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N. Kawamoto

Publications and source records attributed to N. Kawamoto.

15 recordsLinked to original sources
arXiv2026

Range convergence and sharp one-arm asymptotics for the critical percolation cluster in high dimensions

For critical Bernoulli bond percolation on $\Z^d$ in the high-dimensional regime, we prove that the rescaled empirical measure of the cluster of the origin converges, in a suitable $\sigma$-finite sense, to the total occupation measure of super-Brownian motion. Combined with a uniform lower mass bound for the critical cluster with respect to the extrinsic (Euclidean) metric, which we also prove and which is of independent interest, the measure convergence further yields the convergence of the rescaled cluster as a compact set, in the Hausdorff metric. As a consequence, we are able to obtain the sharp one-arm asymptotics $r^2\,\bP(0\leftrightarrow \partial B_r)\to \theta_1\in(0,\infty)$, hence refining a result of Kozma and Nachmias.

math.PR↗
arXiv2012

QCD critical point in the strong coupling lattice QCD and during black hole formation

We discuss the QCD phase diagram from two different point of view. We first investigate the phase diagram structure in the strong coupling lattice QCD with Polyakov loop effects, and show that the the chiral and Z_{N_c} deconfinement transition boundaries deviate at finite mu as suggested from large N_c arguments. Next we discuss the possibility to probe the QCD critical point during prompt black hole formation processes. The thermodynamical evolution during the black hole formation would result in quark matter formation, and the critical point in isospin asymmetric matter may be swept. (T,mu_B) region probed in heavy-ion collisions and the black hole formation processes covers most of the critical point locations predicted in recent lattice Monte-Carlo simulations and chiral effective models.

nucl-th↗
arXiv2008

Brown-Rho Scaling in the Strong Coupling Lattice QCD

We examine the Brown-Rho scaling for meson masses in the strong coupling limit of lattice QCD with one species of staggered fermion. Analytical expression of meson masses is derived at finite temperature and chemical potential. We find that meson masses are approximately proportional to the equilibrium value of the chiral condensate, which evolves as a function of temperature and chemical potential.

nucl-th↗
arXiv2007

Lattice supersymmetry in 1D with two supercharges

A consistent formulation of a fully supersymmetric theory on the lattice has been a long standing challenge. In recent years there has been a renewed interest on this problem with different approaches. At the basis of the formulation we present in the following there is the Dirac-Kahler twisting procedure, which was proposed in the continuum for a number of theories, including N=4 SUSY in four dimensions. Following the formalism developed in recent papers, an exact supersymmetric theory with two supercharges on a one dimensional lattice is realized using a matrix-based model. The matrix structure is obtained from the shift and clock matrices used in two dimensional non-commutative field theories. The matrix structure reproduces on a one dimensional lattice the expected modified Leibniz rule. Recent claims of inconsistency of the formalism are discussed and shown not to be relevant.

hep-lat↗
arXiv2007

Strong coupling limit/region of lattice QCD

We study the phase diagram of quark matter and nuclear properties based on the strong coupling expansion of lattice QCD. Both of baryon and finite coupling correction are found to have effects to extend the hadron phase to a larger mu direction relative to Tc. In a chiral RMF model with logarithmic sigma potential derived in the strong coupling limit of lattice QCD, we can avoid the chiral collapse and normal and hypernuclei properties are well described.

nucl-th↗
arXiv2007

Phase diagram at finite temperature and quark density in the strong coupling region of lattice QCD for color SU(3)

We study the phase diagram of quark matter at finite temperature (T) and chemical potential (mu) in the strong coupling region of lattice QCD for color SU(3). Baryon has effects to extend the hadron phase to a larger mu direction relative to Tc at low temperatures in the strong coupling limit. With the 1/g^2 corrections, Tc is found to decrease rapidly as g decreases, and the shape of the phase diagram becomes closer to that expected in the real world.

hep-lat↗
arXiv2006

Phase diagram at finite temperature and quark density in the strong coupling limit of lattice QCD for color SU(3)

We study the phase diagram of quark matter at finite temperature (T) and finite chemical potential (mu) in the strong coupling limit of lattice QCD for color SU(3). We derive an analytical expression of the effective free energy as a function of T and mu, including baryon effects. The finite temperature effects are evaluated by integrating over the temporal link variable exactly in the Polyakov gauge with anti-periodic boundary condition for fermions. The obtained phase diagram shows the first order phase transition at low temperatures and the second order phase transition at high temperatures separated by the tri-critical point in the chiral limit. Baryon has effects to reduce the effective free energy and to extend the hadron phase to a larger mu direction at low temperatures.

