arXiv subjects

Asato Tsuchiya

Publications and source records attributed to Asato Tsuchiya.

At least 37 records · Page 2Linked to original sources

arXiv2021

A new phase in the Lorentzian type IIB matrix model and the emergence of continuous space-time

The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. In previous studies, Monte Carlo calculations provided interesting results indicating the spontaneous breaking of SO(9) to SO(3) and the emergence of (3+1)-dimensional space-time. However, an approximation was used to avoid the sign problem, which seemed to make the space-time structure singular. In this talk, we report our results obtained by using the complex Langevin method to overcome the sign problem instead of using this approximation. In particular, we discuss the emergence of continuous space-time in a new phase, which we discovered recently.

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arXiv2021

A geometrical representation of the quantum information metric in the gauge/gravity correspondence

We study a geometrical representation of the quantum information metric in the gauge/gravity correspondence. We consider the quantum information metric that measures the distance between the ground states of two theories on the field theory side, one of which is obtained by perturbing the other. We show that the information metric is represented by a back reaction to the volume of a codimension-2 surface on the gravity side if the unperturbed field theory possesses the Poincare symmetry.

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arXiv2021

Color superconductivity in a small box: a complex Langevin study

It is expected that the color superconductivity (CSC) phase appears in QCD at low temperature and high density. On the basis of the lattice perturbation theory, a possible parameter region in which the CSC occurs has been predicted. In this work, we perform complex Langevin simulation on an $8^3\times 128$ lattice using four-flavor staggered fermions. We find, in particular, that the quark number has plateaux with respect to the chemical potential similar to our previous study, indicating the formation of the Fermi sphere. A diquark-antidiquark operator, which is an order parameter of color superconductivity, is formulated on the lattice using the U(1) noise. Our result for this operator is found to fluctuate violently when the Fermi surface coincides with the energy levels of quarks. We also discuss partial restoration of the chiral symmetry at high density.

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arXiv2021

Flavor number dependence of QCD at finite density by the complex Langevin method

We discuss the flavor number dependence of QCD at low temperature and high density by the complex Langevin method. In our previous work, the complex Langevin method is confirmed to satisfy the criterion for correct convergence in certain regions, such as $μ_{\rm q} / T = 5.2-7.2$ on $8^3 \times 16$ and $μ_{\rm q} / T = 1.6-9.6$ on $16^3 \times 32$ using $N_{\rm f} = 4$ staggered fermion at $β= 5.7$. We extend this study to more realistic flavor cases, $N_{\rm f} = 2, 2 + 1, 3$, using Wilson fermions. We present the flavor number dependence of the validity regions of the complex Langevin method and the quark number.

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arXiv2021

Perturbative predictions for color superconductivity on the lattice

We develop a new method to investigate color superconductivity (CSC) on the lattice based on the Thouless criterion, which amounts to solving the linearized gap equation without imposing any ansatz on the structure of the Cooper pairs. We perform explicit calculations at the one-loop level with the staggered fermions on a $8^3 \times 128$ lattice and the Wilson fermions on a $4^3 \times 128$ lattice, which enables us to obtain the critical $β(=6/g^2)$ as a function of the quark chemical potential $μ$, below which the CSC phase is expected to appear. The obtained critical $β$ has sharp peaks at the values of $μ$ corresponding to the discretized energy levels of quarks similarly to what was observed in previous studies on simplified effective models. From the solution to the linearized gap equation, one can read off the flavor and spatial structures of the Cooper pairs at the critical $β$. In the case of massless staggered fermion, in particular, we find that the chiral $\mathrm{U}(1)$ symmetry of the staggered fermions is spontaneously broken by the condensation of the Cooper pairs.

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arXiv2021

Renormalization group and diffusion equation

We study the relationship between the renormalization group and the diffusion equation. We consider the exact renormalization group equation for a scalar field that includes an arbitrary cutoff function and an arbitrary quadratic seed action. As a generalization of the result obtained by Sonoda and Suzuki, we find that the correlation functions of diffused fields with respect to the bare action agree with those of bare fields with respect to the effective action, where the diffused field obeys a generalized diffusion equation determined by the cutoff function and the seed action and agrees with the bare field at the initial time.

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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.

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arXiv2020

Information geometry encoded in bulk geometry

We study how information geometry is described by bulk geometry in the gauge/gravity correspondence. We consider a quantum information metric that measures the distance between the ground states of a CFT and a theory obtained by perturbing the CFT. We find a universal formula that represents the quantum information metric in terms of back reaction to the AdS bulk geometry.

