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| Format: | Preprint |
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2025
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| Online-Zugang: | https://arxiv.org/abs/2508.10112 |
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| _version_ | 1866908989909893120 |
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| author | Adams, Griffen Costin, Ovidiu Dunne, Gerald V. Gukov, Sergei Öner, Oğuz |
| author_facet | Adams, Griffen Costin, Ovidiu Dunne, Gerald V. Gukov, Sergei Öner, Oğuz |
| contents | In recent papers [1,2], a new method to cross the natural boundary has been proposed, and applied to Mordell-Borel integrals arising in the study of Chern-Simons theory, based on decompositions into {\it resurgent cyclic orbits}. Resurgent analysis on the Stokes line leads to a unique transseries decomposition in terms of unary false theta functions, which can be continued across the natural boundary to produce dual $q$-series whose integer-valued coefficients enumerate BPS states. This constitutes a deeper new manifestation of resurgence in quantum field theoretic path integrals. In this paper we show that the algebraic structure of the {\it resurgent cyclic orbits}, combined with just the leading term of the $q$-series, completely determines the large order rate of growth of the dual $q$-series coefficients. The essential exponent of this asymptotic growth has a Cardy-like interpretation [10] of an effective central charge in a 3 dimensional quantum field theory with $\mathcal{N}=2$ supersymmetry related to the Chern-Simons theory through the $3d$-$3d$ correspondence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_10112 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $c_{\rm eff}$ from Resurgence at the Stokes Line Adams, Griffen Costin, Ovidiu Dunne, Gerald V. Gukov, Sergei Öner, Oğuz High Energy Physics - Theory Mathematical Physics Geometric Topology Number Theory In recent papers [1,2], a new method to cross the natural boundary has been proposed, and applied to Mordell-Borel integrals arising in the study of Chern-Simons theory, based on decompositions into {\it resurgent cyclic orbits}. Resurgent analysis on the Stokes line leads to a unique transseries decomposition in terms of unary false theta functions, which can be continued across the natural boundary to produce dual $q$-series whose integer-valued coefficients enumerate BPS states. This constitutes a deeper new manifestation of resurgence in quantum field theoretic path integrals. In this paper we show that the algebraic structure of the {\it resurgent cyclic orbits}, combined with just the leading term of the $q$-series, completely determines the large order rate of growth of the dual $q$-series coefficients. The essential exponent of this asymptotic growth has a Cardy-like interpretation [10] of an effective central charge in a 3 dimensional quantum field theory with $\mathcal{N}=2$ supersymmetry related to the Chern-Simons theory through the $3d$-$3d$ correspondence. |
| title | $c_{\rm eff}$ from Resurgence at the Stokes Line |
| topic | High Energy Physics - Theory Mathematical Physics Geometric Topology Number Theory |
| url | https://arxiv.org/abs/2508.10112 |