arXiv subjects

Jun Nishimura

Publications and source records attributed to Jun Nishimura.

At least 127 records · Page 7Linked to original sources

arXiv2008

The instability of intersecting fuzzy spheres

We discuss the classical and quantum stability of general configurations representing many fuzzy spheres in dimensionally reduced Yang-Mills-Chern-Simons models with and without supersymmetry. By performing one-loop perturbative calculations around such configurations, we find that intersecting fuzzy spheres are classically unstable in the class of models studied in this paper. We also discuss the large-N limit of the one-loop effective action as a function of the distance of fuzzy spheres. This shows, in particular, that concentric fuzzy spheres with different radii, which are identified with the 't Hooft-Polyakov monopoles, are perturbatively stable in the bosonic model and in the D=10 supersymmetric model.

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arXiv2008

Putting M theory on a computer

We propose a non-lattice simulation for studying supersymmetric matrix quantum mechanics in a non-perturbative manner. In particular, our method enables us to put M theory on a computer based on its matrix formulation proposed by Banks, Fischler, Shenker and Susskind. Here we present Monte Carlo results of the same matrix model but in a different parameter region, which corresponds to the 't Hooft large-N limit at finite temperature. In the strong coupling limit the model has a dual description in terms of the N D0-brane solution in 10d type IIA supergravity. Our results provide highly nontrivial evidences for the conjectured duality. In particular, the energy (and hence the entropy) of the non-extremal black hole has been reproduced by solving directly the strongly coupled dynamics of the D0-brane effective theory.

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arXiv2007

High temperature expansion in supersymmetric matrix quantum mechanics

We formulate the high temperature expansion in supersymmetric matrix quantum mechanics with 4, 8 and 16 supercharges. The models can be obtained by dimensionally reducing N=1 U(N) super Yang-Mills theory in D=4,6,10 to 1 dimension, respectively. While the non-zero frequency modes become weakly coupled at high temperature, the zero modes remain strongly coupled. We find, however, that the integration over the zero modes that remains after integrating out all the non-zero modes perturbatively, reduces to the evaluation of connected Green's functions in the bosonic IKKT model. We perform Monte Carlo simulation to compute these Green's functions, which are then used to obtain the coefficients of the high temperature expansion for various quantities up to the next-leading order. Our results nicely reproduce the asymptotic behaviors of the recent simulation results at finite temperature. In particular, the fermionic matrices, which decouple at the leading order, give rise to substantial effects at the next-leading order, reflecting finite temperature behaviors qualitatively different from the corresponding models without fermions.

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arXiv2007

Probability distribution of the index in gauge theory on 2d non-commutative geometry

We investigate the effects of non-commutative geometry on the topological aspects of gauge theory using a non-perturbative formulation based on the twisted reduced model. The configuration space is decomposed into topological sectors labeled by the index nu of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. We study the probability distribution of nu by Monte Carlo simulation of the U(1) gauge theory on 2d non-commutative space with periodic boundary conditions. In general the distribution is asymmetric under nu -> -nu, reflecting the parity violation due to non-commutative geometry. In the continuum and infinite-volume limits, however, the distribution turns out to be dominated by the topologically trivial sector. This conclusion is consistent with the instanton calculus in the continuum theory. However, it is in striking contrast to the known results in the commutative case obtained from lattice simulation, where the distribution is Gaussian in a finite volume, but the width diverges in the infinite-volume limit. We also calculate the average action in each topological sector, and provide deeper understanding of the observed phenomenon.

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arXiv2007

Simulation Results for U(1) Gauge Theory on Non-Commutative Spaces

We present numerical results for U(1) gauge theory in 2d and 4d spaces involving a non-commutative plane. Simulations are feasible thanks to a mapping of the non-commutative plane onto a twisted matrix model. In d=2 it was a long-standing issue if Wilson loops are (partially) invariant under area-preserving diffeomorphisms. We show that non-perturbatively this invariance breaks, including the subgroup SL(2,R). In both cases, d=2 and d=4, we extrapolate our results to the continuum and infinite volume by means of a Double Scaling Limit. In d=4 this limit leads to a phase with broken translation symmetry, which is not affected by the perturbatively known IR instability. Therefore the photon may survive in a non-commutative world.

