Abstract
We present a family of new M2-brane solutions in AdS7× S4 that calculate toroidal BPS surface operators in the mathcal{N} = (2, 0) theory. These observables are conformally invariant and not subject to anomalies so we are able to evaluate their finite expectation values at leading order at large N. In the limit of a thin torus we find a cylinder, which is a natural surface generalization of both the circular and parallel lines Wilson loop. We study and comment on this limit in some detail.
Highlights
The purpose of this note is to present new nontrivial classical M2-brane solutions which have a nontrivial expectation value
What we study here is a version of this observable that preserves a fraction of the supercharges, so is BPS, yet like the circular Wilson loop in N = 4 SYM, it has a nontrivial vacuum expectation value [30,31,32]
Supersymmetry does not depend on the choice of representation, but we focus on operators in the fundamental representation of AN−1, which by the AdS/CFT dictionnary are dual to M2-branes at large N [2]
Summary
In the absence of a Lagrangian description, surface operators in the N = (2, 0) theory are defined indirectly by stating their properties: their geometry, the local breaking of Rsymmetry ( referred to as “scalar coupling”, in analogy with Maldacena-Wilson loops, though there are no fields) and a representation of the ADE algebra underlying the theory This is discussed in great detail in [26] which analyses possible relationships between the geometry and scalar couplings that guarantee preserved supersymmetry. This is compatible with the discrete symmetry of the tori where we exchange φ1 with φ2 and R1 with R2, and in the following we assume without loss of generality that R1 ≥ R2 Beside their supersymmetry, another important property of these operators is that they do not suffer from conformal anomalies, so their expectation value is well-defined.
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