Factorization Method for Simulating QCD at Finite Density

We propose a new method for simulating QCD at finite density. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The so-called overlap problem is completely eliminated by the use of constrained simulations. We test this method in a Random Matrix Theory for finite density QCD, where we are able to reproduce the exact results for the quark number density.Comment: 7 pages, 1 figure, Talk given at 2002 International Workshop on Strong Coupling Gauge Theories and Effective Field Theories (SCGT 02), Nagoya, Japan, 10-13 Dec 200

On Existence of Nontrivial Fixed Points in Large NN Gauge Theory in More than Four Dimensions

Inspired by a possible relation between large $N$ gauge theory and string theory, we search for nontrivial fixed points in large $N$ gauge theory in more than four dimensions. We study large $N$ gauge theory through Monte Carlo simulation of the twisted Eguchi-Kawai model in six dimensions as well as in four dimensions. The phase diagram of the system with the two coupling constants which correspond to the standard plaquette action and the adjoint term has been explored.Comment: 10 pages, latex, 6 figure

A New Method for Simulating QCD at Finite Density

We propose a new method for simulating QCD at finite density, where interesting phases such as the color superconductivity phase is conjectured to appear. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The so-called overlap problem is completely eliminated by the use of constrained simulations. We test this method in a Random Matrix Theory for finite density QCD, where we are able to reproduce the exact results for the quark number density. The achieved system size is large enough to extract the thermodynamic limit. Our results provide a clear understanding of how the expected first order phase transition is induced by the imaginary part of the action. We also discuss the noncommutativity of the zero chemical potential limit and the thermodynamic limit, which is relevant to recent Monte Carlo studies at small chemical potential.Comment: 12 pages, 6 figures, Invited talk at International Symposium on Color Confinement and Hadrons in Quantum Chromodynamics (Confinement 2003), Tokyo, Japan, 21-24 July 200

Recent developments in the type IIB matrix model

We review recent developments in the type IIB matrix model, which was conjectured to be a nonperturbative formulation of superstring theory. In the first part we review the recent results for the Euclidean model, which suggest that SO(10) symmetry is spontaneously broken. In the second part we review the recent results for the Lorentzian model. In particular, we discuss Monte Carlo results, which suggest that (3+1)-dimensional expanding universe emerges dynamically. We also discuss some results suggesting the emergence of exponential expansion and the power-law expansion at later times. The behaviors at much later times are studied by the classical equation of motion. We discuss a solution representing 3d expanding space, which suggests a possible solution to the cosmological constant problem.Comment: 10 pages, 5 figures, talk given at the Workshop on Noncommutative Field Theory and Gravity, Corfu Summer Institute, Corfu, Greece, 8-15 September 2013, to appear in Fortsch. Phy

On the Definition of the Partition Function in Quantum Regge Calculus

We argue that the definition of the partition function used recently to demonstrate the failure of Regge calculus is wrong. In fact, in the one-dimensional case, we show that there is a more natural definition, with which one can reproduce the correct results.Comment: 9 pages, LaTe

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 $\theta$ goes to infinity. We discuss whether the ``planar dominance'' occurs also in the case where $\theta$ 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 $\phi^3$ theory, and confirm that nonplanar diagrams after renormalization do vanish in the above limit.Comment: 14 pages, 7 Figure

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.Comment: 4 pages, 2 figures; (v2) analysis in section 3 improve