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The grin of Cheshire cat resurgence from supersymmetric localization.

Dorigoni, Daniele and Glass, Philip (2018) 'The grin of Cheshire cat resurgence from supersymmetric localization.', SciPost physics., 4 (2). 012.


First we compute the S2 partition function of the supersymmetric CPN−1 model via localization and as a check we show that the chiral ring structure can be correctly reproduced. For the CP1 case we provide a concrete realisation of this ring in terms of Bessel functions. We consider a weak coupling expansion in each topological sector and write it as a finite number of perturbative corrections plus an infinite series of instantonanti-instanton contributions. To be able to apply resurgent analysis we then consider a non-supersymmetric deformation of the localized model by introducing a small unbalance between the number of bosons and fermions. The perturbative expansion of the deformed model becomes asymptotic and we analyse it within the framework of resurgence theory. Although the perturbative series truncates when we send the deformation parameter to zero we can still reconstruct non-perturbative physics out of the perturbative data in a nice example of Cheshire cat resurgence in quantum field theory. We also show that the same type of resurgence takes place when we consider an analytic continuation in the number of chiral fields from N to r ∈ R. Although for generic real r supersymmetry is still formally preserved, we find that the perturbative expansion of the supersymmetric partition function becomes asymptotic so that we can use resurgent analysis and only at the end take the limit of integer r to recover the undeformed model.

Item Type:Article
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Publisher statement:Copyright D. Dorigoni and P. Glass. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.
Date accepted:18 January 2018
Date deposited:19 April 2018
Date of first online publication:27 February 2018
Date first made open access:No date available

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