arXiv subjects

Kazuhiro Sakai

Publications and source records attributed to Kazuhiro Sakai.

At least 37 records · Page 2Linked to original sources

arXiv2020

JT supergravity and Brezin-Gross-Witten tau-function

We study thermal correlation functions of Jackiw-Teitelboim (JT) supergravity. We focus on the case of JT supergravity on orientable surfaces without time-reversal symmetry. As shown by Stanford and Witten recently, the path integral amounts to the computation of the volume of the moduli space of super Riemann surfaces, which is characterized by the Brezin-Gross-Witten (BGW) tau-function of the KdV hierarchy. We find that the matrix model of JT supergravity is a special case of the BGW model with infinite number of couplings turned on in a specific way, by analogy with the relation between bosonic JT gravity and the Kontsevich-Witten (KW) model. We compute the genus expansion of the one-point function of JT supergravity and study its low-temperature behavior. In particular, we propose a non-perturbative completion of the one-point function in the Bessel case where all couplings in the BGW model are set to zero. We also investigate the free energy and correlators when the Ramond-Ramond flux is large. We find that by defining a suitable basis higher genus free energies are written exactly in the same form as those of the KW model, up to the constant terms coming from the volume of the unitary group. This implies that the constitutive relation of the KW model is universal to the tau-function of the KdV hierarchy.

hep-th↗

arXiv2020

Multi-boundary correlators in JT gravity

We continue the systematic study of the thermal partition function of Jackiw-Teitelboim (JT) gravity started in [arXiv:1911.01659]. We generalize our analysis to the case of multi-boundary correlators with the help of the boundary creation operator. We clarify how the Korteweg-de Vries constraints arise in the presence of multiple boundaries, deriving differential equations obeyed by the correlators. The differential equations allow us to compute the genus expansion of the correlators up to any order without ambiguity. We also formulate a systematic method of calculating the WKB expansion of the Baker-Akhiezer function and the 't Hooft expansion of the multi-boundary correlators. This new formalism is much more efficient than our previous method based on the topological recursion. We further investigate the low temperature expansion of the two-boundary correlator. We formulate a method of computing it up to any order and also find a universal form of the two-boundary correlator in terms of the error function. Using this result we are able to write down the analytic form of the spectral form factor in JT gravity and show how the ramp and plateau behavior comes about. We also study the Hartle-Hawking state in the free boson/fermion representation of the tau-function and discuss how it should be related to the multi-boundary correlators.

hep-th↗

arXiv2020

JT gravity, KdV equations and macroscopic loop operators

We study the thermal partition function of Jackiw-Teitelboim (JT) gravity in asymptotically Euclidean $AdS_2$ background using the matrix model description recently found by Saad, Shenker and Stanford [arXiv:1903.11115]. We show that the partition function of JT gravity is written as the expectation value of a macroscopic loop operator in the old matrix model of 2d gravity in the background where infinitely many couplings are turned on in a specific way. Based on this expression we develop a very efficient method of computing the partition function in the genus expansion as well as in the low temperature expansion by making use of the Korteweg-de Vries constraints obeyed by the partition function. We have computed both these expansions up to very high orders using this method. It turns out that we can take a low temperature limit with the ratio of the temperature and the genus counting parameter held fixed. We find the first few orders of the expansion of the free energy in a closed form in this scaling limit. We also study numerically the behavior of the eigenvalue density and the Baker-Akhiezer function using the results in the scaling limit.

hep-th↗

arXiv2019

Holomorphic anomaly of 2d Yang-Mills theory on a torus revisited

We study the large $N$ 't Hooft expansion of the chiral partition function of 2d $U(N)$ Yang-Mills theory on a torus. There is a long-standing puzzle that no explicit holomorphic anomaly equation is known for the partition function, although it admits a topological string interpretation. Based on the chiral boson interpretation we clarify how holomorphic anomaly arises and propose a natural anti-holomorphic deformation of the partition function. Our deformed partition function obeys a fairly traditional holomorphic anomaly equation. Moreover, we find a closed analytic expression for the deformed partition function. We also study the behavior of the deformed partition function both in the strong coupling/large area limit and in the weak coupling/small area limit. In particular, we observe that drastic simplification occurs in the weak coupling/small area limit, giving another nontrivial support for our anti-holomorphic deformation.

