arXiv subjects

Mitsuaki Hirasawa

Publications and source records attributed to Mitsuaki Hirasawa.

At least 19 recordsLinked to original sources

arXiv2026

The QCD energy-momentum tensor on the lattice: non-perturbative renormalization with $N_f=3$

We construct the traceless components of the energy-momentum tensor on the lattice for QCD with $N_f=3$ flavours, such that their correlation functions satisfy the appropriate Ward identities in the continuum limit. To carry out this program, we define the theory on the lattice by the Wilson-plaquette and the $O(a)$-improved Wilson actions for gluons and quarks respectively. The discretization of the space-time entails that (i) the irreducible nonet representation of the SO($4$) group splits into a triplet and a sextet irreducible representations of the hypercubic group, and (ii) for each multiplet non-perturbative determinations of the the gluonic and fermionic renormalization constants are required. The bare gluonic components of the energy-momentum tensor are defined via the clover discretization of the field strength tensor, while the fermionic ones are discretized by appropriate combinations of symmetric covariant derivatives. Either for the triplet or the sextet representations, the two independent renormalization constants are then fixed non-perturbatively by imposing discretized versions of continuum Ward identities for one-point correlation functions in the presence of shifted boundary conditions and an imaginary chemical potential. The non-perturbative calculation is then carried out by Monte Carlo simulations, and the resulting renormalization constants are determined with a final accuracy of a few percent for values of the bare coupling constant squared in the range $0 \leq g_0^2\leq 0.96$.

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arXiv2026

Impact of supersymmetry on the dynamical emergence of the spacetime in the type IIB matrix model with the Lorentz symmetry "gauge fixed"

The type IIB matrix model has been proposed as a nonperturbative formulation of superstring theory. While numerical simulations of this model are essential for probing nonperturbative effects, such as the emergence of time and an expanding 3--dimensional space, they are hindered by the sign problem. We address this using the Complex Langevin Method (CLM). Furthermore, to suppress spurious numerical artifacts that originate from large Lorentz boosts due to the Lorentz symmetry of the model, we nonperturbatively fix the Lorentz symmetry using the Faddeev--Popov procedure. We then study this model to investigate the impact of supersymmetry on the dynamical generation of (3+1)--dimensional spacetime.

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arXiv2026

The emergence of (3+1)-dimensional expanding spacetime from complex Langevin simulations of the Lorentzian type IIB matrix model with deformations

The Lorentzian type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. In this model, the eigenvalue distribution of the $N\times N$ bosonic matrices $A_μ$ $(μ= 0 , \ldots , 9)$ represents an emergent spacetime, which is determined by the dynamics of the model in the large-$N$ limit. Here we perform numerical simulations of the model overcoming the sign problem by the complex Langevin method with the matrix size $N$ up to $128$. In order to avoid the singular drift problem due to the Pfaffian, which appears after integrating out the fermionic matrices, we deform the model in a manner inspired by the supersymmetric deformation, which is used to define the ``polarized type IIB matrix model'' in the Euclidean case. We find that the deformed model exhibits a phase in which (3+1)-dimensional expanding spacetime emerges with both space and time being smooth and real.

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arXiv2026

Phase diagram of 4D SU(3) Yang-Mills theory at $θ=π$ via imaginary theta simulations

It has been speculated that the CP symmetry of 4D SU(3) Yang-Mills theory at $θ=π$ is spontaneously broken in the confined phase, and it is recovered precisely at the deconfining temperature. The direct simulation of the theory at $θ=π$ is, however, difficult due to the sign problem. We therefore simulate the theory with an imaginary theta parameter and perform analytic continuation to the real theta to explore the phase diagram. We implement the stout smearing technique in the hybrid Monte Carlo simulation to recover the topological property of the gauge field. The smearing-time dependence of the observable is investigated using the reweighting method with respect to the smearing step parameters, and a clear scaling behavior is observed. The order parameter of the CP symmetry is then computed in the scaling region to detect symmetry breaking. We report preliminary results on the expected CP breaking and restoration temperature.

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arXiv2025

Evidence of a CP broken deconfined phase in 4D SU(2) Yang-Mills theory at $θ=π$ from imaginary $θ$ simulations

The spontaneous breaking of CP symmetry in 4D SU($N$) pure Yang-Mills theory at $θ=π$ has recently attracted much attention in the context of the higher-form symmetry and the 't Hooft anomaly matching condition. Here we use Monte Carlo simulations to study the $N=2$ case, which is interesting since it is the case opposite to the large-$N$ limit, where explicit calculations are available. In order to circumvent the severe sign problem due to the $θ$ term for real $θ$, we first obtain results at imaginary $θ$, where the sign problem is absent, and make an analytic continuation to real $θ$. We use the stout smearing in defining the $θ$ term in the action to be used in our simulations. Thus we obtain the expectation value of the topological charge and the deconfining temperature at $θ=π$, and provide an evidence that the CP symmetry, which is spontaneously broken at low temperature, gets restored \emph{strictly above} the deconfining temperature. This conclusion is consistent with the anomaly matching condition and yet differs from the prediction in the large-$N$ limit.