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arXiv2007

Monte Carlo studies of supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature

We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with sixteen supercharges at finite temperature. The recently proposed non-lattice simulation enables us to include the effects of fermionic matrices in a transparent and reliable manner. The internal energy nicely interpolates the weak coupling behavior obtained by the high temperature expansion, and the strong coupling behavior predicted from the dual black hole geometry. The Polyakov line takes large values even at low temperature suggesting the absence of a phase transition in sharp contrast to the bosonic case. These results provide highly non-trivial evidences for the gauge/gravity duality.

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arXiv2007

Phase structure of matrix quantum mechanics at finite temperature

We study matrix quantum mechanics at finite temperature by Monte Carlo simulation. The model is obtained by dimensionally reducing 10d U(N) pure Yang-Mills theory to 1d. Following Aharony et al., one can view the same model as describing the high temperature regime of (1+1)d U(N) super Yang-Mills theory on a circle. In this interpretation an analog of the deconfinement transition was conjectured to be a continuation of the black-hole/black-string transition in the dual gravity theory. Our detailed analysis in the critical regime up to N=32 suggests the existence of the non-uniform phase, in which the eigenvalue distribution of the holonomy matrix is non-uniform but gapless. The transition to the gapped phase is of second order. The internal energy is constant (giving the ground state energy) in the uniform phase, and rises quadratically in the non-uniform phase, which implies that the transition between these two phases is of third order.

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arXiv2007

Non-lattice simulation for supersymmetric gauge theories in one dimension

Lattice simulation of supersymmetric gauge theories is not straightforward. In some cases the lack of manifest supersymmetry just necessitates cumbersome fine-tuning, but in the worse cases the chiral and/or Majorana nature of fermions makes it difficult to even formulate an appropriate lattice theory. We propose to circumvent all these problems inherent in the lattice approach by adopting a non-lattice approach in the case of one-dimensional supersymmetric gauge theories, which are important in the string/M theory context.

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arXiv2007

Exact fuzzy sphere thermodynamics in matrix quantum mechanics

We study thermodynamical properties of a fuzzy sphere in matrix quantum mechanics of the BFSS type including the Chern-Simons term. Various quantities are calculated to all orders in perturbation theory exploiting the one-loop saturation of the effective action in the large-N limit. The fuzzy sphere becomes unstable at sufficiently strong coupling, and the critical point is obtained explicitly as a function of the temperature. The whole phase diagram is investigated by Monte Carlo simulation. Above the critical point, we obtain perfect agreement with the all order results. In the region below the critical point, which is not accessible by perturbation theory, we observe the Hagedorn transition. In the high temperature limit our model is equivalent to a totally reduced model, and the relationship to previously known results is clarified.

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arXiv2007

Monte Carlo approach to nonperturbative strings -- demonstration in noncritical string theory

We show how Monte Carlo approach can be used to study the double scaling limit in matrix models. As an example, we study a solvable hermitian one-matrix model with the double-well potential, which has been identified recently as a dual description of noncritical string theory with worldsheet supersymmetry. This identification utilizes the nonperturbatively stable vacuum unlike its bosonic counterparts, and therefore it provides a complete constructive formulation of string theory. Our data with the matrix size ranging from 8 to 512 show a clear scaling behavior, which enables us to extract the double scaling limit accurately. The ``specific heat'' obtained in this way agrees nicely with the known result obtained by solving the Painleve-II equation with appropriate boundary conditions.

