arXiv subjects

Fumihiko Toyoda

Publications and source records attributed to Fumihiko Toyoda.

At least 19 recordsLinked to original sources

arXiv2024

Chiral condensate in a holographic dilute nuclear matter

We study chiral condensate in cold nuclear matter on the basis of holographic theory, which would be dual to a baryon system in quantum chromodynamics (QCD) in the confinement phase. Our model is a holographic model based on the D$3$/D$7$ branes. The magnitude of the chiral condensate obtained in our model is found to gradually increase with increasing baryon density $n$ within the range of the dilute nucleon gas, $n<1$, where our model is available. This is a result for the chiral condensate in the holographic model as a function of $n$, which can be compared to the chiral perturbation theory.

hep-th↗

arXiv2023

Instability of holographic cold compact stars with a color superconducting core

We study a holographic model of quantum chromodynamics, which can describe a color superconductor and a dilute nucleon gas phase. The two phases are adjoined in the phase diagram at a critical value of the chemical potential. In other words, a first-order transition from the ordinary nucleon gas to the color superconductor is found by increasing the chemical potential. This model is suitable to investigate the possibility of a cold compact star with a color superconducting core. The equation of state of the star is given by the holographic model considered in this article, and we find that it is impossible in the present model to find a hybrid star of nuclear matter and the color superconductor core through the relation of mass and radius of the star by solving the Tolman-Oppenheimer-Volkoff equations. Several other interesting implications are given by using the equation of state.

hep-th↗

arXiv2021

Stiff equation of state for a holographic nuclear matter as instanton gas

In a holographic model, which was used to investigate the color superconducting phase of QCD, a dilute gas of instantons is introduced to study the nuclear matter. The free energy of the nuclear matter is computed as a function of the baryon chemical potential in the probe approximation. Then the equation of state is obtained at low temperature. Using the equation of state for the nuclear matter, the Tolman-Oppenheimer-Volkov equations for a cold compact star are solved. We find the mass-radius relation of the star, which is similar to the one for quark star. This similarity implies that the instanton gas given here is a kind of self-bound matter.

hep-th↗

arXiv2020

Extension to Imaginary Chemical Potential in a Holographic Model

We extend a bottom up holographic model, which has been used in studying the color superconductivity in QCD, to the imaginary chemical potential ($μ_I$) region, and the phase diagram is studied on the $μ_I$-temperature (T) plane. The analysis is performed for the case of the probe approximation and for the background where the back reaction from the flavor fermions are taken into account. For both cases, we could find the expected Roberge-Weiss (RW) transitions. In the case of the back-reacted solution, a bound of the color number $N_c$ is found to produce the RW periodicity. It is given as $N_c\geq 1.2$. Furthermore, we could assure the validity of this extended model by comparing our result with the one of the lattice QCD near $μ_I=0$.

hep-th↗

arXiv2019

Color Superconductivity in Holographic SYM Theory

A holographic bottom-up model used in studying the superconducting system is applied to search for the color superconducting phase of supersymmetric Yang-Mills theory. We apply the probe analysis of this model to the supersymmetric Yang-Mills theory in both the confinement and deconfinement phases. In this analysis, we find the color superconductivity in both phases when the baryon chemical potential exceeds a certain critical value. This result implies that, above the critical chemical potential, a color non-singlet diquark operator, namely the Cooper pair, has its vacuum expectation value even in the confinement phase. In order to improve this peculiar situation, we proceed the analysis by taking account of the full back-reaction from the probe. As a result, the color superconducting phase, which is observed in the probe approximation, disappears in both the confinement and deconfinement phases when parameters of the theory are set within their reasonable values.

hep-th↗

arXiv2018

Tunneling in Quantum Cosmology and Holographic SYM theory

We study the time evolution of early universe which is developed by a cosmological constant $Λ_4$ and supersymmetric Yang-Mills (SYM) fields in the Friedmann-Robertson-Walker (FRW) space-time. The renormalized vacuum expectation value of energy-momentum tensor of the SYM theory is obtained in a holographic way. It includes a radiation of the SYM field, parametrized as $C$. The evolution is controlled by this radiation $C$ and the cosmological constant $Λ_4$. For positive $Λ_4$, an inflationary solution is obtained at late time. When $C$ is added, the quantum mechanical situation at early time is fairly changed. Here we perform the early time analysis in terms of two different approaches, (i) the Wheeler-DeWitt equation and (ii) Lorentzian path-integral with the Picard-Lefschetz method by introducing an effective action. The results of two methods are compared.

hep-th↗

arXiv2017

Holographic Cosmology and Phase Transitions of SYM theory

We study the time development of strongly coupled ${\cal N}=4$ supersymmetric Yang Mills (SYM) theory on cosmological Friedmann-Robertson-Walker (FRW) backgrounds via the AdS/CFT correspondence. We implement the cosmological background as a boundary metric fulfilling the Friedmann equation with a four-dimensional cosmological constant and a dark radiation term. We analyze the dual bulk solution of the type IIB supergravity and find that the time-dependence of the FRW background strongly influences the dynamical properties of the SYM theory. We in particular find a phase transition between a confined and a deconfined phase. We also argue that some cosmological solutions could be related to the inflationary scenario.

