Scientific article
Open access

Resumming the string perturbation series

Published inThe journal of high energy physics, vol. 1505, p. 038-073
  • Open Access - SCOAP3
Publication date2015

We use the AdS/CFT correspondence to study the resummation of a perturbative genus expansion appearing in the type II superstring dual of ABJM theory. Although the series is Borel summable, its Borel resummation does not agree with the exact non-perturbative answer due to the presence of complex instantons. The same type of behavior appears in the WKB quantization of the quartic oscillator in Quantum Mechanics, which we analyze in detail as a toy model for the string perturbation series. We conclude that, in these examples, Borel summability is not enough for extracting non-perturbative information, due to non-perturbative effects associated to complex instantons. We also analyze the resummation of the genus expansion for topological string theory on local ℙ 1 × ℙ 1 $$ {\mathrm{\mathbb{P}}}^1\times {\mathrm{\mathbb{P}}}^1 $$ , which is closely related to ABJM theory. In this case, the non-perturbative answer involves membrane instantons computed by the refined topological string, which are crucial to produce a well-defined result. We give evidence that the Borel resummation of the perturbative series requires such a non-perturbative sector.

  • Nonperturbative Effects
  • 1/N Expansion
  • Topological Strings
  • Matrix Models
Citation (ISO format)
GRASSI, Alba, MARINO BEIRAS, Marcos, ZAKANY, Szabolcs. Resumming the string perturbation series. In: The journal of high energy physics, 2015, vol. 1505, p. 038–073. doi: 10.1007/JHEP05(2015)038
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Article (Published version)
ISSN of the journal1029-8479

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