hep-th↗

arXiv2019

E_n Jacobi forms and Seiberg-Witten curves

We discuss Jacobi forms that are invariant under the action of the Weyl group of type E_n (n=6,7,8). For n=6,7 we explicitly construct a full set of generators of the algebra of E_n weak Jacobi forms. We first construct n+1 independent E_n Jacobi forms in terms of Jacobi theta functions and modular forms. By using them we obtain Seiberg-Witten curves of type E_6 and E_7 for the E-string theory. The coefficients of each curve are E_n weak Jacobi forms of particular weights and indices specified by the root system, realizing the generators whose existence was shown some time ago by Wirthmüller.

hep-th↗

arXiv2018

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.

hep-th↗

arXiv2018

Spatial distribution of the Milky Way hot gaseous halo constrained by Suzaku X-ray observations

The formation mechanism of the hot gaseous halo associated with the Milky Way Galaxy is still under debate. We report new observational constraints on the gaseous halo using 107 lines-of-sight of the Suzaku X-ray observations at $75^{\circ} 15^{\circ}$ with a total exposure of 6.4 Ms. The gaseous halo spectra are represented by a single-temperature plasma model in collisional ionization equilibrium. The median temperature of the observed fields is 0.26 keV ($3.0\times10^6$ K) with a typical fluctuation of $\sim30$%. The emission measure varies by an order of magnitude and marginally correlates with the Galactic latitude. Despite the large scatter of the data, the emission measure distribution is roughly reproduced by a disk-like density distribution with a scale length of $\sim7$ kpc, a scale height of $\sim2$ kpc, and a total mass of $\sim5\times10^7$ $M_{\odot}$. In addition, we found that a spherical hot gas with the $β$-model profile hardly contributes to the observed X-rays but that its total mass might reach $\gtrsim10^9$ $M_{\odot}$. Combined with indirect evidence of an extended gaseous halo from other observations, the hot gaseous halo likely consists of a dense disk-like component and a rarefied spherical component; the X-ray emissions primarily come from the former but the mass is dominated by the latter. The disk-like component likely originates from stellar feedback in the Galactic disk due to the low scale height and the large scatter of the emission measures. The median [O/Fe] of $\sim0.25$ shows the contribution of the core-collapse supernovae and supports the stellar feedback origin.

astro-ph.GA↗

arXiv2017

Topological string amplitudes for the local half K3 surface

We study topological string amplitudes for the local half K3 surface. We develop a method of computing higher-genus amplitudes along the lines of the direct integration formalism, making full use of the Seiberg-Witten curve expressed in terms of modular forms and E_8-invariant Jacobi forms. The Seiberg-Witten curve was constructed previously for the low-energy effective theory of the non-critical E-string theory in R^4 x T^2. We clarify how the amplitudes are written as polynomials in a finite number of generators expressed in terms of the Seiberg-Witten curve. We determine the coefficients of the polynomials by solving the holomorphic anomaly equation and the gap condition, and construct the amplitudes explicitly up to genus three. The results encompass topological string amplitudes for all local del Pezzo surfaces.

hep-th↗

arXiv2016

BPS index and 4d N=2 superconformal field theories

We study the BPS index for the four-dimensional rank-one N=2 superconformal field theories H_0, H_1, H_2, E_6, E_7, E_8. We consider compactifications of the E-string theory on T^2 in which these theories arise as low energy limits. Using this realization we clarify the general structure of the BPS index. The index is characterized by two exponents and a sequence of invariants. We determine the exponents and the first few invariants.

