Surface operators in superspace

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.

Pictures from super Chern-Simons theory

“…We have seen from a preliminary work that the same phenomena is at work also in the present context. Feynman diagrams computations will be presented somewhere else [20].…”

“…). In other words we have distributed the PCO Y (0|2) on the gauge fields A (1|0) 7 Care must be used in defining the product of two pseudoforms since it might lead to divergencies in the Feynman diagrams [20].…”

Surface Operators in Superspace

“…Our construction can be generalized to define (p|m)-integral currents, that is conserved integral forms, or more generally (p|q)-form currents with 0 < q < m described by conserved pseudo-forms. The physical meaning of this conservation laws and the corresponding exotic symmetries has still to be understood and will be discussed elsewhere [63]. Furthermore, our approach can be exploited to generalize to supermanifolds the recent formulation of a continuum field theory for probe particles and dipoles with reduced mobility (fractons and lineons) [50,51,52,53,54,55].…”

“…Finally, section 8 is devoted to some conclusions and perspectives. In particular, we address the fact that our construction opens the possibility of studying a continuum theory for fractons and lineons in superspace (superfractons and superlineons), as we will discuss in a forthcoming paper [63]. Four appendices follow, one summarising our conventions in six dimensions, one recalling basic definitions about the Hodge operator in supermanifolds, one including an alternative discussion of conservation laws that makes use of an explicit surface parametrization, and finally one where we define a supersymmetric version of the linking number between two supersurfaces, required to define the action of charge operators on superWS and higher dimensional objects.…”

Cohomology of Lie Superalgebras: Forms, Integral Forms and Coset Superspaces

“…Given a supermanifold M , say of dimension n|m, differential forms in Ω • (M ) are not enough to define a coherent notion of integration on M . This leads to the introduction of integral forms, which are geometrically as important as differential forms, see [37] and the recent papers [8,6,7,25,39,9,10,11,15,16,17,18,12,3]. Loosely speaking, whereas differential forms lead to a consistent geometric integration on ordinary bosonic submanifolds (i.e.…”