arXiv subjects

Shinji Shimasaki

Publications and source records attributed to Shinji Shimasaki.

At least 19 recordsLinked to original sources

arXiv2026

Derivation of the NS5-brane limit of the plane wave matrix model

From the gauge/gravity duality, it was predicted that there exists a nontrivial double scaling limit of the plane wave matrix model (the BMN matrix model), which describes the type IIA little string theory (LST) on $R\times S^5$. We show on the gauge theory side that such a limit indeed exists for the partition function and in a certain 1/4 BPS sector of the matrix model, and consequently derive an eigenvalue integral, which is expected to describe the 1/4 BPS sector of LST.

hep-th↗

arXiv2025

On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density

In our previous paper [JHEP 10 (2020) 144], we found that the complex Langevin (CL) method works for QCD at finite density on the $16^3 \times 32$ lattice in the low-temperature high-density regime within the range $\mu / T = 1.6 - 9.6$ with $\mu$ and $T$ being the quark chemical potential and the temperature, which enabled us to see a clear trend towards the formation of the Fermi sphere. Here we investigate the validity of the CL method on the $24^3 \times 12$ lattice in the deconfined phase near the deconfinement phase transition. As before, we use four-flavor staggered fermions and judge the validity using the criterion based on the probability distribution of the drift term. The spatial extent is $L = (1.3 - 2.7 {\rm ~fm} )> \Lambda_{\rm LQCD}^{-1} \sim 1{\rm ~fm}$, in contrast to our previous study with $L < \Lambda_{\rm LQCD}^{-1}$. We find that the CL method works in a broad region up to $\mu / T = 4.8$, while it starts to fail as we approach the phase boundary due to the singular drift problem, which can be understood qualitatively by extending the Banks-Casher relation to the case at finite density.

hep-lat↗

arXiv2022

On the existence of the NS5-brane limit of the plane wave matrix model

We consider a double scaling limit of the plane wave matrix model (PWMM), in which the gravity dual geometry of PWMM reduces to a class of spherical NS5-brane solutions. We identify the form of the scaling limit for the dual geometry of PWMM around a general vacuum and then translate the limit into the field theoretic language. We also show that the limit indeed exists at least in a certain planar 1/4-BPS sector of PWMM by using the localization computation analytically. In addition, we employ the hybrid Monte Carlo method to compute the matrix integral obtained by the localization method, near the parameter region where the supergravity approximation is valid. Our numerical results, which are considered to be the first computation of quantum loop correction to the Lin-Maldacena geometry, suggest that the double scaling limit exists beyond the planar sector.

hep-th↗

arXiv2020

Complex Langevin calculations in QCD at finite density

We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with $β= 5.7$ and four-flavor staggered fermions with degenerate quark mass $m a = 0.01$ and nonzero quark chemical potential $μ$. We confirm that a sufficient condition for correct convergence is satisfied for $μ/T = 5.2 - 7.2$ on a $8^3 \times 16$ lattice and $μ/T = 1.6 - 9.6$ on a $16^3 \times 32$ lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to $μ$ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) $\times$ 4 (flavor) $\times$ 2 (spin) $=24$. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.

hep-lat↗

arXiv2019

Exploring the QCD phase diagram at finite density by the complex Langevin method on a $16^3\times 32$ lattice

We explore the QCD phase diagram at finite density with four-flavor staggered fermions using the complex Langevin method, which is a promising approach to overcome the sign problem. In our previous work on an $8^3 \times 16$ lattice at $β= 5.7$ with the quark mass $m = 0.01$, we have found that the baryon number density has a clear plateau as a function of the chemical potential. In this study, we use a $16^3 \times 32$ lattice to reduce finite volume effects and find that the plateau structure survives. Moreover, the number of quarks in the plateau region turns out to be 24, which is exactly the same as the one obtained previously on the $8^3 \times 16$ lattice. We provide a simple interpretation of this number, which suggests that the Fermi sphere is starting to form.

hep-lat↗

arXiv2019

Complex Langevin calculations in finite density QCD at large $μ/T$ with the deformation technique

It is well known that investigating QCD at finite density by standard Monte Carlo methods is extremely difficult due to the sign problem. Some years ago, the complex Langevin method with gauge cooling was shown to work at high temperature, i.e., in the deconfined phase. The same method was also applied to QCD in the so-called heavy dense limit in the whole temperature region. In this paper we attempt to apply this method to the large $μ/T$ regime with moderate quark mass using four-flavor staggered fermions on a $4^3\times 8$ lattice. While a straightforward application faces with the singular-drift problem, which spoils the validity of the method, we overcome this problem by the deformation technique proposed earlier. Explicit results for the quark number density and the chiral condensate obtained in this way for $3.2\leq μ/T\leq 5.6$ are compared with the results for the phase-quenched model obtained by the standard rational hybrid Monte Carlo calculation. This reveals a clear difference, which is qualitatively consistent with the Silver Blaze phenomenon.