hep-th↗

arXiv2015

Chiral Symmetry of SYM theory in hyperbolic space at finite temperature

We study a holographic gauge theory living in the AdS$_4$ space-time at finite temperature. The gravity dual is obtained as a solution of the type IIB superstring theory with two free parameters, which correspond to four dimensional (4D) cosmological constant ($λ$) and the dark radiation ($C$) respectively. The theory studied here is in confining and chiral symmetry broken phase for $λ<0$ and small $C$. When $C$ is increased, the transition to the deconfinement phase has been observed at a finite value of $C/|λ|$. It is shown here that the chiral symmetry is still broken for a finite range of $C/|λ|$ in the deconfinement phase. In other words, the chiral phase transition occurs at a larger value of $C/|λ|$ than the one of the deconfinement transition. So there is a parameter range of a new deconfinement phase with broken chiral symmetry. In order to study the properties of this phase, we performed a holographic analysis for the meson mass-spectrum and other quantities in terms of the probe D7 brane. The results of this analysis are compared with a linear sigma model. Furthermore, the entanglement entropy is examined to search for a sign of the chiral phase trantion. Several comments are given for these analyses.

hep-th↗

arXiv2014

Glueball instability and thermalization driven by dark radiation

We study glueballs in the holographic gauge theories living in a curved space-time. The dual bulk is obtained as a solution of the type IIB superstring theory with two parameters, which correspond to four dimensional (4D) cosmological constant $λ$ and the dark radiation $C$ respectively. The theory is in the confining phase for $λ<0$ and small $C$, then we observe stable glueball states in this theory. However, the stability of the glueball states is lost when the density of the dark radiation ($C$) increases and exceeds a critical point. Above this point, the dark radiation works as the heat bath of the Yang-Mills theory since the event horizon appears. Thus the system is thermalized, and the theory is in a finite temperature deconfinement phase, namely in the QGP phase. We observe this transition process through the glueball spectra which varies dramatically with $C$. We also examined the entanglement entropy of the system to find a clue of this phase transition and the role of the dark radiation $C$ in the entanglement entropy.

hep-th↗

arXiv2014

Holographic cold nuclear matter and neutron star

We have previously found a new phase of cold nuclear matter based on a holographic gauge theory, where baryons are introduced as instanton gas in the probe D8/$\overline{\rm D8}$ branes. In our model, we could obtain the equation of state (EOS) of our nuclear matter by introducing fermi momentum. Then, here we apply this model to the neutron star and study its mass and radius by solving the Tolman-Oppenheimer-Volkoff (TOV) equations in terms of the EOS given here. We give some comments for our holographic model from a viewpoint of the other field theoretical approaches.

hep-th↗

arXiv2013

Holographic cold nuclear matter as dilute instanton gas

We study cold nuclear matter based on the holographic gauge theory, where baryons are introduced as the instantons in the probe D8/D8 branes according to the Sakai-Sugimoto model. Within a dilute gas approximation of instantons, we search for the stable states via the variational method and fix the instanton size. We find the first order phase transition from the vacuum to the nuclear matter phase as we increase the chemical potential. At the critical chemical potential, we could see a jump in the baryon density from zero to a finite definite value. While the size of the baryon in the nuclear matter is rather small compared to the nucleus near the transition point, where the charge density is also small, it increases with the baryon density. Those behaviors obtained here are discussed by relating them to the force between baryons.

hep-th↗

arXiv2012

Holographic Glueballs and Infrared Wall Driven by Dilaton

We study glueballs in the holographic gauge theories, supersymmetric and non-super symmetric cases, which are given by the type IIB superstring solutions with non-trivial dilaton. In both cases, the dilaton reflects the condensate of the gauge field strength, $ $, which is responsible to the linear confining potential between the quark and anti-quark. Then we could see the meson spectra. On the other hand, the glueball spectra are not found in the supersymmetric case. We need a sharp wall, which corresponds to an infrared cutoff, in order to obtain the glueballs. In the non-supersymmetric case, the quantized glueballs are actually observed due to the existence of such a wall driven by the dilaton. The strings and D-branes introduced as building blocks of hadrons are pushed out by this wall, and we could see the Regge behavior of the higher spin meson and glueball states. We find that the slope of the glueball trajectory is half of the flavor meson's one. As for the low spin glueballs, they are studied by solving the fluctuations of the bulk fields, and their discrete spectra are shown.

hep-th↗

arXiv2011

Holographic Approach to Regge Trajectory and Rotating D5 brane

We study the Regge trajectories of holographic mesons and baryons by considering rotating strings and D5 brane, which is introduced as the baryon vertex. Our model is based on the type IIB superstring theory with the background of asymptotic $AdS_5\times S^5$. This background is dual to a confining supersymmetric Yang-Mills theory (SYM) with gauge condensate, $ $, which determines the tension of the linear potential between the quark and anti-quark. Then the slope of the meson trajectory ($α'_{M}$) is given by this condensate as $α'_{M}=1/\sqrt{π }$ at large spin $J$. This relation is compatible with the other theoretical results and experiments. For the baryon, we show the importance of spinning baryon vertex to obtain a Regge slope compatible with the one of $N$ and $Δ$ series. In both cases, mesons and baryons, the trajectories are shifted to large mass side with the same slope for increasing current quark mass.