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arXiv2007

The index of the overlap Dirac operator on a discretized 2d non-commutative torus

The index, which is given in terms of the number of zero modes of the Dirac operator with definite chirality, plays a central role in various topological aspects of gauge theories. We investigate its properties in non-commutative geometry. As a simple example, we consider the U(1) gauge theory on a discretized 2d non-commutative torus, in which general classical solutions are known. For such backgrounds we calculate the index of the overlap Dirac operator satisfying the Ginsparg-Wilson relation. When the action is small, the topological charge defined by a naive discretization takes approximately integer values, and it agrees with the index as suggested by the index theorem. Under the same condition, the value of the index turns out to be a multiple of N, the size of the 2d lattice. By interpolating the classical solutions, we construct explicit configurations, for which the index is of order 1, but the action becomes of order N. Our results suggest that the probability of obtaining a non-zero index vanishes in the continuum limit, unlike the corresponding results in the commutative space.

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arXiv2006

A non-perturbative study of 4d U(1) non-commutative gauge theory -- the fate of one-loop instability

Recent perturbative studies show that in 4d non-commutative spaces, the trivial (classically stable) vacuum of gauge theories becomes unstable at the quantum level, unless one introduces sufficiently many fermionic degrees of freedom. This is due to a negative IR-singular term in the one-loop effective potential, which appears as a result of the UV/IR mixing. We study such a system non-perturbatively in the case of pure U(1) gauge theory in four dimensions, where two directions are non-commutative. Monte Carlo simulations are performed after mapping the regularized theory onto a U(N) lattice gauge theory in d=2. At intermediate coupling strength, we find a phase in which open Wilson lines acquire non-zero vacuum expectation values, which implies the spontaneous breakdown of translational invariance. In this phase, various physical quantities obey clear scaling behaviors in the continuum limit with a fixed non-commutativity parameter $θ$, which provides evidence for a possible continuum theory. The extent of the dynamically generated space in the non-commutative directions becomes finite in the above limit, and its dependence on $θ$ is evaluated explicitly. We also study the dispersion relation. In the weak coupling symmetric phase, it involves a negative IR-singular term, which is responsible for the observed phase transition. In the broken phase, it reveals the existence of the Nambu-Goldstone mode associated with the spontaneous symmetry breaking.

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arXiv2006

Dynamical aspects of the fuzzy CP$^{2}$ in the large $N$ reduced model with a cubic term

``Fuzzy CP^2'', which is a four-dimensional fuzzy manifold extension of the well-known fuzzy analogous to the fuzzy 2-sphere (S^2), appears as a classical solution in the dimensionally reduced 8d Yang-Mills model with a cubic term involving the structure constant of the SU(3) Lie algebra. Although the fuzzy S^2, which is also a classical solution of the same model, has actually smaller free energy than the fuzzy CP^2, Monte Carlo simulation shows that the fuzzy CP^2 is stable even nonperturbatively due to the suppression of tunneling effects at large N as far as the coefficient of the cubic term ($α$) is sufficiently large. As αis decreased, both the fuzzy CP$^2$ and the fuzzy S^2 collapse to a solid ball and the system is essentially described by the pure Yang-Mills model (α= 0). The corresponding transitions are of first order and the critical points can be understood analytically. The gauge group generated dynamically above the critical point turns out to be of rank one for both CP^2 and S^2 cases. Above the critical point, we also perform perturbative calculations for various quantities to all orders, taking advantage of the one-loop saturation of the effective action in the large-N limit. By extrapolating our Monte Carlo results to N=\infty, we find excellent agreement with the all order results.