hep-lat↗

arXiv2018

Exploring the phase diagram of finite density QCD at low temperature by the complex Langevin method

Monte Carlo studies of QCD at finite density suffer from the sign problem, which becomes easily uncontrollable as the chemical potential $μ$ is increased even for a moderate lattice size. In this work we make an attempt to approach the high density low temperature region by the complex Langevin method (CLM) using four-flavor staggered fermions with reasonably small quark mass on a $8^3 \times 16$ lattice. Unlike the previous work on a $4^3 \times 8$ lattice, the criterion for correct convergence is satisfied within a wide range of $μ$ without using the deformation technique. In particular, the baryon number density exhibits a plateau behavior consistent with the formation of eight baryons, and it starts to grow gradually at some $μ$.

hep-lat↗

arXiv2018

Can the complex Langevin method see the deconfinement phase transition in QCD at finite density?

Exploring the phase diagram of QCD at finite density is a challenging problem since first-principle calculations based on standard Monte Carlo methods suffer from the sign problem. As a promising approach to this issue, the complex Langevin method (CLM) has been pursued intensively.In this work, we investigate the applicability of the CLM in the vicinity of the deconfinement phase transition using the four-flavor staggered fermions. In particular, we look for a signal of the expected first order phase transition within the validity region of the CLM.

hep-lat↗

arXiv2018

Testing the criterion for correct convergence in the complex Langevin method

Recently the complex Langevin method (CLM) has been attracting attention as a solution to the sign problem, which occurs in Monte Carlo calculations when the effective Boltzmann weight is not real positive. An undesirable feature of the method, however, was that it can happen in some parameter regions that the method yields wrong results even if the Langevin process reaches equilibrium without any problem. In our previous work, we proposed a practical criterion for correct convergence based on the probability distribution of the drift term that appears in the complex Langevin equation. Here we demonstrate the usefulness of this criterion in two solvable theories with many dynamical degrees of freedom, i.e., two-dimensional Yang-Mills theory with a complex coupling constant and the chiral Random Matrix Theory for finite density QCD, which were studied by the CLM before. Our criterion can indeed tell the parameter regions in which the CLM gives correct results.

hep-lat↗

arXiv2018

Supersymmetry in Closed Chains of Coupled Majorana Modes

We consider a closed chain of even number of Majorana zero modes with nearest-neighbour couplings which are different site by site generically, thus no any crystal symmetry. Instead, we demonstrate the possibility of an emergent supersymmetry (SUSY), which is accompanied by gapless Fermionic excitations. In particular, the condition can be easily satisfied by tuning only one coupling, regardless of how many other couplings are there. Such a system can be realized by four Majorana modes on two parallel Majorana nanowires with their ends connected by Josephson junctions and bodies connected by an external superconducting ring. By tuning the Josephson couplings with a magnetic flux $Φ$ through the ring, we get the gapless excitations at $Φ_{SUSY}=\pm fΦ_0$ with $Φ_0= hc/2e$, which is signaled by a zero-bias conductance peak in tunneling conductance. We find this $f$ generally a fractional number and oscillating with increasing Zeeman fields that parallel to the nanowires, which provide a unique experimental signature for the existence of Majorana modes.

cond-mat.supr-con↗

arXiv2017

Spherical transverse M5-branes from the plane wave matrix model

We consider matrix theoretical description of transverse M5-branes in M-theory on the 11-dimensional maximally supersymmetric pp-wave background. We apply the localization to the plane wave matrix model (PWMM) and show that the transverse spherical fivebranes with zero light cone energy in M-theory are realized as the distribution of low energy moduli of the $SO(6)$ scalar fields in PWMM.

hep-th↗

arXiv2017

Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique

We study QCD at finite density and low temperature by using the complex Langevin method. We employ the gauge cooling to control the unitarity norm and introduce a deformation parameter in the Dirac operator to avoid the singular-drift problem. The reliability of the obtained results are judged by the probability distribution of the magnitude of the drift term. By making extrapolations with respect to the deformation parameter using only the reliable results, we obtain results for the original system. We perform simulations on a $4^3\times 3$ lattice and show that our method works well even in the region where the reweighting method fails due to the severe sign problem. As a result we observe a delayed onset of the baryon number density as compared with the phase-quenched model, which is a clear sign of the Silver Blaze phenomenon.