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arXiv2020

The emergence of expanding space-time and intersecting D-branes from classical solutions in the Lorentzian type IIB matrix model

The type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. As such, it is expected to explain the origin of space--time and matter at the same time. This has been partially demonstrated by the previous Monte Carlo studies on the Lorentzian version of the model, which suggested the emergence of (3+1)-dimensional expanding space--time. Here we investigate the same model by solving numerically the classical equation of motion, which is expected to be valid at late times since the action becomes large due to the expansion of space. Many solutions are obtained by the gradient descent method starting from random matrix configurations, assuming a quasi-direct-product structure for the (3+1)-dimensions and the extra 6 dimensions. We find that these solutions generally admit the emergence of expanding space--time and a block-diagonal structure in the extra dimensions, the latter being important for the emergence of intersecting D-branes. For solutions corresponding to D-branes with appropriate dimensionality, the Dirac operator is shown to acquire a zero mode in the limit of infinite matrix size.

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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.

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arXiv2019

On the structure of the emergent 3d expanding space in the Lorentzian type IIB matrix model

The emergence of (3+1)-dimensional expanding space-time in the Lorentzian type IIB matrix model is an intriguing phenomenon which was observed in Monte Carlo studies of this model. In particular, this may be taken as a support to the conjecture that the model is a nonperturbative formulation of superstring theory in (9+1) dimensions. In this paper we investigate the space-time structure of the matrices generated by simulating this model and its simplified versions, and find that the expanding part of the space is described essentially by the Pauli matrices. We argue that this is due to an approximation used in the simulation to avoid the sign problem, which actually amounts to replacing $e^{iS_{\rm b}}$ by $e^{βS_{\rm b}}$ ($β>0$) in the partition function, where $S_{\rm b}$ is the bosonic part of the action. We also discuss the possibility of obtaining a regular space-time with the (3+1)-dimensional expanding behavior in the original model with the correct $e^{iS_{\rm b}}$ factor.

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arXiv2019

Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model

The Lorentzian type IIB matrix model has been studied as a promising candidate for a nonperturbative formulation of superstring theory. In particular, the emergence of (3+1)D expanding space-time was observed by Monte Carlo studies of this model. It has been found recently, however, that the matrix configurations generated by the simulation is singular in that the submatrices representing the expanding 3D space have only two large eigenvalues associated with the Pauli matrices. This problem has been attributed to the approximation used to avoid the sign problem in simulating the model. Here we investigate the model using the complex Langevin method to overcome the sign problem instead of using the approximation. Our results indicate a clear departure from the Pauli-matrix structure, while the (3+1)D expanding behavior is kept intact.

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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 $μ$.

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arXiv2018

Renormalization on the fuzzy sphere

We study renormalization on the fuzzy sphere, which is a typical example of non-commutative spaces. We numerically simulate a scalar field theory on the fuzzy sphere, which is described by a Hermitian matrix model. We define correlation functions by using the Berezin symbol and show that they are made independent of the matrix size, which plays a role of a UV cutoff, by tuning one parameter of the theory. We also find that the theories on the phase boundary are universal. They behave as a conformal field theory at short distances, while they universally differ from it at long distances due to the UV/IR mixing.

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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.

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arXiv2018

Renormalization on the fuzzy sphere

We study renormalization on the fuzzy sphere. We numerically simulate a scalar field theory on it, which is described by a Hermitian matrix model. We show that correlation functions defined by using the Berezin symbol are made independent of the matrix size, which is viewed as a UV cutoff, by tuning a parameter of the theory. We also find that the theories on the phase boundary are universal. They behave as a conformal field theory at short distances, while they show an effect of UV/IR mixing at long distances.

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arXiv2018

Equivalence of large-$N$ gauge theories on a group manifold and its coset space

It was shown in arXiv:0912.1456 that the large-$N$ reduction holds on group manifolds in the sense that a large-$N$ gauge theory on a group manifold is realized by a matrix model which is obtained by dimensionally reducing the original theory to zero dimension. In this note, generalizing the above statement, we show that a large-$N$ gauge theory on a group manifold is equivalent to a theory which is obtained by reducing the original theory to its coset space. This is analogous to the statement of the large-$N$ reduction on flat spaces that large-$N$ gauge theories are independent of the volume.

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arXiv2017

Correlation functions and renormalization in a scalar field theory on the fuzzy sphere

We study renormalization in a scalar field theory on the fuzzy sphere. The theory is realized by a matrix model, where the matrix size plays the role of a UV cutoff. We define correlation functions by using the Berezin symbol identified with a field and calculate them nonperturbatively by Monte Carlo simulation. We find that the 2-point and 4-point functions are made independent of the matrix size by tuning a parameter and performing a wave function renormalization. The results strongly suggest that the theory is nonperturbatively renormalizable in the ordinary sense.

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