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arXiv2006

Dynamical aspects of the plane-wave matrix model at finite temperature

We study dynamical aspects of the plane-wave matrix model at finite temperature. One-loop calculation around general classical vacua is performed using the background field method, and the integration over the gauge field moduli is carried out both analytically and numerically. In addition to the trivial vacuum, which corresponds to a single M5-brane at zero temperature, we consider general static fuzzy-sphere type configurations. They are all 1/2 BPS, and hence degenerate at zero temperature due to supersymmetry. This degeneracy is resolved, however, at finite temperature, and we identify the configuration that gives the smallest free energy at each temperature. The Hagedorn transition in each vacuum is studied by using the eigenvalue density method for the gauge field moduli, and the free energy as well as the Polyakov line is obtained analytically near the critical point. This reveals the existence of fuzzy sphere phases, which may correspond to the plasma-ball phases in N=4 SU(\infty) SYM on S^1 X S^3. We also perform Monte Carlo simulation to integrate over the gauge field moduli. While this confirms the validity of the analytic results near the critical point, it also shows that the trivial vacuum gives the smallest free energy throughout the high temperature regime.

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arXiv2006

Planar Dominance in Non-commutative Field Theories at Infinite External Momentum

In perturbative expansion of field theories on a non-commutative geometry, it is known that planar diagrams dominate when the non-commutativity parameter $θ$ goes to infinity. We discuss whether the ``planar dominance'' occurs also in the case where $θ$ is finite, but the external momentum goes to infinity instead. While this holds trivially at the one-loop level, it is not obvious at the two-loop level in particular in the presence of UV divergences. We perform explicit two-loop calculations in the six-dimensional $ϕ^3$ theory, and confirm that nonplanar diagrams after renormalization do vanish in the above limit.

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arXiv2005

Impact of supersymmetry on the nonperturbative dynamics of fuzzy spheres

We study a 4d supersymmetric matrix model with a cubic term, which incorporates fuzzy spheres as classical solutions, using Monte Carlo simulations and perturbative calculations. The fuzzy sphere in the supersymmetric model turns out to be always stable if the large-N limit is taken in such a way that various correlation functions scale. This is in striking contrast to analogous bosonic models, where the fuzzy sphere decays into the pure Yang-Mills vacuum due to quantum effects when the coefficient of the cubic term becomes smaller than a critical value. We also find that the power-law tail of the eigenvalue distribution, which exists in the supersymmetric model without the cubic term, disappears in the presence of the fuzzy sphere in the large-N limit. Coincident fuzzy spheres turn out to be unstable, which implies that the dynamically generated gauge group is U(1).

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arXiv2005

Perturbative versus nonperturbative dynamics of the fuzzy S^2*S^2

We study a matrix model with a cubic term, which incorporates both the fuzzy S^2*S^2 and the fuzzy S^2 as classical solutions. Both of the solutions decay into the vacuum of the pure Yang-Mills model (even in the large-N limit) when the coefficient of the cubic term is smaller than a critical value, but the large-N behavior of the critical point is different for the two solutions. The results above the critical point are nicely reproduced by the all order calculations in perturbation theory. By comparing the free energy, we find that the true vacuum is given either by the fuzzy S^2 or by the ``pure Yang-Mills vacuum'' depending on the coupling constant. In Monte Carlo simulation we do observe a decay of the fuzzy S^2*S^2 into the fuzzy S^2 at moderate N, but the decay probability seems to be suppressed at large N. The above results, together with our previous results for the fuzzy CP^2, reveal certain universality in the large-N dynamics of four-dimensional fuzzy manifolds realized in a matrix model with a cubic term.

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arXiv2005

Perturbative dynamics of fuzzy spheres at large N

We clarify some peculiar aspects of the perturbative expansion around a classical fuzzy-sphere solution in matrix models with a cubic term. While the effective action in the large-N limit is saturated at the one-loop level, we find that the ``one-loop dominance'' does not hold for generic observables due to one-particle reducible diagrams. However, we may exploit the one-loop dominance for the effective action and obtain various observables to all orders from one-loop calculation by simply shifting the center of expansion to the ``quantum solution'', which extremizes the effective action. We confirm the validity of this method by comparison with the direct two-loop calculation and with Monte Carlo results in the 3d Yang-Mills-Chern-Simons matrix model. From the all order result we find that the perturbative expansion has a finite radius of convergence.

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