hep-lat↗

arXiv2017

Unification of the complex Langevin method and the Lefschetz-thimble method

Recently there has been remarkable progress in solving the sign problem, which occurs in investigating statistical systems with a complex weight. The two promising methods, the complex Langevin method and the Lefschetz thimble method, share the idea of complexifying the dynamical variables, but their relationship has not been clear. Here we propose a unified formulation, in which the sign problem is taken care of by both the Langevin dynamics and the holomorphic gradient flow. We apply our formulation to a simple model in three different ways and show that one of them interpolates the two methods by changing the flow time.

hep-lat↗

arXiv2017

Combining the complex Langevin method and the generalized Lefschetz-thimble method

The complex Langevin method and the generalized Lefschetz-thimble method are two closely related approaches to the sign problem, which are both based on complexification of the original dynamical variables. The former can be viewed as a generalization of the stochastic quantization using the Langevin equation, whereas the latter is a deformation of the integration contour using the so-called holomorphic gradient flow. In order to clarify their relationship, we propose a formulation which combines the two methods by applying the former method to the real variables that parametrize the deformed integration contour in the latter method. Three versions, which differ in the treatment of the residual sign problem in the latter method, are considered. By applying them to a single-variable model, we find, in particular, that one of the versions interpolates the complex Langevin method and the original Lefschetz-thimble method.

hep-lat↗

arXiv2017

On the transverse M5-branes in matrix theory

It has been a long-standing problem how the transverse M5-branes are described in the matrix-model formulations of M-theory. We consider this problem for M-theory on the maximally supersymmetric pp-wave geometry, which admits transverse spherical M5-branes with zero light-cone energy. By using the localization, we directly analyze the strong coupling region of the corresponding matrix theory called the plane wave matrix model (PWMM). Under the assumption that the low energy modes of the scalar fields in PWMM become mutually commuting in the strong coupling region, we show that the eigenvalue density of the $SO(6)$ scalars in the low energy region exactly agrees with the shape of the spherical M5-branes in the decoupling limit. This result gives a strong evidence that the transverse M5-branes are indeed contained in the matrix theory and the theory realizes a second quantization of the M-theory.

hep-th↗

arXiv2016

The argument for justification of the complex Langevin method and the condition for correct convergence

The complex Langevin method is a promising approach to the complex-action problem based on a fictitious time evolution of complexified dynamical variables under the influence of a Gaussian noise. Although it is known to have a restricted range of applicability, the use of gauge cooling made it applicable to various interesting cases including finite density QCD in certain parameter regions. In this paper, we revisit the argument for justification of the method. In particular, we point out a subtlety in the use of time-evolved observables, which play a crucial role in the previous argument. This requires that the probability of the drift term should fall off exponentially or faster at large magnitude. We argue that this is actually a necessary and sufficient condition for the method to be justified. Using two simple examples, we show that our condition tells us clearly whether the results obtained by the method are trustable or not. We also discuss a new possibility for the gauge cooling, which can reduce the magnitude of the drift term directly.

hep-lat↗

arXiv2016

On the condition for correct convergence in the complex Langevin method

The complex Langevin method (CLM) provides a promising way to perform the path integral with a complex action using a stochastic equation for complexified dynamical variables. It is known, however, that the method gives wrong results in some cases, while it works, for instance, in finite density QCD in the deconfinement phase or in the heavy dense limit. Here we revisit the argument for justification of the CLM and point out a subtlety in using the time-evolved observables, which play a crucial role in the argument. This subtlety requires that the probability distribution of the drift term should fall off exponentially or faster at large magnitude. We demonstrate our claim in some examples such as chiral Random Matrix Theory and show that our criterion is indeed useful in judging whether the results obtained by the CLM are trustable or not.

hep-lat↗

arXiv2016

Gauge cooling for the singular-drift problem in the complex Langevin method --- an application to finite density QCD

We study full QCD at finite density and low temperature with light quark mass using the complex Langevin method. Since the singular drift problem turns out to be mild on a $4^3 \times 8$ lattice we use, the gauge cooling is performed only to control the unitarity norm in this exploratory study. We report on our preliminary data obtained from the complex Langevin simulation up to certain Langevin time. While the data are still noisy due to lack of statistics, the onset of the baryon number density seems to occur at larger $μ$ than half the pion mass, which is the value for the phase quenched QCD. The validity of our simulation is tested by the recently proposed criterion based on the probability distribution of the drift term.

hep-lat↗