arXiv subjects

B. Petersson

Publications and source records attributed to B. Petersson.

At least 37 records · Page 2Linked to original sources

arXiv2001

Geometry of Reduced Supersymmetric 4D Yang-Mills Integrals

We study numerically the geometric properties of reduced supersymmetric non-compact SU(N) Yang-Mills integrals in D=4 dimensions, for N = 2,3, ..., 8. We show that in the range of large eigenvalues of the matrices A^mu, the original D-dimensional rotational symmetry is spontaneously broken and the dominating field configurations become one-dimensional, as anticipated by studies of the underlying surface theory. We also discuss possible implications of our results for the IKKT model.

hep-lat↗

arXiv2001

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.

hep-lat↗

arXiv2000

Large N limit of the IKKT matrix model

Using the dynamical triangulation approach we perform a numerical study of a supersymmetric random surface model that corresponds to the large N limit of the four-dimensional version of the IKKT matrix model. We show that the addition of fermionic degrees of freedom suppresses the spiky world-sheet configurations that are responsible for the pathological behaviour of the purely bosonic model. We observe that the distribution of the gyration radius has a power-like tail p(R) ~ R^{-2.4}. We check numerically that when the number of fermionic degrees of freedom is not susy-balanced, p(R) grows with $R$ and the model is not well-defined. Numerical sampling of the configurations in the tail of the distribution shows that the bosonic degrees of freedom collapse to a one-dimensional tube with small transverse fluctuations. Assuming that the vertex positions can fluctuate independently within the tube, we give a theoretical argument which essentially explains the behaviour of p(R) in the different cases, in particular predicting p(R) ~ R^{-3} in the supersymmetric case. Extending the argument to six and ten dimensions, we predict p(R) ~ R^{-7} and p(R) ~ R^{-15}, respectively.

hep-lat↗

arXiv2000

High Temperature 3D QCD: Dimensional Reduction at Work

We investigate the three-dimensional SU(3) gauge theory at finite temperature in the framework of dimensional reduction. The large scale properties of this theory are expected to be conceptually more complicated than in four dimensions. The dimensionally reduced action is computed in closed analytical form. The resulting effective two-dimensional theory is studied numerically both in the electric and magnetic sector. We find that dimensional reduction works excellently down to temperatures of 1.5 times the deconfinement phase transition temperature and even on rather short length scales. We obtain strong evidence that for ${\rm QCD}_3$, even at high temperature the colour averaged potential is represented by the exchange of a single state, at variance with the usual Debye screening picture involving a pair of electric gluons.

hep-lat↗

arXiv1999

The Weak-Coupling Limit of 3D Simplicial Quantum Gravity

We investigate the weak-coupling limit, kappa going to infinity, of 3D simplicial gravity using Monte Carlo simulations and a Strong Coupling Expansion. With a suitable modification of the measure we observe a transition from a branched polymer to a crinkled phase. However, the intrinsic geometry of the latter appears similar to that of non-generic branched polymer, probable excluding the existence of a sensible continuum limit in this phase.

hep-lat↗

arXiv1998

The Weak-Coupling Limit of Simplicial Quantum Gravity

In the weak-coupling limit, kappa_0 going to infinity, the partition function of simplicial quantum gravity is dominated by an ensemble of triangulations with the ratio N_0/N_D close to the upper kinematic limit. For a combinatorial triangulation of the D--sphere this limit is 1/D. Defining an ensemble of maximal triangulations, i.e. triangulations that have the maximal possible number of vertices for a given volume, we investigate the properties of this ensemble in three dimensions using both Monte Carlo simulations and a strong-coupling expansion of the partition function, both for pure simplicial gravity and a with a suitable modified measure. For the latter we observe a continuous phase transition to a crinkled phase and we investigate the fractal properties of this phase.

hep-lat↗

arXiv1998

The Strong-Coupling Expansion in Simplicial Quantum Gravity

We construct the strong-coupling series in 4d simplicial quantum gravity up to volume 38. It is used to calculate estimates for the string susceptibility exponent gamma for various modifications of the theory. It provides a very efficient way to get a first view of the phase structure of the models.

hep-lat↗

arXiv1998

4d Simplicial Quantum Gravity: Matter Fields and the Corresponding Effective Action

Four-dimensional simplicial quantum gravity is modified either by coupling it to U(1) gauge fields or by introducing a measure weighted by the orders of the triangles. Strong coupling expansion and Monte Carlo simulations are used. Although the two modifications of the standard pure-gravity model are apparently very distinct, they produce strikingly similar results, as far as the geometry of random manifolds is concerned. In particular, for an appropriate choice of couplings, the branched polymer phase is replaced by a crinkled phase, characterized by the susceptibility exponent $γ< 0$ and the fractal dimension $d_H > 2$. The quasi-equivalence between the two models is exploited to get further insight into the extended phase diagram of the theory.

hep-lat↗

arXiv1997

4d Simplicial Quantum Gravity Interacting with Gauge Matter Fields

The effect of coupling non-compact $U(1)$ gauge fields to four dimensional simplicial quantum gravity is studied using strong coupling expansions and Monte Carlo simulations. For one gauge field the back-reaction of the matter on the geometry is weak. This changes, however, as more matter fields are introduced. For more than two gauge fields the degeneracy of random manifolds into branched polymers does not occur, and the branched polymer phase seems to be replaced by a new phase with a negative string susceptibility exponent $γ$ and fractal dimension $d_H \approx 4$.

