New approach to the complex-action problem and its application to a nonperturbative study of superstring theory

Abstract. Current status of theoretical researches on the QCD phase diagram at finite temperature and baryon chemical potential is reviewed with special emphasis on the origin of various phases and their symmetry breaking patterns. Topics include; quark deconfinement, chiral symmetry restoration, order of the phase transitions, QCD critical point(s), colour superconductivity, various inhomogeneous states and implications from QCD-like theories.

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“…(The plaquette P or energy E is useful as well [129,130,131].) The density of states in this case reads…”

Section: Lattice Qcd At Low Baryon Densitymentioning

confidence: 99%

The phase diagram of dense QCD

Fukushima¹,

Hatsuda²

2010

Rep. Prog. Phys.

901

945

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“…In particular, totally reduced models [9] (the D = 0 case) have been studied in refs. [10,11,12,13,14]. The complex Pfaffian, which appears from integration over the fermionic matrices, causes a technical obstacle in numerical simulation, which may be overcome by a new method proposed in ref.…”

mentioning

confidence: 99%

“…The complex Pfaffian, which appears from integration over the fermionic matrices, causes a technical obstacle in numerical simulation, which may be overcome by a new method proposed in ref. [14]. In fact, the phase of the Pfaffian is speculated to induce the spontaneous breaking of SO(10) symmetry down to SO(4), a scenario for the dynamical generation of four-dimensional space-time [15] suggested from the Gaussian expansion method [16].…”

mentioning

confidence: 99%

Monte Carlo Studies of Supersymmetric Matrix Quantum Mechanics with Sixteen Supercharges at Finite Temperature

et al. 2008

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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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“…It has been recognized from those works that the fermionic part of the action plays a crucial role [5,6,7,8,9,10,11].…”

Section: Introductionmentioning

confidence: 99%

“…[27]. The improved Taylor expansion (ITE), as it is referred, opened a way toward more general applications that 1 A novel technique called the factorization method is proposed to resolve the complex action problem in the Monte Carlo simulations [11,12]. incorporate quadratic and other types of interactions.…”

Section: Introductionmentioning

confidence: 99%

Improved perturbation method and its application to the IIB matrix model

Aoyama

Shibusa

2006

Nuclear Physics B

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We present a new scheme for extracting approximate values in "the improved perturbation method", which is a sort of resummation technique capable of evaluating a series outside the radius of convergence.We employ the distribution profile of the series that is weighted by nth-order derivatives with respect to the artificially introduced parameters. By those weightings the distribution becomes more sensitive to the "plateau" structure in which the consistency condition of the method is satisfied. The scheme works effectively even in such cases that the system involves many parameters. We also propose that this scheme has to be applied to each observable separately and be analyzed comprehensively.We apply this scheme to the analysis of the IIB matrix model by the improved perturbation method obtained up to eighth order of perturbation in the former works. We consider here the possibility of spontaneous breakdown of Lorentz symmetry, and evaluate the free energy and the anisotropy of space-time extent. In the present analysis, we find an SO(10)-symmetric vacuum besides the SO(4)-and SO(7)-symmetric vacua that have been observed. It is also found that there are two distinct SO(4)-symmetric vacua that have almost the same value of free energy but the extent of space-time is different. From the approximate values of free energy, we conclude that the SO(4)-symmetric vacua are most preferred among those three types of vacua.

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New approach to the complex-action problem and its application to a nonperturbative study of superstring theory

Cited by 110 publications

References 26 publications

The phase diagram of dense QCD

The phase diagram of dense QCD

Monte Carlo Studies of Supersymmetric Matrix Quantum Mechanics with Sixteen Supercharges at Finite Temperature

Improved perturbation method and its application to the IIB matrix model

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