A Study of the Complex Action Problem in a Simple Model for Dynamical Compactification in Superstring Theory Using the Factorization Method

The IIB matrix model proposes a mechanism for dynamically generating four dimensional space--time in string theory by spontaneous breaking of the ten dimensional rotational symmetry $\textrm{SO}(10)$. Calculations using the Gaussian expansion method (GEM) lend support to this conjecture. We study a simple $\textrm{SO}(4)$ invariant matrix model using Monte Carlo simulations and we confirm that its rotational symmetry breaks down, showing that lower dimensional configurations dominate the path integral. The model has a strong complex action problem and the calculations were made possible by the use of the factorization method on the density of states $\rho_n(x)$ of properly normalized eigenvalues $\tilde\lambda_n$ of the space--time moment of inertia tensor. We study scaling properties of the factorized terms of $\rho_n(x)$ and we find them in agreement with simple scaling arguments. These can be used in the finite size scaling extrapolation and in the study of the region of configuration space obscured by the large fluctuations of the phase. The computed values of $\tilde\lambda_n$ are in reasonable agreement with GEM calculations and a numerical method for comparing the free energy of the corresponding ansatze is proposed and tested.Comment: 7 pages, 4 figures, Talk presented at the XXVIII International Symposium on Lattice Field Theory, Lattice2010, Villasimius, Italy, June 201

A general approach to the sign problem - the factorization method with multiple observables

The sign problem is a notorious problem, which occurs in Monte Carlo simulations of a system with the partition function whose integrand is not real positive. The basic idea of the factorization method applied on such a system is to control some observables in order to determine and sample efficiently the region of configuration space which gives important contribution to the partition function. We argue that it is crucial to choose appropriately the set of the observables to be controlled in order for the method to work successfully in a general system. This is demonstrated by an explicit example, in which it turns out to be necessary to control more than one observables. Extrapolation to large system size is possible due to the nice scaling properties of the factorized functions, and known results obtained by an analytic method are shown to be consistently reproduced.Comment: 6 pages, 3 figures, (v2) references added (v3) Sections IV, V and VI improved, final version accepted by PR

The Area Law in Matrix Models for Large N QCD Strings

We study the question whether matrix models obtained in the zero volume limit of 4d Yang-Mills theories can describe large N QCD strings. The matrix model we use is a variant of the Eguchi-Kawai model in terms of Hermitian matrices, but without any twists or quenching. This model was originally proposed as a toy model of the IIB matrix model. In contrast to common expectations, we do observe the area law for Wilson loops in a significant range of scale of the loop area. Numerical simulations show that this range is stable as N increases up to 768, which strongly suggests that it persists in the large N limit. Hence the equivalence to QCD strings may hold for length scales inside a finite regime.Comment: 12 pages, 4 figure

Production of 92Nb, 92Mo, and 146Sm in the gamma-process in SNIa

The knowledge of the production of extinct radioactivities like 92Nb and 146Sm by photodisintegration processes in ccSN and SNIa models is essential for interpreting abundances in meteoritic material and for Galactic Chemical Evolution (GCE). The 92Mo/92Nb and 146Sm/144Sm ratios provide constraints for GCE and production sites. We present results for SNIa with emphasis on nuclear uncertainties.Comment: 6 pages, 4 figures, Proceedings of the 13th Symposium on Nuclei in the Cosmos (NIC XIII), July 2014, Debrecen, Hungar

The Factorization Method for Simulating Systems With a Complex Action

We propose a method for Monte Carlo simulations of systems with a complex action. The method has the advantages of being in principle applicable to any such system and provides a solution to the overlap problem. We apply it in random matrix theory of finite density QCD where we compare with analytic results. In this model we find non--commutativity of the limits $\mu\to 0$ and $N\to\infty$ which could be of relevance in QCD at finite density.Comment: Talk by K.N.A. at Confinement 2003, Tokyo, July 2003, 5 pages, 4 figures, ws-procs9x6.cl

Monte Carlo Studies of the Dimensionally Reduced 4d SU(N) Super Yang-Mills Theory

We simulate a supersymmetric matrix model obtained from dimensional reduction of 4d SU(N) super Yang-Mills theory. The model is well defined for finite N and it is found that the large N limit obtained by keeping g^2 N fixed gives rise to well defined operators which represent string amplitudes. The space-time structure which arises dynamically from the eigenvalues of the bosonic matrices is discussed, as well as the effect of supersymmetry on the dynamical properties of the model. Eguchi-Kawai equivalence of this model to ordinary gauge theory does hold within a finite range of scale. We report on new simulations of the bosonic model for N up to 768 that confirm this property, which comes as a surprise since no quenching or twist is introduced.Comment: 6 pages, 7 figures, Talk presented by K.N.A. at the HEP 2000 Annual Workshop of the Hellenic Society for the Study of High Energy Physics at the University of Ioannina. References added, minor correction