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2015

Resurgence and Topological Strings

Vonk, Marcel

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The mathematical idea of resurgence allows one to obtain nonperturbative information from the large-order behavior of perturbative expansions.

This idea can be very fruitful in physics applications, in particular if one does not have access to such nonperturbative information from first principles.
An important example is topological string theory, which is a priori only defined as an asymptotic perturbative expansion in the coupling constant g_s.
We show how the idea of resurgence can be combined with the holomorphic anomaly equation to extend the perturbative definition of the topological string and obtain, in a model-independent way, a large amount of information about its nonperturbative structure.

Resurgence and Topological Strings · Around

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J. Écalle, “Les Fonctions Résurgentes,” Prépub. Math. Univ. Paris-Sud 81-05
1985
Earlier work this paper cites.
M. Bershadsky, S. Cecotti, H. Ooguri and C. Vafa, “Holomorphic anomalies in topological field theories,” Nucl. Phys. B 405
1993
Earlier work this paper cites.
by same author“Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes,” Commun. Math. Phys. 165
1994
Earlier work this paper cites.

Similar

B. Haghighat, A. Klemm and M. Rauch, “Integrability of the holomorphic anomaly equations,” JHEP 0810
Original
2008
Cited alongside, same era.
S. Pasquetti and R. Schiappa, “Borel and Stokes Nonperturbative Phenomena in Topological String Theory and c=1 Matrix Models,” Annales Henri Poincare 11
Original
2010
Cited alongside, same era.
R. C. Santamaría, J. D. Edelstein, R. Schiappa and M. Vonk, “Resurgent Transseries and the Holomorphic Anomaly,” arXiv:1308.1695 [hep-th]
Original
Cited in the paper.
by same author“Resurgent Transseries and the Holomorphic Anomaly: Nonperturbative Closed Strings in Local ℂ ℙ 2 \mathbb{C}\mathbb{P}^{2} ,” arXiv:1407.4821 [hep-th]
Original
Cited in the paper.
I. Aniceto and R. Schiappa, “Nonperturbative Ambiguities and the Reality of Resurgent Transseries,” arXiv:1308.1115 [hep-th]
Original
Cited in the paper.
K. Hori, S. Katz, A. Klemm, R. Pandharipande, R. Thomas, C. Vafa, R. Vakil and E. Zaslow, “Mirror symmetry,” (Clay mathematics monographs. 1)
Cited in the paper.

Then

N. Drukker, M. Marino and P. Putrov, “Nonperturbative aspects of ABJM theory,” JHEP 1111
Original
2011
Later among the works it cites.
I. Aniceto, R. Schiappa and M. Vonk, “The Resurgence of Instantons in String Theory,” Commun. Num. Theor. Phys. 6
Original
2012
Later among the works it cites.

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