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arXiv2025

Numerical evidence for a CP broken deconfined phase at $θ=π$ in 4D SU(2) Yang-Mills theory through simulations at imaginary $θ$

We investigate the possibility of the spontaneous breaking of CP symmetry in 4D SU(2) Yang-Mills at $θ=π$, which has recently attracted much attention in the context of the higher-form symmetry and the 't Hooft anomaly matching condition. Here we provide a numerical evidence that the CP symmetry is indeed spontaneously broken at low temperature and it gets restored above the deconfining temperature at $θ=π$, which is consistent with the anomaly matching condition and yet differs from the situation predicted in the large-$N$ limit. We avoid the severe sign problem by performing simulations at imaginary $θ$. We obtain the critical temperature of the CP restoration and that of deconfinement at $θ=π$ by analytic continuation, which leads to the above conclusion.

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arXiv2025

Computation of the latent heat of the deconfinement phase transition of SU(3) Yang-Mills theory

We investigate the thermal properties of $\mathrm{SU}(3)$ Yang-Mills theory across the deconfinement phase transition considering the framework of shifted boundary conditions in the temporal direction. By measuring the entropy density $s(T_c)/T_c^3$ on both sides of the phase transition at the critical temperature $T_c$, we can retrieve the latent heat $h$. Additionally, we compute $h$ from the discontinuity in the trace anomaly of the energy-momentum tensor. Simulations are performed at five different values of the lattice spacing, allowing us to extrapolate the results to the continuum limit. The two observables produce compatible results, giving the combined estimate $h = 1.175(10)$ in the continuum limit, achieving a precision of about 1 %. Moreover, we determine the critical temperature in physical units with permille accuracy, yielding $T_c \sqrt{t_0} = 0.24915(29)$. These results allow us to connect the confined and the deconfined phases with precision, and we present an improved computation of the Equation of State across the phase transition for temperatures between $0$ and $3.4 T_c$.

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arXiv2025

A precise study of the SU(3) Yang-Mills theory across the deconfinement transition

We perform a detailed computation of key quantities across the first-order deconfinement phase transition of the SU(3) Yang-Mills theory. Specifically, we calculate the entropy density, $s(T_c)/T_c^3$, on both sides of the transition and determine the latent heat $h$. The calculations are carried out in the lattice regularization with the Wilson action, employing shifted boundary conditions in the temporal direction. Our simulations are performed at five different values of the lattice spacing in order to extrapolate the results to the continuum limit. The latent heat can be measured also as the discontinuity in the trace anomaly of the energy-momentum tensor: our result using the entropy density is compatible with the one obtained from the trace anomaly, giving a combined estimate $h=1.175(10)$. Additionally, we determine the critical temperature $T_c$ in physical units with permille accuracy, yielding $T_c \sqrt{t_0} = 0.24915(29)$. These results allow to connect with precision the confined and the deconfined phases and we present an improved computation of the Equation of State across the deconfinement transition for $T$ between 0 and $3.4 T_c$.

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arXiv2024

The effects of SUSY on the emergent spacetime in the Lorentzian type IIB matrix model

The Lorentzian type IIB matrix model is a promising candidate for a nonperturbative formulation of superstring theory. Recently we performed complex Langevin simulations by adding a Lorentz invariant mass term as an IR regulator and found a (1+1)-dimensional expanding spacetime with a Lorentzian signature emerging dynamically at late times when the fermionic contribution is omitted. Here we find that this is merely an artifact of the Lorentz boosts by showing that the spontaneous breaking of rotational symmetry is eliminated if one chooses a Lorentz frame appropriately. On the other hand, when we include the fermionic contribution, we find some evidence suggesting the emergence of a smooth (3+1)-dimensional expanding Lorentzian spacetime.

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arXiv2024

Determination of the CP restoration temperature at $θ=π$ in 4D SU(2) Yang-Mills theory through simulations at imaginary $θ$

The 't Hooft anomaly matching condition provides constraints on the phase structure at $θ=π$ in 4D SU($N$) Yang-Mills theory. In particular, assuming that the theory is confined and the CP symmetry is spontaneously broken at low temperature, it cannot be restored below the deconfining temperature at $θ=π$. Here we investigate the CP restoration at $θ=π$ in the 4D SU(2) case and provide numerical evidence that the CP restoration occurs at a temperature higher than the deconfining temperature unlike the known results in the large-$N$ limit, where the CP restoration occurs precisely at the deconfining temperature. The severe sign problem at $θ=π$ is avoided by focusing on the tail of the topological charge distribution at $θ=0$, which can be probed by performing simulations at imaginary $θ$. By analytic continuation with respect to $θ$, we obtain the topological charge at real $θ$.

