Near BPS Wilson loop in βdeformed theories
Abstract
We propose a definition of the Wilson loop operator in the Script N = 1 βdeformed supersymmetric YangMills theory. Although the operator is not BPS, it has a finite expectation value at least up to order (g^{2}N)^{2}. This does not happen generally for a generic nonBPS Wilson loop whose expectation value is UV divergent. For this reason we call this a nearBPS Wilson loop. We derive the general form of the boundary condition satisfied by the dual string worldsheet and find that it is deformed. Finiteness of the expectation value of the Wilson loop fixes the boundary condition to be one which is characterized by the vielbein of the deformed supergravity metric. The Wilson loop operators provide natural candidates as dual descriptions to some of the existing Dbrane configurations in the LuninMaldacena background. We also construct the string dual configuration for a near1/4 BPS circular Wilson loop operator. The string lies on a deformed threesphere instead of a twosphere as in the undeformed case. The expectation value of the Wilson loop operator is computed using the AdS/CFT correspondence and is found to be independent of the deformation. We conjecture that the exact expectation value of the Wilson loop is given by the same matrix model as in the undeformed case.
 Publication:

Journal of High Energy Physics
 Pub Date:
 October 2007
 DOI:
 10.1088/11266708/2007/10/108
 arXiv:
 arXiv:0708.0797
 Bibcode:
 2007JHEP...10..108C
 Keywords:

 High Energy Physics  Theory
 EPrint:
 LaTeX. v2: corrections and comments added (22 pages). v3: proof of the finitness of the vev of the Wilson loop is extended to the next to leading order. appendices C and D added. version to appear in JHEP (23 pages)