MG14 - Talk detail

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In this talk we shall review and discuss results obtained over the past few years concerning the resurgent structure of perturbative and instanton series in diverse examples of both gauge theory and string theory. Most interesting quantum theoretic problems are not exactly solvable and must resort to perturbation theory if one is to compute any observables. Perturbation theory, however, is generically divergent, with its coefficients growing factorially fast with the order. This is known to be due to instantons. Interestingly enough, generically, also all perturbative expansions around any instanton sector are also factorially divergent. Resurgence is the property that all these divergent perturbative series relate to each other in a very precise way --- to the extent that, in fact, perturbation theory already contains, encoded in the large-order behavior of its coefficients, all information concerning all nonperturbative sectors of a given theory. Further, resurgent analysis, transseries, and resummation procedures, yield precise ways in which to extract information out of this plethora of asymptotic series. We shall review these ideas and describe how they apply to uncover new properties and phenomena in gauge and string theories.

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