The four LEP collaborations, ALEPH, DELPHI, L3 and OPAL, have searched for the neutral Higgs bosons which are predicted by the Minimal Supersymmetric Standard Model (MSSM). The data of the four collaborations are statistically combined and examined for their consistency with the background hypothesis and with a possible Higgs boson signal. The combined LEP data show no significant excess of events which would indicate the production of Higgs bosons. The search results are used to set upper bounds on the cross-sections of various Higgs-like event topologies. The results are interpreted within the MSSM in a number of "benchmark" models, including CP-conserving and CP-violating scenarios. These interpretations lead in all cases to large exclusions in the MSSM parameter space. Absolute limits are set on the parameter tan β and, in some scenarios, on the masses of neutral Higgs bosons.

In this Report, QCD results obtained from a study of hadronic event structure in high energy e+e− interactions with the L3 detector are presented. The operation of the LEP collider at many different collision energies from 91 to 209 GeV offers a unique opportunity to test QCD by measuring the energy dependence of different observables. The main results concern the measurement of the strong coupling constant, alpha_s, from hadronic event shapes and the\ud study of effects of soft gluon coherence in charged particle multiplicity and momentum distributions

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Single- and multi-photon events with missing energy are selected in 619 pb−1 of data collected by the L3 detector at LEP at centre-of-mass energies between 189 GeV and 209 GeV. The cross sections of the process e+e− → vv-bar gamma (gamma) are found to be in agreement with the Standard Model expectations, and the number of light neutrino species is determined, including lower energy data, to be N = 2.98 +/- 0.05 +/- 0.04.\ud Selection results are given in the form of tables which can be used to test future models involving single- and multi-photon signatures at LEP. These final states are also predicted by models with large extra dimensions and by several supersymmetric\ud models. No evidence for such models is found. Among others, lower limits between 1.5 TeV and 0.65 TeV are set, at 95% confidence level, on the new scale of gravity for the number of extra dimensions between 2 and 8

A short introduction is given on the functional renormalization group method, putting emphasis on its nonperturbative aspects. The method enables to find nontrivial fixed points in quantum field theoretic models which make them free from divergences and leads to the concept of asymptotic safety. It can be considered as a generalization of the asymptotic freedom which plays a key role in the perturbative renormalization. We summarize and give a short discussion of some important models, which are asymptotically safe such as the Gross-Neveu model, the nonlinear $\sigma$ model, the sine-Gordon model, and we consider the model of quantum Einstein gravity which seems to show asymptotic safety, too. We also give a detailed analysis of infrared behavior of such scalar models where a spontaneous symmetry breaking takes place. The deep infrared behaviorof the broken phase cannot be treated within the framework of perturbative calculations. We demonstrate that there exists an infrared fixed point in the broken phase whichcreates a new scaling regime there, however its structure is hidden by the singularity of the renormalization group equations. The theory spaces of these models show several similar properties, namely the models have the same phase and fixed point structure. The quantum Einstein gravity also exhibits similarities when considering the global aspects of its theory space since the appearing two phases there show analogies with the symmetric and the broken phases of the scalar models. These results be nicely uncovered by the functional renormalization group method.Comment: 34 pages, 21 figures. Based on the talk presented at the Theoretical Physics School on Quantum Gravity, Szeged, Hungary, 27-31 August 2012. Final version, to appear in Annals of Physic

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The renormalization group flow is presented for the two-dimensional sine-Gordon model within the framework of the functional renormalization group method by including the wave-function renormalization constant. The Kosterlitz-Thouless-Berezinski type phase structure is recovered as the interpolating scaling law between two competing IR attractive area of the global renormalization group flow.

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