BPS Wilson loops in N $\mathcal{N}$ ≥ 2 superconformal Chern-Simons-matter theories

Mauri, Andrea  ( Dipartimento di Fisica, Università degli Studi di Milano-Bicocca and INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126, Milano, Italy) ; Ouyang, Hao  (0000000119573309, Institute of High Energy Physics, & Theoretical Physics Center for Science Facilities, Chinese Academy of Sciences, 19B Yuquan Road, Beijing, 100049, China) (0000 0004 1797 8419, School of Physical Sciences, University of Chinese Academy of Sciences, 19A Yuquan Road, Beijing, 100049, China) ; Penati, Silvia  ( Dipartimento di Fisica, Università degli Studi di Milano-Bicocca and INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126, Milano, Italy) ; Wu, Jun-Bao (0000 0004 1761 2484, Center for Joint Quantum Studies, School of Science, Tianjin University, 135 Yaguan Road, Tianjin, 300350, China) (0000 0001 2256 9319, Center for High Energy Physics, Peking University, 5 Yiheyuan Road, Beijing, 100871, China) ; Zhang, Jiaju  ( Dipartimento di Fisica, Università degli Studi di Milano-Bicocca and INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, I-20126, Milano, Italy)

23 November 2018

Abstract: In N $\mathcal{N}$ ≥ 2 superconformal Chern-Simons-matter theories we construct the infinite family of Bogomol’nyi-Prasad-Sommerfield (BPS) Wilson loops featured by constant parametric couplings to scalar and fermion matter, including both line Wilson loops in Minkowski spacetime and circle Wilson loops in Euclidean space. We find that the connection of the most general BPS Wilson loop cannot be decomposed in terms of double-node connections. Moreover, if the quiver contains triangles, it cannot be interpreted as a super-matrix inside a superalgebra. However, for particular choices of the parameters it reduces to the well-known connections of 1/6 BPS Wilson loops in Aharony-Bergman-Jafferis-Maldacena (ABJM) theory and 1/4 BPS Wilson loops in N $\mathcal{N}$ = 4 orbifold ABJM theory. In the particular case of N $\mathcal{N}$ = 2 orbifold ABJM theory we identify the gravity duals of a subset of operators. We investigate the cohomological equivalence of fermionic and bosonic BPS Wilson loops at quantum level by studying their expectation values, and find strong evidence that the cohomological equivalence holds quantum mechanically, at framing one. Finally, we discuss a stronger formulation of the cohomological equivalence, which implies non-trivial identities for correlation functions of composite operators in the defect CFT defined on the Wilson contour and allows to make novel predictions on the corresponding unknown integrals that call for a confirmation.

Published in: JHEP 1811 (2018) 145