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Localization of path integrals in physics, recent developments and applications in gauge and gravity theories
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A certain class of integrals localize over the fixed point set of some symmetry. At the neighbourhood of these points the stationary phase approximation becomes exact. This technique, known as localization, has recently received special attention in the computation of supersymmetric path integrals in the context of AdS/CFT correspondence. In these lectures I will review and explain this technique. Spectacular results have been achieved in the computation of 't Hooft-Wilson loops in N=4 SYM, also on Chern-Simons matter theories in three dimensions, in particular ABJM theory, and more recently in the computation of the entropy of supersymmetric black holes. All these results are exact which constitute an extraordinary step in establishing an exact holography in the context of AdS/CFT correspondence. |
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