hep-th↗

arXiv2014

A reduced BPS index of E-strings

We study the BPS spectrum of E-strings in a situation where the global E_8 symmetry is broken down to D_4 + D_4 by a certain twist. We find that the refined BPS index in this setup serves as a reduced BPS index of E-strings, which gives a novel trigonometric generalization of the Nekrasov partition function for four-dimensional N=2 supersymmetric SU(2) gauge theory with N_f=4 massless flavors. We determine the perturbative part of this index and also first few unrefined instanton corrections. By using these results together with the modular anomaly equation, the genus expansion of the free energy can be computed efficiently up to very high order. We also determine the unrefined elliptic genus of four E-strings under the twist.

hep-th↗

arXiv2014

Structual Study of Galactic Hot Gas toward Markarian 421 from X-Ray Absorption and Emission Lines

We present a structural study of the hot ISM in the Galactic halo along the sight line toward the bright active galactic nucleus Mkn 421. The OVII and OVIII absorption lines were measured with the Low Energy Transmission Grating Spectrograph aboard Chandra toward Mkn 421, and the OVII and OVIII emission lines were observed in the adjacent fields of the sight line with the X-ray Imaging Spectrometer aboard Suzaku. We jointly analyzed the absorption and the emission spectra assuming exponential distributions of the gas temperature and density from the Galactic plane, and constrained the temperature and density at the plane to be $(3.2^{+0.6}_{-0.7})\times 10^6\,\mathrm{K}$ and $(1.2^{+0.5}_{-0.4})\times 10^{-3}\,\mathrm{cm^{-3}}$, with the scale heights of $1.6^{+1.7}_{-0.7}\,\mathrm{kpc}$ and $>2.8\,\mathrm{kpc}$ respectively. The results are consistent with those obtained in the LMC X-3 direction and the PKS 2155-304 direction, describing a thick disk-like hot gas with its height of a few kpc from the Galactic plane.

astro-ph.HE↗

arXiv2014

Thermodynamic limit of the Nekrasov-type formula for E-string theory

We give a proof of the Nekrasov-type formula proposed by one of the authors for the Seiberg-Witten prepotential for the E-string theory on R^4 x T^2. We take the thermodynamic limit of the Nekrasov-type formula following the example of Nekrasov-Okounkov and reproduce the Seiberg-Witten description of the prepotential. The Seiberg-Witten curve obtained directly from the Nekrasov-type formula is of genus greater than one. We find that this curve is transformed into the known elliptic curve by a simple map. We consider the cases in which the low energy theory has E_8, E_7+A_1 or E_6+A_2 as a global symmetry.

hep-th↗

arXiv2013

Integrability of BPS equations in ABJM theory

We investigate BPS equations which determine the configuration of an M2-M5 bound state preserving half of the supersymmetries in the ABJM theory. We argue that the BPS equations are classically integrable, showing that they admit a Lax representation. The integrable structure of the BPS equations is closely related to that of the Nahm equations. Using this relation we formulate an efficient way of constructing solutions of the BPS equations from those of the Nahm equations. As an illustration of our method, we construct explicitly the most general solutions describing two M2-branes suspended between two parallel M5-branes as well as two semi-infinite M2-branes ending on an M5-brane. These include previously unknown new solutions. We also discuss a reduction of the BPS equations in connection with the periodic Toda chain.

hep-th↗

arXiv2013

Long Term Variability of O VII Line Intensity toward the Lockman Hole Observed with Suzaku from 2006 to 2011

Long-term time variabilities of the OVII (0.57 keV) emission in the soft X-ray diffuse background were studied using six Suzaku annual observations of blank sky towards the Lockman Hole made from 2006 to 2011. After time intervals in which the emission was enhanced on time scales of a few tens of ks were removed, the O VII intensity was found to be constant from 2006 to 2009 within the 90% statistical errors. The intensity in 2010 and 2011 was higher by 2-3 LU (photons/s/cm/sr) than the earlier values. The most plausible origin of the fast variable component is Solar wind charge exchange (SWCX). The intensity increase is not positively correlated with the proton flux at the L1 point. Since all the observations were made in the same season of a year, the variation cannot be explained by parallax of the SWCX induced X-ray emission from the Heliosphere. We consider that it is related to the geometrical change of slow and fast solar wind structures associated with the 11 year solar activity. The observed variation was compared with that expected from the SWCX induced X-ray emission model.

