Resurgence provides a unique analytic continuation across natural boundaries for Chern-Simons q-series that matches 3-manifold orientation reversal via Mordell integral decompositions.
On the Gauge Theory/Geometry Correspondence
7 Pith papers cite this work. Polarity classification is still indexing.
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abstract
The 't Hooft expansion of SU(N) Chern-Simons theory on $S^3$ is proposed to be exactly dual to the topological closed string theory on the $S^2$ blow up of the conifold geometry. The $B$-field on the $S^2$ has magnitude $Ng_s=\lambda$, the 't Hooft coupling. We are able to make a number of checks, such as finding exact agreement at the level of the partition function computed on {\it both} sides for arbitrary $\lambda$ and to all orders in 1/N. Moreover, it seems possible to derive this correspondence from a linear sigma model description of the conifold. We propose a picture whereby a perturbative D-brane description, in terms of holes in the closed string worldsheet, arises automatically from the coexistence of two phases in the underlying U(1) gauge theory. This approach holds promise for a derivation of the AdS/CFT correspondence.
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Links resurgence of the topological string partition function to DT wall-crossing via an isomorphism of alien derivative algebras to the Kontsevich-Soibelman Lie algebra, with Borel singularities matched to specific DT invariants.
A 2-form connection is defined in the space of open string field theory solutions, producing invariant higher holonomies and 3-form curvature potentially corresponding to the B-field.
Functional renormalization group applied to the O(N) vector model generates an emergent regular AdS_{d+1} geometry whose near-horizon thermodynamics reproduces the first law and Bekenstein-Hawking area law with temperature matching the boundary field theory.
Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.
Two open-string descriptions of branes on the resolved conifold are equivalent; integrating out one stack yields an effective potential that reproduces the backreaction and matches giant-graviton actions on the deformed conifold.
The spin one-point function in the critical Ising chain has a natural boundary of analyticity on the negative real axis after Borel resummation, with singularities matching those of an odd-divisor sum series.
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All the D-Branes of Resurgence
Negative-tension ZZ-branes are required by resurgence to build complete transseries for minimal-string free energies, with analytic Stokes data and extensions to JT gravity and other string models.