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Asato Tsuchiya

Publications and source records attributed to Asato Tsuchiya.

At least 55 records · Page 3Linked to original sources
arXiv2017

A new method for probing the late-time dynamics in the Lorentzian type IIB matrix model

The type IIB matrix model has been investigated as a possible nonperturbative formulation of superstring theory. In particular, it was found by Monte Carlo simulation of the Lorentzian version that the 9-dimensional rotational symmetry of the spatial matrices is broken spontaneously to the 3-dimensional one after some "critical time". In this paper we develop a new simulation method based on the effective theory for the submatrices corresponding to the late time. Using this method, one can obtain the results for $N\times N$ matrices by simulating matrices typically of the size $O(\sqrt{N})$. We confirm the validity of this method and demonstrate its usefulness in simplified models.

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arXiv2017

A generalized volume law for entanglement entropy on the fuzzy sphere

We investigate entanglement entropy in a scalar field theory on the fuzzy sphere. The theory is realized by a matrix model. In our previous study, we confirmed that entanglement entropy in the free case is proportional to the square of the boundary area of a focused region. Here we argue that this behavior of entanglement entropy can be understood by the fact that the theory is regularized by matrices, and further examine the dependence of entanglement entropy on the matrix size. In the interacting case, by performing Monte Carlo simulations, we observe a transition from a generalized volume law, which is obtained by integrating the square of area law, to the square of area law.

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arXiv2017

Universality and the dynamical space-time dimensionality in the Lorentzian type IIB matrix model

The type IIB matrix model is one of the most promising candidates for a nonperturbative formulation of superstring theory. In particular, its Lorentzian version was shown to exhibit an interesting real-time dynamics such as the spontaneous breaking of the 9-dimensional rotational symmetry to the 3-dimensional one. This result, however, was obtained after regularizing the original matrix integration by introducing "infrared" cutoffs on the quadratic moments of the Hermitian matrices. In this paper, we generalize the form of the cutoffs in such a way that it involves an arbitrary power ($2p$) of the matrices. By performing Monte Carlo simulation of a simplified model, we find that the results become independent of $p$ and hence universal for $p \gtrsim 1.3$. For $p$ as large as 2.0, however, we find that large-$N$ scaling behaviors do not show up, and we cannot take a sensible large-$N$ limit. Thus we find that there is a certain range of $p$ in which a universal large-$N$ limit can be taken. Within this range of $p$, the dynamical space-time dimensionality turns out to be $(3+1)$, while for $p=2.0$, where we cannot take a sensible large-$N$ limit, we observe a (5+1)d structure.

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arXiv2016

Large-scale computation of the exponentially expanding universe in a simplified Lorentzian type IIB matrix model

The type IIB matrix model is a conjectured nonperturbative formulation of superstring theory. Recent studies on the Lorentzian version of the model have shown that only three out of nine spatial directions start to expand after some critical time. On the other hand, due to the unbounded action of the Lorentzian model, one has to introduce infrared (IR) cutoffs in order to make the partition function finite. In this work we investigate whether the effects of the IR cutoffs disappear in the infinite volume limit. For that purpose, we study a simplified model with large matrix size up to $N=256$ by Monte Carlo simulation. First we confirm the exponentially expanding behavior of the "universe". Then we generalize the form of the IR cutoffs by one parameter, and find that the results become universal in some region of the parameter. It is suggested that the effects of IR cutoffs disappear in this region, which is confirmed also from the studies of Schwinger-Dyson equations.

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arXiv2015

Entanglement entropy in scalar field theory on the fuzzy sphere

We study entanglement entropy on the fuzzy sphere. We calculate it in a scalar field theory on the fuzzy sphere, which is given by a matrix model. We use a method that is based on the replica method and applicable to interacting fields as well as free fields. For free fields, we obtain the results consistent with the previous study, which serves as a test of the validity of the method. For interacting fields, we perform Monte Carlo simulations at strong coupling and see a novel behavior of entanglement entropy.

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arXiv2015

Power-law expansion of the Universe from the bosonic Lorentzian type IIB matrix model

Recent studies on the Lorentzian version of the type IIB matrix model show that (3+1)D expanding universe emerges dynamically from (9+1)D space-time predicted by superstring theory. Here we study a bosonic matrix model obtained by omitting the fermionic matrices. With the adopted simplification and the usage of a large-scale parallel computer, we are able to perform Monte Carlo calculations with matrix size up to $N=512$, which is twenty times larger than that used previously for the studies of the original model. When the matrix size is larger than some critical value $N_{\rm c}\simeq 110$, we find that (3+1)D expanding universe emerges dynamically with a clear large-$N$ scaling property. Furthermore, at sufficiently late times, we observe a power-law behavior $t^{1/2}$ of the spatial extent with respect to time $t$, which is reminiscent of the expanding behavior of the Friedmann-Robertson-Walker universe in the radiation dominated era. We discuss possible implications of this result on the original model including fermionic matrices.