hep-th↗

arXiv2010

Stability of D brane Anti D brane Systems in Confining Gauge Theories

We study the stability of a special form of D brane embedding which is regarded as a bound state of D$_n$ and anti-D$_n$-brane embedded in a 10D supergravity background which is dual to a confining gauge theory. For D5 branes with $U(1)$ flux, their bound state configuration can be regarded as the baryonium vertex. For D branes of $n=6$ and 8 without the $U(1)$ flux, their bound states have been used to introduce flavor quarks in the dual supersymmetric Yang-Mills theory. In any case, it would be important to assure that they are free from tachyon instability. For all these cases, we could show their stability with respect to this point.

hep-th↗

arXiv2010

Holographic Penta and Hepta Quark State in Confining Gauge Theories

We study a new embedding solutions of D5 brane in an asymptotic AdS${}_5\times S^5$ space-time, which is dual to a confining $SU(N_c)$ gauge theory. The D5 brane is wrapped on $S^5$ as in the case of the vertex of holographic baryon. However, the solution given here is different from the usual baryon vertex in the point that it couples to $k$-anti-quarks and $N_c+k$ quarks on the opposite two points of $S^5$, the north and south poles, respectively. The total quark number of this state is preserved as $N_c$ when minus one is assigned to anti-quark, then it forms a color singlet like the baryon. However, this includes anti-quarks and quarks, whose number is larger than that of the baryon. When we set as $N_c=3$, we find the so called penta and hepta-quark states. We study the dynamical properties of these states by solving the vertex and string configurations for such states. The mass spectra of these states and the tension of the stretched vertex are estimated, and they are compared with that of the baryon.

hep-th↗

arXiv2009

Baryonium in Confining Gauge Theories

We show a new class of embedding solutions of D5 brane, which wraps on $S^5$ in the AdS${}_5\times S^5$ space-time and contains fundamental strings as U(1) flux to form a baryon vertex. The new solution given here is different from the baryon vertex since it consists of two same side (north or south) poles of $S^5$ as cusps, which are put on different points in our three dimensional space. This implies that the same magnitude of electric displacement exists at each cusp, but their orientations are opposite due to the flux number conservation. This configuration is therefore regarded as a D5-$\bar{D5}$ bound state, and we propose this as the vertex of a baryonium state, which is made of a baryon and an anti-baryon. By attaching quarks and anti-quarks to the two cusps of this vertex, it is possible to construct a realistic baryonium.

hep-th↗

arXiv2008

Multi-quark baryons and color screening at finite temperature

We study baryons in SU(N) gauge theories at finite temperature according to the gauge/string correspondence based on IIB string theory. The baryon is constructed out of D5 brane and $N$ fundamental strings to form a color singlet $N$-quark bound state. At finite temperature and in the deconfining phase, we could find $k(<N)$-quark ``baryons''. Thermal properties of such $k$-quark baryons and also of the $N$-quark baryon are examined. We study the temperature dependence of color screening distance and Debye length of the baryon of $k$-quark and $N$-quark. We also estimate the melting temperature, where the baryons decay into quarks and gluons completely.

hep-th↗

arXiv2008

String Junction Model, Cluster Hypothesis, Penta-Quark Baryon and Tetra-Quark Meson

Thirty years ago we proposed string junction model of hadrons and examined structure and reaction of hadrons including exotic ones. Mass $m$ of exotic hadrons of light quarks is roughly given by $m \sim N_J\cdot m_B$, where $N_J$ is the total number of junctions and $m_B \sim 1$ GeV is the ordinary light baryon mass. In this paper we introduce "cluster hypothesis" into the model by which mass of a complex hadron is given by the sum of masses of clusters composing it. The hypothesis guarantees the established picture that mass differences of hadrons of the same string junction structure are due to those of the constituent quarks. A candidate for penta-quark baryon $Θ$(1530 MeV, $S=+1)$ including a strange anti-quark ${\sb}$ and that for tetra-quark meson $Z^+$(4430 MeV) recently reported by the Bell collaboration are examined in parallel. $Θ$ is considered to have non-strange partners, which are lighter by the mass difference $Δ_s$ between strange and non-strange quarks. Mass of such light penta-quark baryons with $N_J=3$ is expected to be about 3 GeV. Several parameters of the model are estimated such as mass of junction of $m_J \sim O(10)$ MeV. While mass of light tetra-quark meson with $N_J=2$ is expected to be about 2 GeV, $Z^+$(4430 MeV) containing $(u,c,{\db},{\cb})$ gives a clue to determine some parameters of the model, e.g., inter-junction string energy $m_{IJ}$.

hep-ph↗