Wilson Loops at Large N and the Quantum M2-Brane.

The Wilson loop operator in the U(N)_{k}×U(N)_{-k} Aharony-Bergman-Jafferis-Maldacena theory at large N and fixed level k has a dual description in terms of a wrapped M2-brane in the M-theory given by the product of four-dimensional anti de Sitter space (AdS_{4}) and S^{7}/Z_{k}. We consider the localization result for the 1/2-Bogomol'nyi-Prasad-Sommerfield circular Wilson loop expectation value W in this regime and compare it to the prediction of the M2-brane theory. The leading large N exponential factor is matched as expected by the classical action of the M2-brane solution with AdS_{2}×S^{1} geometry.

Comments on open string with 'massive' boundary term.

We discuss possible definition of open string path integral in the presence of additional boundary couplings corresponding to the presence of masses at the ends of the string. These couplings are not conformally invariant implying that as in a non-critical string case one is to integrate over the one-dimensional metric or reparametrizations of the boundary. We compute the partition function on the disc in the presence of an additional constant gauge field background and comment on the structure of the corresponding scattering amplitudes.