Supersymmetric Wilson Loops, Superstring-like Observables, and the Natural Coupling of Superstrings To Supersymmetric Gauge Theories

We obtain an explicit expression for the supersymmetric Wilson loop in terms of chiral superfields and supercurrents in superspace. The result turns out to be different from what one would expects from the simple replacement of Lie algebraic valued connection in the exponent with the corresponding super-Lie algebraic one. In the abelian supersymmetric gauge theories, generalizing the super-particle coupling represented by the exponent of the supersymmetric Wilson loop, we show there exist a unique dimensionless coupling of the superstring to abelian supersymmetric gauge theories that respects all known symmetries. The coupling is expressed in terms of chiral currents in superspace. The natural superstring coupling gives rise to a new observable that is ”stringy” in nature and has no analogue in non-supersymmetric gauge theories. + E-Mail address: [email protected] ∗ E-Mail address: [email protected] Wilson loop observables [1,2] have found a variety of applications in the study of gauge theories, ranging from phenomenology to topological field theories [3]. This is because they are gauge invariant observables characterized by a dimensionless coupling constant. In abelian gauge theories they can be interpreted quantum mechanically as the amplitude of the creation and annihilation of e−e+ resulting from the unique coupling between the Maxwell’s field and the point particle with dimensionless coupling constant. In non-abelian gauge theories, this interpretation can be extended formally, in the sense that the particle-Yang-Mills coupling can only be realized by the Wilson loop