Dimensional reduction in QCD: Lessons from lower dimensions

In this contribution we present the results of a series of investigations of dimensional reduction, applied to SU(3) gauge theory in 2 + 1 dimensions. We review earlier results, present a new reduced model with Z(3) symmetry, and discuss the results of numerical simulations of this model.Comment: 10 pages, Talk given at Workshop on Finite Density QCD, Nara Japan 10-12 Jul 200

Z(3) Symmetric Dimensional Reduction of (2+1)D QCD

Here we present a candidate for a Z(3)-symmetric reduced action for the description of the (2+1)D SU(3) gauge theoryComment: 2 pages, Statistical QCD pro

Three dimensional finite temperature SU(3) gauge theory in the confined region and the string picture

We determine the correlation between Polyakov loops in three dimensional SU(3) gauge theory in the confined region at finite temperature. For this purpose we perform lattice calculations for the number of steps in the temperature direction equal to six. This is expected to be in the scaling region of the lattice theory. We compare the results to the bosonic string model. The agreement is very good for temperatures T<0.7T_c, where T_c is the critical temperature. In the region 0.7T_c<T<T_c we enter the critical region, where the critical properties of the correlations are fixed by universality to be those of the two dimensional three state Potts model. Nevertheless, by calculating the critical lattice coupling, we show that the ratio of the critical temperature to the square root of the zero temperature string tension, where the latter is taken from the literature, remains very near to the string model prediction.Comment: 11 pages, 1 figure, 1 tabl

Critical Behaviour of the 3d Gross-Neveu and Higgs-Yukawa Models

We measure the critical exponents of the three dimensional Gross-Neveu model with two four-component fermions. The exponents are inferred from the scaling behaviour of observables on different lattice sizes. We also calculate the exponents, through a second order epsilon-expansion around 4d, for the three dimensional Higgs-Yukawa model, which is expected to be in the same universality class and we find that the exponents agree. We conclude that the equivalence of the two models remains valid in 3d at fixed small N_f values.Comment: 14 Latex pages 8 PSfigures included at the end,BI-TP-93/31,AZPH-TH/93-19,SPhT 93/0

Dimensional reduction and a Z(3) symmetric model

We present first results from a numerical investigation of a Z(3) symmetric model based on dimensional reduction.Comment: Talk presented at XXI International Symposium on Lattice Field Theory lattice2003(Non-zero temperature and density

QCD with Adjoint Scalars in 2D: Properties in the Colourless Scalar Sector

We present a numerical study of an SU(3) gauged 2D model for adjoint scalar fields, defined by dimensional reduction of pure gauge QCD in (2+1)D at high temperature. In the symmetric phase of its global Z_2 symmetry, two colourless boundstates, even and odd under Z_2, are identified. Their respective contributions (poles) in correlation functions of local composite operators A_n of degree n=2p and 2p+1 in the scalar fields (p=1,2) fulfill factorization. The contributions of two particle states (cuts) are detected. Their size agrees with estimates based on a meanfield-like decomposition of the p=2 operators into polynomials in p=1 operators. No sizable signal in any A_n correlation can be attributed to 1/n times a Debye screening length associated with n elementary fields. These results are quantitatively consistent with the picture of scalar ``matter'' fields confined within colourless boundstates whose residual ``strong'' interactions are very weak.Comment: 27 pages, improved presentation of results and some references added, as accepted by Nucl. Phys.

Screening Masses in Dimensionally Reduced (2+1)D Gauge Theory

We discuss the screening masses and residue factorisation of the SU(3) (2+1)D theory in the dimensional reduction formalism. The phase structure of the reduced model is also investigated.Comment: 3 pages, Lattice 2001(gaugetheories

A matter of time: Implicit acquisition of recursive sequence structures

A dominant hypothesis in empirical research on the evolution of language is the following: the fundamental difference between animal and human communication systems is captured by the distinction between regular and more complex non-regular grammars. Studies reporting successful artificial grammar learning of nested recursive structures and imaging studies of the same have methodological shortcomings since they typically allow explicit problem solving strategies and this has been shown to account for the learning effect in subsequent behavioral studies. The present study overcomes these shortcomings by using subtle violations of agreement structure in a preference classification task. In contrast to the studies conducted so far, we use an implicit learning paradigm, allowing the time needed for both abstraction processes and consolidation to take place. Our results demonstrate robust implicit learning of recursively embedded structures (context-free grammar) and recursive structures with cross-dependencies (context-sensitive grammar) in an artificial grammar learning task spanning 9 days. Keywords: Implicit artificial grammar learning; centre embedded; cross-dependency; implicit learning; context-sensitive grammar; context-free grammar; regular grammar; non-regular gramma

Wild Pfister forms over Henselian fields, K-theory, and conic division algebras

The epicenter of this paper concerns Pfister quadratic forms over a field $F$ with a Henselian discrete valuation. All characteristics are considered but we focus on the most complicated case where the residue field has characteristic 2 but $F$ does not. We also prove results about round quadratic forms, composition algebras, generalizations of composition algebras we call conic algebras, and central simple associative symbol algebras. Finally we give relationships between these objects and Kato's filtration on the Milnor $K$-groups of $F$