Konstantinos N. Anagnostopoulos

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

We present the first Monte Carlo results for supersymmetric matrix quantum mechanics with 16 supercharges at finite temperature. The recently proposed nonlattice 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 asymptotes at low temperature to a characteristic behavior for a deconfined theory, suggesting the absence of a phase transition. These results provide highly nontrivial evidence for the gauge-gravity duality.

Large N Dynamics of Dimensionally Reduced 4D SU(N) Super Yang-Mills Theory

We perform Monte Carlo simulations of a supersymmetric matrix model, which is obtained by dimensional reduction of 4D SU(N) super Yang-Mills theory. The model can be considered as a four-dimensional counterpart of the IIB matrix model. We extract the space-time structure represented by the eigenvalues of bosonic matrices. In particular we compare the large-N behavior of the space-time extent with the result obtained from a low-energy effective theory. We measure various Wilson loop correlators which represent string amplitudes and we observe a non-trivial universal scaling in N. We also observe that the Eguchi-Kawai equivalence to ordinary gauge theory does hold at least within a finite range of scale. Comparison with the results for the bosonic case clarifies the role of supersymmetry in the large-N dynamics. It does affect the multi-point correlators qualitatively, but the Eguchi-Kawai equivalence is observed even in the bosonic case.

Monte Carlo studies of the IIB matrix model at large N

The low-energy effective theory of the IIB matrix model developed by H. Aoki et al. is written down explicitly in terms of bosonic variables only. The effective theory is then studied by Monte Carlo simulations in order to investigate the possibility of a spontaneous breakdown of ten-dimensional Lorentz invariance. The imaginary part of the effective action, which causes the so-called sign problem in the simulation, is dropped by hand. The extent of the eigenvalue distribution of the bosonic matrices shows a power-law large-N behavior, consistent with a simple branched-polymer prediction. We observe, however, that the eigenvalue distribution becomes more and more isotropic in the ten-dimensional space-time as we increase N. This suggests that if the spontaneous breakdown of Lorentz invariance really occurs in the IIB matrix model, a crucial role must be played by the imaginary part of the effective action.

A linguistic multicriteria analysis system combining fuzzy sets theory, ideal and anti-ideal points for location site selection

Most multicriteria methods try to model human thinking and insert the results of this modelling into their procedures. Following this path, the proposed multicriteria approach first captures the imprecision and vagueness of data by using linguistic variables. At a second level, it utilises human processes of decision-making by creating decision rules and modelling them with functions used in fuzzy sets theory. This method also is compatible with the way fuzzy logic models and combines fuzzy propositions. The proposed method considers the ideal solution and the anti-ideal solution and assesses each alternative in terms of distance as well as similarity to the ideal solution and the anti-ideal solution. Distance and similarity measures for fuzzy numbers are used and their aggregation is guided by the decision rules in order to construct decision functions. Further, OWA operators with maximal entropy are used to aggregate across all criteria and determine the overall score of each alternative. It is shown that the proposed method presents flexibility in modelling the decision makers preferences and it is also appropriate and effective to handle multicriteria problems of considerable complexity.

A new perspective on matter coupling in two-dimensional gravity

We provide compelling evidence that a previously introduced model of non-perturbative 2d Lorentzian quantum gravity exhibits (two-dimensional) flat-space behaviour when coupled to Ising spins. The evidence comes from both a high-temperature expansion and from Monte Carlo simulations of the combined gravity-matter system. This weak-coupling behaviour lends further support to the conclusion that the Lorentzian model is a genuine alternative to Liouville quantum gravity in two dimensions, with a different, and much ‘smoother’ critical behaviour.

The factorization method for systems with a complex action. A test in Random Matrix Theory for finite density QCD

Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method can be applied to any system with a complex action, and it eliminates the so-called overlap problem completely. We test the new approach 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.

QUANTUM GEOMETRY OF 2D GRAVITY COUPLED TO UNITARY MATTER

Abstract We show that there exists a divergent correlation length in 2D quantum gravity for the matter fields close to the critical point provided one uses the invariant geodesic distance as the measure of distance. The corresponding reparameterization invariant two-point functions satisfy all scaling relations known from the ordinary theory of critical phenomena and the KPZ exponents are determined by the power-like fall-off of these two-point functions. The only difference compared to flat space is the appearance of a dynamically generated fractal dimension d h in the scaling relations. We analyze numerically the fractal properties of space-time for the Ising and three-states Potts model coupled to two-dimensional quantum gravity using finite size scaling as well as small distance scaling of invariant correlation functions. Our data are consistent with d h = 4, but we cannot rule out completely 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). We compute the moments 〈 L 〉 and the loop-length distribution function and show that the fractal properties associated with these observables are identical, with good accuracy, to the pure gravity case.

On the spontaneous breakdown of Lorentz symmetry in matrix models of superstrings

In string or M theories, the spontaneous breaking of 10D or 11D Lorentz symmetry is required to describe our space-time. A direct approach to this issue is provided by the type IIB matrix model. We study its 4D version, which corresponds to the zero volume limit of 4D super

Geometrical interpretation of the Knizhnik-Polyakov-Zamolodchikov exponents

\mathrm{SU}(N)

THE QUANTUM SPACE-TIME OF C = -2 GRAVITY

Yang-Mills theory. Based on the moment of inertia as a criterion, spontaneous symmetry breaking (SSB) seems to occur, so that only one extended direction remains, as first observed by Bialas and Burda et al. However, using Wilson loops as probes of space-time we do not observe any sign of SSB in Monte Carlo simulations where N is as large as 48. This agrees with an earlier observation that the phase of the fermionic integral, which is absent in the 4D model, should play a crucial role if SSB of Lorentz symmetry really occurs in the 10D type IIB matrix model.