astro-ph.HE↗

arXiv2012

Seiberg-Witten prepotential for E-string theory and global symmetries

We obtain Nekrasov-type expressions for the Seiberg-Witten prepotential for the six-dimensional (1,0) supersymmetric E-string theory compactified on T^2 with nontrivial Wilson lines. We consider compactification with four general Wilson line parameters, which partially break the E_8 global symmetry. In particular, we investigate in detail the cases where the Lie algebra of the unbroken global symmetry is E_n + A_{8-n} with n=8,7,6,5 or D_8. All our Nekrasov-type expressions can be viewed as special cases of the elliptic analogue of the Nekrasov partition function for the SU(N) gauge theory with N_f=2N flavors. We also present a new expression for the Seiberg-Witten curve for the E-string theory with four Wilson line parameters, clarifying the connection between the E-string theory and the SU(2) Seiberg-Witten theory with N_f=4 flavors.

hep-th↗

arXiv2012

Seiberg-Witten prepotential for E-string theory and random partitions

We find a Nekrasov-type expression for the Seiberg-Witten prepotential for the six-dimensional non-critical E_8 string theory toroidally compactified down to four dimensions. The prepotential represents the BPS partition function of the E_8 strings wound around one of the circles of the toroidal compactification with general winding numbers and momenta. We show that our expression exhibits expected modular properties. In particular, we prove that it obeys the modular anomaly equation known to be satisfied by the prepotential.

hep-th↗

arXiv2011

g-Functions and gluon scattering amplitudes at strong coupling

We study gluon scattering amplitudes/Wilson loops in N=4 super Yang-Mills theory at strong coupling by calculating the area of the minimal surfaces in AdS_3 based on the associated thermodynamic Bethe ansatz system. The remainder function of the amplitudes is computed by evaluating the free energy, the T- and Y-functions of the homogeneous sine-Gordon model. Using conformal field theory (CFT) perturbation, we examine the mass corrections to the free energy around the CFT point corresponding to the regular polygonal Wilson loop. Based on the equivalence between the T-functions and the g-functions, which measure the boundary entropy, we calculate corrections to the T- and Y-functions as well as express them at the CFT point by the modular S-matrix. We evaluate the remainder function around the CFT point for 8 and 10-point amplitudes explicitly and compare these analytic expressions with the 2-loop formulas. The two rescaled remainder functions show very similar power series structures.

hep-th↗

arXiv2011

An X-ray Spectroscopic Study of the Hot Interstellar Medium Toward the Galactic Bulge

We present a detailed spectroscopic study of the hot gas toward the Galactic bulge along the 4U 1820-303 sight line by a combination analysis of emission and absorption spectra. In addition to the absorption lines of OVII Kalpha, OVII Kbeta, OVIII Kalpha and NeIX Kalpha by Chandra LTGS as shown by previous works, Suzaku detected clearly the emission lines of OVII, OVIII, NeIX and NeX from the vicinity. We used simplified plasma models with constant temperature and density. Evaluation of the background and foreground emission was performed carefully, including stellar X-ray contribution based on the recent X-ray observational results and stellar distribution simulator. If we assume that one plasma component exists in front of 4U1820-303 and the other one at the back, the obtained temperatures are T= 1.7 +/- 0.2 MK for the front-side plasma and T=3.9(+0.4-0.3) MK for the backside. This scheme is consistent with a hot and thick ISM disk as suggested by the extragalactic source observations and an X-ray bulge around the Galactic center.

astro-ph.HE↗