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

$$ \hat{Z} $$ 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 been conjectured to be a new homological invariant of 3-manifolds which can shed light onto the superconformal and topologically twisted index of 3d $$ \mathcal{N} $$ N = 2 theories proposed by GPPV. In particular, the resurgent analysis of $$ \hat{Z} $$ Z ̂ has been fruitful in discovering analytic properties of the WRT invariants. The resurgent analysis of these $$ \hat{Z} $$ Z ̂ -invariants has been performed for the cases of Σ(2, 3, 5), Σ(2, 3, 7) by GMP, Σ(2, 5, 7) by Chun, and, more recently, some additional Seifert manifolds by Chung and Kucharski, independently. In this paper, we extend and generalize the resurgent analysis of $$ \hat{Z} $$ Z ̂ on a family of Brieskorn homology spheres Σ(2, 3, 6n + 5) where n ∈ ℤ+ and 6n + 5 is a prime. By deriving $$ \hat{Z} $$ Z ̂ for Σ(2, 3, 6n + 5) according to GPPV and Hikami, we provide a formula where one can quickly compute the non-perturbative contributions to the full analytic continuation of SU(2) Chern-Simons partition function.

Nonperturbative matching between equal-time and lightcone quantization

We investigate the nonperturbative relation between lightcone (LC) and standard equal-time (ET) quantization in the context of λϕ4 theory in d = 2. We discuss the perturbative matching between bare parameters and the failure of its naive nonperturbative extension. We argue that they are nevertheless the same theory nonperturbatively, and that furthermore the nonperturbative map between bare parameters can be extracted from ET perturbation theory via Borel resummation of the mass gap. We test this map by using it to compare physical quantities computed using numerical Hamiltonian truncation methods in ET and LC.