Resurgence analysis of 2d Yang-Mills theory on a torus

We study the large $N$ 't Hooft expansion of the partition function of 2d $U(N)$ Yang-Mills theory on a torus. We compute the $1/N$ genus expansion of both the chiral and the full partition function of 2d Yang-Mills using the recursion relation found by Kaneko and Zagier with a slight modification. Then we study the large order behavior of this genus expansion, from which we extract the non-perturbative correction using the resurgence relation. It turns out that the genus expansion is not Borel summable and the coefficient of 1-instanton correction, the so-called Stokes parameter, is pure imaginary. We find that the non-perturbative correction obtained from the resurgence is reproduced from a certain analytic continuation of the grand partition function of a system of non-relativistic fermions on a circle. Our analytic continuation is different from that considered in hep-th/0504221.Comment: 45 pages; v2: references added; v3: typos correcte

A proof of loop equations in 2d topological gravity

We study multi-boundary correlators in 2d Witten-Kontsevich topological gravity. We present a proof of the loop equations obeyed by the correlators. While the loop equations were derived a long time ago, our proof is fully explicit in the presence of general couplings $t_k$. We clarify all the details, in particular the treatment of the genus zero part of the one-boundary correlator. The loop equations are verified by several new examples, including the correlators of Jackiw-Teitelboim gravity in the genus expansion and the exact correlators in the Airy case. We also discuss the free boson/fermion representation of the correlators and compare it with the formulation of Marolf and Maxfield and the string field theory of Ishibashi and Kawai. We find similarities but also some differences.Comment: 33 pages, v2: some explanations added, published versio

Spectral form factor in the τ\tau-scaling limit

We study the spectral form factor (SFF) of general topological gravity in the limit of large time and fixed temperature. It has been observed recently that in this limit, called the tau-scaling limit, the genus expansion of the SFF can be summed up and the late-time behavior of the SFF such as the ramp-plateau transition can be studied analytically. In this paper we develop a technique for the systematic computation of the higher order corrections to the SFF in the strict tau-scaling limit. We obtain the first five corrections in a closed form for the general background of topological gravity. As concrete examples, we present the results for the Airy case and Jackiw-Teitelboim gravity. We find that the above higher order corrections are the Fourier transforms of the corrections to the sine-kernel approximation of the Christoffel-Darboux kernel in the dual double-scaled matrix integral, which naturally explains their structure. Along the way we also develop a technique for the systematic computation of the corrections to the sine-kernel formula, which have not been fully explored in the literature before.Comment: 29 pages, v2: typos corrected, published versio

X-ray Iron absorption line in Swift J1858.6-0814

We present the spectral analysis of bright steady states in an outburst of the transient neutron star low-mass X-ray binary (NS-LMXB) Swift J1858.6-0814 observed with NICER. We detected an ionized iron K absorption line (H-like Fe) at 6.97keV in the spectrum. We estimated the photoionization parameter using the ratio of the equivalent widths (EWs) of the FeXXVI (H-like) (17+\-5eV) and FeXXV (He-like) (<3eV) and discuss the origin of the iron absorption line. The irradiated gas producing the absorption line would locate within (3-6)*1E9cm from the X-ray source. We suggest that the observed H-like Fe absorption line originates from the highly-ionized gas in the inner accretion disk in Swift J1858.6-0814.Comment: 6 pages, 5 figure

Late time behavior of nn-point spectral form factors in Airy and JT gravities

We study the late time behavior of $n$-point spectral form factors (SFFs) in two-dimensional Witten-Kontsevich topological gravity, which includes both Airy and JT gravities as special cases. This is conducted in the small $\hbar$ expansion, where $\hbar \sim e^{- {1}/{G_N}}$ is the genus counting parameter and nonperturbative in Newton's constant $G_N$. For one-point SFF, we study its absolute square at two different late times. We show that it decays by power law at $t \sim \hbar^{-2/3}$ while it decays exponentially at $t \sim \hbar^{-1}$ due to the higher order corrections in $\hbar$. We also study general $n (\ge 2)$-point SFFs at $t \sim \hbar^{-1}$ in the leading order of the $\hbar$ expansion. We find that they are characterized by a single function, which is essentially the connected two-point SFF and is determined by the classical eigenvalue density $\rho_0(E)$ of the dual matrix integral. These studies suggest that qualitative behaviors of $n$-point SFFs are similar in both Airy and JT gravities, where our analysis in the former case is based on exact results.Comment: 31 pages, 7 figures. v2: Improved calculation of integrals in section 4.