# A resurgence analysis of the $SU(2)$ Chern-Simons partition functions on a Brieskorn homology sphere $\Sigma(2,5,7)$

@article{Chun2017ARA, title={A resurgence analysis of the \$SU(2)\$ Chern-Simons partition functions on a Brieskorn homology sphere \$\Sigma(2,5,7)\$}, author={Sungbong Chun}, journal={arXiv: High Energy Physics - Theory}, year={2017} }

We perform a resurgence analysis of the $SU(2)$ Chern-Simons partition function on a Brieksorn homology sphere $\Sigma(2,5,7)$. Starting from an exact Chern-Simons partition function, we study the Borel resummation of its perturbative expansion.

## 13 Citations

### Resurgent analysis of SU(2) Chern-Simons partition function on Brieskorn spheres Σ(2, 3, 6n + 5)

- MathematicsJournal of High Energy Physics
- 2021

Abstract
$$ \hat{Z} $$
Z
̂
-invariants, which can reconstruct the analytic continuation of the SU(2) Chern-Simons partition functions via Borel resummation, were discovered by GPV and have…

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### Resurgent Analysis for Some 3-manifold Invariants

- Mathematics
- 2020

We study resurgence for some 3-manifold invariants when $G_{\mathbb{C}}=SL(2, \mathbb{C})$. We discuss the case of an infinite family of Seifert manifolds for general roots of unity and the case of…

### Resurgence Analysis of Quantum Invariants: Seifert Manifolds and Surgeries on The Figure Eight Knot

- Mathematics
- 2018

We provide a resurgence analysis of the quantum invariants of all Seifert fibered three manifold, with oriented base of genus zero and at least three exceptional fibers. This generalizes results of…

### BPS invariants for 3-manifolds at rational level K

- MathematicsJournal of High Energy Physics
- 2021

Abstract
We consider the Witten-Reshetikhin-Turaev invariants or Chern-Simons partition functions at or around roots of unity $$ q={e}^{\frac{2\pi i}{K}} $$
q
=
e
2
πi
K
with a…

### BPS invariants for Seifert manifolds

- MathematicsJournal of High Energy Physics
- 2020

We calculate the homological blocks for Seifert manifolds from the exact ex- pression for the G = SU( N ) Witten-Reshetikhin-Turaev invariants of Seifert manifolds obtained by Lawrence, Rozansky, and…

### Ẑ invariants at rational τ

- MathematicsJournal of High Energy Physics
- 2019

Abstract
Ẑ invariants of 3-manifolds were introduced as series in q = e
2πiτ
in order to categorify Witten-Reshetikhin-Turaev invariants corresponding to τ = 1/k. However modularity properties…

### Asymptotic expansions of the Witten–Reshetikhin–Turaev invariants of mapping tori I

- MathematicsTransactions of the American Mathematical Society
- 2018

In this paper we engage in a general study of the asymptotic expansion of the Witten–Reshetikhin–Turaev invariants of mapping tori of surface mapping class group elements. We use the geometric…

### Witten-Reshetikhin-Turaev invariants and homological blocks for plumbed homology spheres

- Mathematics
- 2022

. In this paper, we prove a conjecture by Gukov–Pei–Putrov–Vafa for a wide class of plumbed 3-manifolds. Their conjecture states that Witten–Reshetikhin–Turaev (WRT) invariants are radial limits of…

### 3d modularity

- MathematicsJournal of High Energy Physics
- 2019

Abstract
We find and propose an explanation for a large variety of modularity-related symmetries in problems of 3-manifold topology and physics of 3d
$$ \mathcal{N} $$
N
= 2 theories…

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