli, M. Probst, A. Stergiou, M. Trépanier, and G. Watts for invaluable discussions. N. D.’s research is supported by STFC Grants No. ST/T000759/1 and No. ST/P000258/1. Z. K. is supported by CSC Grant No. 201906340174. G. S. is funded by STFC Grant No. ST/W507556/1.
Publisher Copyright:
© 2022 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the "https://creativecommons.org/licenses/by/4.0/"Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by SCOAP3.

PY - 2022/11/11

Y1 - 2022/11/11

N2 - Just as exactly marginal operators allow one to deform a conformal field theory along the space of theories known as the conformal manifold, appropriate operators on conformal defects allow for deformations of the defects. When a defect breaks a global symmetry, there is a contact term in the conservation equation with an exactly marginal defect operator. The resulting defect conformal manifold is the symmetry breaking coset, and its Zamolodchikov metric is expressed as the two-point function of the exactly marginal operator. As the Riemann tensor on the conformal manifold can be expressed as an integrated four-point function of the marginal operators, we find an exact relation to the curvature of the coset space. We confirm this relation against previously obtained four-point functions for insertions into the 1/2 BPS Wilson loop in N=4 SYM and 3D N=6 theory and the 1/2 BPS surface operator of the 6D N=(2,0) theory.

AB - Just as exactly marginal operators allow one to deform a conformal field theory along the space of theories known as the conformal manifold, appropriate operators on conformal defects allow for deformations of the defects. When a defect breaks a global symmetry, there is a contact term in the conservation equation with an exactly marginal defect operator. The resulting defect conformal manifold is the symmetry breaking coset, and its Zamolodchikov metric is expressed as the two-point function of the exactly marginal operator. As the Riemann tensor on the conformal manifold can be expressed as an integrated four-point function of the marginal operators, we find an exact relation to the curvature of the coset space. We confirm this relation against previously obtained four-point functions for insertions into the 1/2 BPS Wilson loop in N=4 SYM and 3D N=6 theory and the 1/2 BPS surface operator of the 6D N=(2,0) theory.

UR - http://www.scopus.com/inward/record.url?scp=85141918966&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.129.201603

DO - 10.1103/PhysRevLett.129.201603

M3 - Article

C2 - 36462019

AN - SCOPUS:85141918966

SN - 0031-9007

VL - 129

JO - Physical Review Letters

JF - Physical Review Letters

IS - 20

M1 - 201603

ER -