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arXiv2023

The emergence of expanding space-time in the Lorentzian type IIB matrix model with a novel regularization

The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. However, it was recently found that a Euclidean space-time appears in the conventional large-$N$ limit. In this work, we study the model with a Lorentz invariant mass term which can be considered as an IR regulator. By performing complex Langevin simulations to overcome the sign problem, we observe the emergence of expanding space-time with Lorentzian signature.

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arXiv2023

Numerical studies on the finite-temperature CP restoration in 4D SU(N) gauge theory at $θ=π$

Recent studies on the 't Hooft anomaly matching condition have suggested a nontrivial phase structure in 4D SU($N$) gauge theory at $θ=π$. In the large-$N$ limit, it has been found that CP symmetry at $θ=π$ is broken in the confined phase, while it restores in the deconfined phase, which is indeed one of the possible scenarios. However, at small $N$, one may find other situations that are consistent with the consequence of the anomaly matching condition. Here we investigate this issue for $N=2$ by direct lattice calculations. The crucial point to note is that the CP restoration can be probed by the sudden change of the tail of the topological charge distribution at $θ=0$, which can be seen by simulating the theory at imaginary $θ$ without the sign problem. Our results suggest that the CP restoration at $θ=π$ occurs at temperature higher than the deconfining temperature unlike the situation in the large-$N$ limit.

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arXiv2022

The emergence of expanding space-time in a novel large-$N$ limit of the Lorentzian type IIB matrix model

The Lorentzian type IIB matrix model is a promising candidate for a non-perturbative formulation of superstring theory. However, it was found recently that a Euclidean space-time appears in the conventional large-$N$ limit. In this work, we add a Lorentz invariant mass term to the original model and consider a limit, in which the coefficient of the mass term vanishes at large $N$. By performing complex Langevin simulations to overcome the sign problem, we observe the emergence of expanding space-time with the Lorentzian signature.

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arXiv2022

Progress in the numerical studies of the type IIB matrix model

The type IIB matrix model, also known as the IKKT model, has been proposed as a promising candidate for a non-perturbative formulation of superstring theory. Based on this proposal, various attempts have been made to explain how our four-dimensional space-time can emerge dynamically from superstring theory. In this article, we review the progress in numerical studies on the type IIB matrix model. We particularly focus on the most recent results for the Euclidean and Lorentzian versions, which are obtained using the complex Langevin method to overcome the sign problem. We also review the earlier results obtained using conventional Monte Carlo methods and clarify the relationship among different calculations.

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arXiv2022

Complex Langevin studies of the emergent space-time in the type IIB matrix model

The type IIB matrix model has been proposed as a non-perturbative definition of superstring theory since 1996. We study a simplified model that describes the late time behavior of the type IIB matrix model non-perturbatively using Monte Carlo methods, and we use the complex Langevin method to overcome the sign problem. We investigate a scenario where the space-time signature changes dynamically from Euclidean at early times to Lorentzian at late times. We discuss the possibility of the emergence of the (3+1)D expanding universe.

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arXiv2021

Relationship between the Euclidean and Lorentzian versions of the type IIB matrix model

The type IIB matrix model was proposed as a non-perturbative formulation of superstring theory in 1996. We simulate a model that describes the late time behavior of the IIB matrix model by applying the complex Langevin method to overcome the sign problem. We clarify the relationship between the Euclidean and the Lorentzian versions of the type IIB matrix model in a recently discovered phase. By introducing a constraint, we obtain a model where the spacetime metric is Euclidean at early times, whereas it {\it dynamically} becomes Lorentzian at late times.

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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 new technique for solving the freezing problem in the complex Langevin simulation of 4D SU(2) gauge theory with a theta term

We apply the complex Langevin method (CLM) to overcome the sign problem in 4D SU(2) gauge theory with a theta term extending our previous work on the 2D U(1) case. The topology freezing problem can be solved by using open boundary conditions in all spatial directions, and the criterion for justifying the CLM is satisfied even for large $θ$ as far as the lattice spacing is sufficiently small. However, we find that the CP symmetry at $θ=π$ remains to be broken explicitly even in the continuum and infinite-volume limits due to the chosen boundary conditions. In particular, this prevents us from investigating the interesting phase structures suggested by the 't Hooft anomaly matching condition. We also try the so-called subvolume method, which turns out to have a similar problem. We therefore discuss a new technique within the CLM, which enables us to circumvent the topology freezing problem without changing the boundary conditions.

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