Wilson Loops at Large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math> and the Quantum M2-Brane
Simone Giombi, A.A. Tseytlin
Abstract
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. We show that the subleading k-dependent prefactor in W is also exactly reproduced by the one-loop term in the partition function of the wrapped M2-brane (with all Kaluza-Klein modes included). This appears to be the first case of an exact matching of the overall numerical prefactor in the Wilson loop expectation value against the dual holographic result. It provides an example of a consistent quantum M2-brane computation, suggesting various generalizations.