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<p>For a 3d gauged linear sigma model parametrized by a Kähler manifold <i>X</i>, the 3d BPS index defines a <i>q</i>-series that can be analytically continued in the Kähler modulus by standard methods. It is argued that an SL(2<i>,</i> ℤ)-transform of the Birkhoff connection matrix captures non-perturbative corrections to the 3d GLSM. As an application, a 3d lift of the standard 2d GLSM for the resolved conifold is shown to provide a world-volume dual for the non-perturbative topological string on the resolved conifold. The perturbative 3d BPS index computes the Gopakumar-Vafa partition function, while the analytic continuation matches existing proposals for a non-perturbative completion of the topological string.</p>

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Non-perturbative corrections to 3d BPS indices and topological strings

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  • 发表日期：

    2025年6月12日

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  • Hans Jockers

摘要

For a 3d gauged linear sigma model parametrized by a Kähler manifold X, the 3d BPS index defines a q-series that can be analytically continued in the Kähler modulus by standard methods. It is argued that an SL(2, ℤ)-transform of the Birkhoff connection matrix captures non-perturbative corrections to the 3d GLSM. As an application, a 3d lift of the standard 2d GLSM for the resolved conifold is shown to provide a world-volume dual for the non-perturbative topological string on the resolved conifold. The perturbative 3d BPS index computes the Gopakumar-Vafa partition function, while the analytic continuation matches existing proposals for a non-perturbative completion of the topological string.