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arXiv2015

A renormalization group method for studying the early universe in the Lorentzian IIB matrix model

We propose a new method for studying the early universe in the Lorentzian version of the IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. This method is based on the idea of renormalization group, and it enables us to study the time-evolution of the universe for much longer time than in the previous work, which showed that the SO(9) rotational symmetry is spontaneously broken down to SO(3) after a "critical time". We demonstrate how this method works in a simplified model, which is expected to capture the behaviors of the original model when the space is not so large. In particular, we present clear evidence that the three-dimensional space expands exponentially after the critical time in this simplified model.

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arXiv2014

Realizing three generations of the Standard Model fermions in the type IIB matrix model

We discuss how the Standard Model particles appear from the type IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. In particular, we are concerned with a constructive definition of the theory, in which we start with finite-N matrices and take the large-N limit afterwards. In that case, it was pointed out recently that realizing chiral fermions in the model is more difficult than it had been thought from formal arguments at N=infinity and that introduction of a matrix version of the warp factor is necessary. Based on this new insight, we show that two generations of the Standard Model fermions can be realized by considering a rather generic configuration of fuzzy S^2 and fuzzy S^2 * S^2 in the extra dimensions. We also show that three generations can be obtained by squashing one of the S^2's that appear in the configuration. Chiral fermions appear at the intersections of the fuzzy manifolds with nontrivial Yukawa couplings to the Higgs field, which can be calculated from the overlap of their wave functions.

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arXiv2013

Direct test of the AdS/CFT correspondence by Monte Carlo studies of N=4 super Yang-Mills theory

We perform nonperturbative studies of N=4 super Yang-Mills theory by Monte Carlo simulation. In particular, we calculate the correlation functions of chiral primary operators to test the AdS/CFT correspondence. Our results agree with the predictions obtained from the AdS side that the SUSY non-renormalization property is obeyed by the three-point functions but \emph{not} by the four-point functions investigated in this paper. Instead of the lattice regularization, we use a novel regularization of the theory based on an equivalence in the large-N limit between the N=4 SU(N) theory on RxS^3 and a one-dimensional SU(N) gauge theory known as the plane-wave (BMN) matrix model. The equivalence extends the idea of large-N reduction to a curved space and, at the same time, overcomes the obstacle related to the center symmetry breaking. The adopted regularization preserves 16 SUSY, which is crucial in testing the AdS/CFT correspondence with the available computer resources. The only SUSY breaking effects, which come from the momentum cutoff $Λ$ in R direction, are made negligible by using sufficiently large $Λ$.

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arXiv2013

Realizing chiral fermions in the type IIB matrix model at finite N

We discuss how chiral fermions can appear in the type IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. In particular, we are concerned with a constructive definition of the theory, in which we start with a finite-N configuration and take the large-N limit later on. We point out that there exists a certain necessary condition which the structure of the extra dimensions should satisfy. As an example, we consider a previous proposal using intersecting branes and show that chiral fermions can indeed be realized in four dimensions by introducing a matrix counterpart of warped space-time. This is remarkable in view of the well-known difficulty in realizing chiral fermions in lattice gauge theory.

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arXiv2013

Monte Carlo studies on the expanding behavior of the early universe in the Lorentzian type IIB matrix model

The type IIB matrix model is a conjectured nonperturbative formulation of superstring theory. Recently the Lorentzian version of the model has been studied by Monte Carlo simulation, and it has been shown that only three out of nine spatial directions start to expand after a critical time. We extend this work by investigating the expanding behavior for much longer time. We find that the 3d space expands exponentially for some period of time, which may be interpreted as inflation. We also simulate a simplified model, which is expected to capture some qualitative features of the original model at much later times. We observe that the exponential expansion eventually changes into a power-law t^(1/2) behavior, which agrees with the expanding behavior of the Friedmann-Robertson-Walker (FRW) universe in the radiation dominated era.

