Surface operators in superspace
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Springer
Received: June 24, 2020 Accepted: October 9, 2020 Published: November 11, 2020
Surface operators in superspace
a
Dipartimento di Scienze e Alta Tecnologia (DiSAT), Universit` a degli Studi dell’Insubria, via Valleggio 11, 22100 Como, Italy b INFN, Sezione di Milano, via G. Celoria 16, 20133 Milano, Italy c Dipartimento di Scienze e Innovazione Tecnologica (DiSIT), Universit` a del Piemonte Orientale, viale T. Michel, 11, 15121 Alessandria, Italy d INFN, Sezione di Torino, via P. Giuria 1, 10125 Torino, Italy e Arnold-Regge Center, via P. Giuria 1, 10125 Torino, Italy f Dipartimento di Fisica, Universit` a degli studi di Milano-Bicocca, and INFN, Sezione di Milano-Bicocca, Piazza della Scienza 3, 20126 Milano, Italy
E-mail: [email protected], [email protected], [email protected] Abstract: We generalize the geometrical formulation of Wilson loops recently introduced in [1] to the description of Wilson Surfaces. For N = (2, 0) theory in six dimensions, we provide an explicit derivation of BPS Wilson Surfaces with non-trivial coupling to scalars, together with their manifestly supersymmetric version. We derive explicit conditions which allow to classify these operators in terms of the number of preserved supercharges. We also discuss kappa-symmetry and prove that BPS conditions in six dimensions arise from kappa-symmetry invariance in eleven dimensions. Finally, we discuss super-Wilson Surfaces — and higher dimensional operators — as objects charged under global p-form (super)symmetries generated by tensorial supercurrents. To this end, the construction of conserved supercurrents in supermanifolds and of the corresponding conserved charges is developed in details. Keywords: Superspaces, Wilson, ’t Hooft and Polyakov loops ArXiv ePrint: 2006.08633v2
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP11(2020)050
JHEP11(2020)050
C.A. Cremonini,a,b P.A. Grassic,d,e and S. Penatif
Contents 1
2 Supergeometry and Picture Changing Operators
4
3 Wilson surfaces
6
4 Super Wilson Surfaces
7
5 Super Wilson Surfaces in six dimensions 5.1 Generalized surface operators 5.2 Super Wilson Surfaces in components 5.3 BPS surface operators
9 10 11 12
6 Kappa symmetry 6.1 Kappa symmetry for generalized Wilson surfaces
15 17
7 Tensor currents 7.1 (p + 1)-form currents 7.2 (p + 1)-form supercurrents 7.3 Charged defects
18 19 21 23
8 Conclusions and perspectives
24
A Conventions in six dimensions
26
B Hodge operator in supermanifolds
27
C Charge conservation in the extended manifold
28
D Linking number and PCO
29
1
Introduction
In gauge theories an important physical quantity is the Wilson loop defined as the holonomy of the gauge connection along a one-dimensional contour. This has a natural generalization to higher dimensional contours, whenever the theory lives in D > 3 dimensions and contains higher-rank tensor fields. In particular, Wilson Surfaces (WS) are defined in terms of a surface integral of a two-form tensor [2] W [σ] = e
Γ[
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