Supersymmetric Wilson loops via integral forms

Abstract

We study supersymmetric Wilson loops from a geometrical perspective. To this end, we propose a new formulation of these operators in terms of an integral form associated to the immersion of the loop into a supermanifold. This approach provides a unifying description of Wilson loops preserving different sets of supercharges, and clarifies the flow between them. Moreover, it allows to exploit the powerful techniques of super-differential calculus for investigating their symmetries.As remarkable examples, we discuss supersymmetry and kappa-symmetry invariance.

Surface operators in superspace

“…Within the general context of supersymmetric theories, in this paper we introduce superWS -that is the manifestly supersymmetric version of operators of the form (1.1) -and study their properties and invariances. This is carried out using supergeometry, basically rephrasing what has been done in [1] for super-Wilson loops. We first reformulate expression (1.1) as an integral on the entire manifold by making use of a Poincaré dual which localizes the integral on the surface.…”

“…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.…”

“…A more extensive discussion on supergeometry can be found in [64][65][66], whereas applications of this formalism to field theories have been developed in [67][68][69][70][71]. A geometric formulation of (super) Wilson Loops has been recently proposed in [1].…”

“…When the submanifold N is one-dimensional and ω (1|0) is a gauge connection, equation (2.6) provides a geometric construction of (super) Wilson loops [1]. Many properties of the Wilson operator, like supersymmetry and kappa invariance, are dictated by the behavior of the PCO.…”

Exact results in AdS$_4$/CFT$_3$

“…A manifestly supersymmetric version of (2.1) can be formulated in superspace, in terms of the integral of a superconnection on a supercontour[48]. A rheonomic formulation of these operators has been recently proposed in[49].…”