hep-lat↗
arXiv2003

Dirac-Kaehler fermion with noncommutative differential forms on a lattice

Noncommutativity between a differential form and a function allows us to define differential operator satisfying Leibniz's rule on a lattice. We propose a new associative Clifford product defined on the lattice by introducing the noncommutative differential forms. We show that this Clifford product naturally leads to the Dirac-Kähler fermion on the lattice.

hep-lat↗
arXiv2000

Recursive sampling simulations of 3D gravity coupled to scalar fermions

We study numerically the phase structure of a model of 3D gravity interacting with scalar fermions. We measure the 3D counterpart of the "string" susceptibility exponent as a function of the inverse Newton coupling $α$. We show that there are two phases separated by a critical point around $α_c \simeq 2$. The numerical results support the hypothesis that the phase structures of 3D and 2D simplicial gravity are qualitatively similar, the inverse Newton coupling in 3D playing the role of the central charge of matter in 2D.

hep-lat↗
arXiv1999

Lattice Chern-Simons Gravity via Ponzano-Regge Model

We propose a lattice version of Chern-Simons gravity and show that the partition function coincides with Ponzano-Regge model and the action leads to the Chern-Simons gravity in the continuum limit. The action is explicitly constructed by lattice dreibein and spin connection and is shown to be invariant under lattice local Lorentz transformation and gauge diffeomorphism. The action includes the constraint which can be interpreted as a gauge fixing condition of the lattice gauge diffeomorphism.

hep-th↗
arXiv1998

Quantization of Even-Dimensional Actions of Chern-Simons Form with Infinite Reducibility

We investigate the quantization of even-dimensional topological actions of Chern-Simons form which were proposed previously. We quantize the actions by Lagrangian and Hamiltonian formulations {à} la Batalin, Fradkin and Vilkovisky. The models turn out to be infinitely reducible and thus we need infinite number of ghosts and antighosts. The minimal actions of Lagrangian formulation which satisfy the master equation of Batalin and Vilkovisky have the same Chern-Simons form as the starting classical actions. In the Hamiltonian formulation we have used the formulation of cohomological perturbation and explicitly shown that the gauge-fixed actions of both formulations coincide even though the classical action breaks Dirac's regularity condition. We find an interesting relation that the BRST charge of Hamiltonian formulation is the odd-dimensional fermionic counterpart of the topological action of Chern-Simons form. Although the quantization of two dimensional models which include both bosonic and fermionic gauge fields are investigated in detail, it is straightforward to extend the quantization into arbitrary even dimensions. This completes the quantization of previously proposed topological gravities in two and four dimensions.

hep-th↗
arXiv1997

Intrinsic Geometric Structure of c=-2 Quantum Gravity

We couple c=-2 matter to 2-dimensional gravity within the framework of dynamical triangulations. We use a very fast algorithm, special to the c=-2 case, in order to test scaling of correlation functions defined in terms of geodesic distance and we determine the fractal dimension d_H with high accuracy. We find d_H=3.58(4), consistent with a prediction coming from the study of diffusion in the context of Liouville theory, and that the quantum space-time possesses the same fractal properties at all distance scales similarly to the case of pure gravity.

hep-lat↗
arXiv1997

The quantum space-time of c=-2 gravity

We study the fractal structure of space-time of two-dimensional quantum gravity coupled to c=-2 conformal matter by means of computer simulations. We find that the intrinsic Hausdorff dimension d_H = 3.58 +/- 0.04. This result supports the conjecture d_H = -2 α_1/α_{-1}, where α_n is the gravitational dressing exponent of a spinless primary field of conformal weight (n+1,n+1), and it disfavours the alternative prediction d_H = 2/|γ|. On the other hand ~ r^{2n} for n>1 with good accuracy, i.e. the boundary length l has an anomalous dimension relative to the area of the surface.

hep-lat↗
arXiv1996

Quantum geometry of topological gravity

We study a c=-2 conformal field theory coupled to two-dimensional quantum gravity by means of dynamical triangulations. We define the geodesic distance r on the triangulated surface with N triangles, and show that dim[r^{d_H}]= dim[N], where the fractal dimension d_H = 3.58 +/- 0.04. This result lends support to the conjecture d_H = -2α_1/α_{-1}, where α_{-n} is the gravitational dressing exponent of a spin-less primary field of conformal weight (n+1,n+1), and it disfavors the alternative prediction d_H = -2/γ_{str}. On the other hand, we find dim[l] = dim[r^2] with good accuracy, where l is the length of one of the boundaries of a circle with (geodesic) radius r, i.e. the length l has an anomalous dimension relative to the area of the surface. It is further shown that the spectral dimension d_s = 1.980 +/- 0.014 for the ensemble of (triangulated) manifolds used. The results are derived using finite size scaling and a very efficient recursive sampling technique known previously to work well for c=-2.

hep-lat↗