hep-lat↗

arXiv1997

Beyond the c=1 Barrier in Two-Dimensional Quantum Gravity

We introduce a simple model of touching random surfaces, by adding a chemical potential rho for ``minimal necks'', and study this model numerically coupled to a Gaussian model in d-dimensions (for central charge c = d = 0, 1 and 2). For c <= 1, this model has a phase transition to branched polymers, for sufficiently large rho. For c = 2, however, the extensive simulations indicate that this transition is replaced by a cross-over behavior on finite lattices --- the model is always in the branched polymer phase. This supports recent speculations that, in 2d-gravity, the behavior observe in simulations for $c \leq 1$, is dominated by finite size effects, which are exponentially enhanced as c -> 1+.

hep-lat↗

arXiv1997

Universality of hypercubic random surfaces

We study universality properties of the Weingarten hyper-cubic random surfaces. Since a long time ago the model with a local restriction forbidding surface self-bendings has been thought to be in a different universality class from the unrestricted model defined on the full set of surfaces. We show that both models in fact belong to the same universality class with the entropy exponent gamma = 1/2 and differ by finite size effects which are much more pronounced in the restricted model.

hep-th↗

arXiv1997

Focusing on the Fixed Point of 4D Simplicial Gravity

Our earlier renormalization group analysis of simplicial gravity is extended. A high statistics study of the volume and coupling constant dependence of the cumulants of the node distribution is carried out. It appears that the phase transition of the theory is of first order, contrary to what is generally believed.

hep-lat↗

arXiv1996

Thermodynamics of Four-Flavour QCD with Improved Staggered Fermions

We have calculated the pressure and energy density in four-flavour QCD using improved fermion and gauge actions. We observe a strong reduction of finite cut-off effects in the high temperature regime, similar to what has been noted before for the SU(3) gauge theory. Calculations have been performed on $16^3\times 4$ and 16^4 lattices for two values of the quark mass, $ma = 0.05$ and 0.1. A calculation of the string tension at zero temperature yields a critical temperature $T_c/\sqrtσ = 0.407 \pm 0.010$ for the smaller quark mass value.

hep-lat↗

arXiv1996

Topology in 4D simplicial quantum gravity

We simulate 4d simplicial gravity for three topologis S4, S3xS1, (S1)^4 and show that the free energy for these three fixed topology ensembles is the same in the thermodynamic limit. We show, that the next-to-leading order corrections, at least away from the critical point, can be described by kinematic sources.

hep-lat↗

arXiv1996

An investigation of the 2D attractive Hubbard model

We present an investigation of the 2D attractive Hubbard model, considered as an effective model relevant to superconductivity in strongly interacting electron systems. We use both hybrid Monte Carlo simulations and existing hopping parameter expansions to explore the low temperature domain. The increaseof the static S-wave pair correlation with decreasing temperature is analyzed in terms of an expected Kosterlitz-Thouless superconducting transition. The evidence for this transition is weak: If it exists, its temperature is very low and depends weakly on the band filling near half filling. The number of unpaired electrons remains nearly constant with temperature at fixed attractive potential strength. In contrast, the static magnetic susceptibility decreases fast with temperature, and cannot be related only to pair formation. We introduce a method by which the Pade approximants of the existing series for the susceptibility give sensible results down to rather low temperature region, as shown by comparison with our numerical data.

cond-mat.str-el↗

arXiv1996

A Study of Finite Temperature Gauge Theory in (2+1) Dimensions

We determine the critical couplings and the critical exponents of the finite temperature transition in SU(2) and SU(3) pure gauge theory in (2+1) dimensions. We also measure Wilson loops at $T=0$ on a wide range of $β$ values using APE smearing to improve the signal. We extract the string tension $σ$ from a fit to large distances, including a string fluctuation term. With these two entities we calculate $T_c/\sqrtσ$.

hep-lat↗

arXiv1996

QCD Thermodynamics with Improved Actions

The thermodynamics of the SU(3) gauge theory has been analyzed with tree level and tadpole improved Symanzik actions. A comparison with the continuum extrapolated results for the standard Wilson action shows that improved actions lead to a drastic reduction of finite cut-off effects already on lattices with temporal extent $N_τ=4$. Results for the pressure, the critical temperature, surface tension and latent heat are presented. First results for the thermodynamics of four-flavour QCD with an improved staggered action are also presented. They indicate similarly large improvement factors for bulk thermodynamics.

hep-lat↗

arXiv1996

Appearence of Mother Universe and Singular Vertices in Random Geometries

We discuss a general mechanism that drives the phase transition in the canonical ensemble in models of random geometries. As an example we consider a solvable model of branched polymers where the transition leading from tree- to bush-like polymers relies on the occurrence of vertices with a large number of branches. The source of this transition is a combination of the constraint on the total number of branches in the canonical ensemble and a nonlinear one-vertex action. We argue that exactly the same mechanism, which we call constrained mean-field, plays the crucial role in the phase transition in 4d simplicial gravity and, when applied to the effective one-vertex action, explains the occurrence of both the mother universe and singular vertices at the transition point when the system enters the crumpled phase.

hep-lat↗