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arXiv2012

Local field theory from the expanding universe at late times in the IIB matrix model

Recently we have shown that (3+1)-dimensional expanding universe appears dynamically and uniquely from the Lorentzian version of the IIB matrix model, which is considered as a nonperturbative formulation of superstring theory. Similarly, it is possible that the Standard Model appears uniquely at the electroweak scale from the same model at late times. In order to pursue such a possibility, we discuss how to derive the effective local field theory for the massless modes that appear at late times in the same formulation. As a concrete example, we consider the massless modes associated with the spontaneous breaking of (9+1)-dimensional Poincare symmetry and supersymmetry.

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arXiv2012

Late time behaviors of the expanding universe in the IIB matrix model

Recently we have studied the Lorentzian version of the IIB matrix model as a nonperturbative formulation of superstring theory. By Monte Carlo simulation, we have shown that the notion of time ---as well as space---emerges dynamically from this model, and that we can uniquely extract the real-time dynamics, which turned out to be rather surprising: after some "critical time", the SO(9) rotational symmetry of the nine-dimensional space is spontaneously broken down to SO(3) and the three-dimensional space starts to expand rapidly. In this paper, we study the same model based on the classical equations of motion, which are expected to be valid at later times. After providing a general prescription to solve the equations, we examine a class of solutions, which correspond to manifestly commutative space. In particular, we find a solution with an expanding behavior that naturally solves the cosmological constant problem.

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arXiv2012

Factorization of the Effective Action in the IIB Matrix Model

We study the low-energy effective action of the IIB matrix model in the derivative interpretation, where the diffeomorphism invariance is manifest and arbitrary manifolds are described by matrices. We show that it is expressed as a sum of terms, each of which is factorized into a product of diffeomorphism invariant action functionals: $S=\sum_{i}c_is_i+\sum_{i,j}c_{ij}s_is_j+\sum_{i,j,k}c_{ijk}s_is_js_k+\...$. Each action functional $s_i$ is an ordinary local action of the form $s_i=\int d^Dx\sqrt{-g} O_i(x)$, where $O_i(x)$ is a scalar operator. This is also true for the background consisting of block diagonal matrices. In this case, the effective action can be interpreted as describing a multiverse where the universes described by the blocks are connected by wormholes.

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arXiv2012

Expanding (3+1)-dimensional universe from a Lorentzian matrix model for superstring theory in (9+1)-dimensions

We reconsider the matrix model formulation of type IIB superstring theory in (9+1)-dimensional space-time. Unlike the previous proposal in which the Wick rotation was used to make the model well-defined, we regularize the Lorentzian model by introducing infrared cutoffs in both the spatial and temporal directions. Monte Carlo studies reveal that the two cutoffs can be removed in the large-N limit and that the theory thus obtained has no parameters other than one scale parameter. Moreover, we find that three out of nine spatial directions start to expand at some "critical time", after which the space has SO(3) symmetry instead of SO(9).

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arXiv2011

Testing the AdS/CFT correspondence by Monte Carlo calculation of BPS and non-BPS Wilson loops in 4d N=4 super-Yang-Mills theory

We test the AdS/CFT correspondence by calculating Wilson loops in N = 4 super Yang-Mills theory on R*S^3 in the planar limit. Our method is based on a novel large-N reduction, which reduces the problem to Monte Carlo calculations in the plane-wave matrix model or the BMN matrix model, which is a 1d gauge theory with 16 supercharges. By using the gauge-fixed momentumspace simulation, we obtain results respecting 16 supersymmetries. We report on the Monte Carlo results for the BPS circular Wilson loop, which reproduce the exact result up to strong coupling. As a future prospect, we calculate a track-shapedWilson loop from the gravity side, which shows that a clear test of the AdS/CFT for the non-BPS case is also feasible.

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arXiv2011

Expanding universe as a classical solution in the Lorentzian matrix model for nonperturbative superstring theory

Recently we have shown by Monte Carlo simulation that expanding (3+1)-dimensional universe appears dynamically from a Lorentzian matrix model for type IIB superstring theory in (9+1)-dimensions. The mechanism for the spontaneous breaking of rotational symmetry relies crucially on the noncommutative nature of the space. Here we study the classical equations of motion as a complementary approach. In particular, we find a unique class of SO(3) symmetric solutions, which exhibits the time-dependence compatible with the expanding universe. The space-space noncommutativity is exactly zero, whereas the space-time noncommutativity becomes significant only towards the end of the expansion. We interpret the Monte Carlo results and the classical solution as describing the behavior of the model at earlier time and at later time, respectively.

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