QCD phase diagram and the critical point

The recent progress in understanding the QCD phase diagram and the physics of the QCD critical point is reviewed.Comment: 18 pages, 11 figures, for proceedings of "Finite Density QCD at Nara", July 200

Conformal Window of Gauge Theories with Four-Fermion Interactions and Ideal Walking

We investigate the effects of four-fermion interactions on the phase diagram of strongly interacting theories for any representation as function of the number of colors and flavors. We show that the conformal window, for any representation, shrinks with respect to the case in which the four-fermion interactions are neglected. The anomalous dimension of the mass increases beyond the unity value at the lower boundary of the new conformal window. We plot the new phase diagram which can be used, together with the information about the anomalous dimension, to propose ideal models of walking technicolor. We discover that when the extended technicolor sector, responsible for giving masses to the standard model fermions, is sufficiently strongly coupled the technicolor theory, in isolation, must have an infrared fixed point for the full model to be phenomenologically viable. Using the new phase diagram we show that the simplest one family and minimal walking technicolor models are the archetypes of models of dynamical electroweak symmetry breaking. Our predictions can be verified via first principle lattice simulations.Comment: RevTeX4, 22 pages, 16 figure

Transition temperature and the equation of state from lattice QCD, Wuppertal-Budapest results

The QCD transition is studied on lattices up to $N_t=16$. The chiral condensate is presented as a function of the temperature, and the corresponding transition temperature is extracted. The equation of state is determined on lattices with $N_t=6,8,10$ and at some temperature values with $N_t=12$. The pressure and the trace anomaly are presented as functions of the temperature in the range 100 ...1000 MeV . Using the same configurations we determine the continuum extrapolated phase diagram of QCD on the $\mu-T$ plane for small to moderate chemical potentials. Two transition lines are defined with two quantities, the chiral condensate and the strange quark number susceptibility.Comment: 4 pages, 2 figures, Proceedings for Quark Matter 201

Electroweak phase transition by four dimensional simulations

The finite temperature phase transition in the SU(2)-Higgs model at a Higgs boson mass $M_H \simeq 35$ GeV is studied in numerical simulations on four dimensional lattices with time-like extensions up to $L_t=5$. $T_c/M_H$ is extrapolated to the continuum limit and a comparison with the perturbative prediction is made. A one-loop calculation to the coupling anisotropies of the SU(2)-Higgs model on lattices with asymmetric lattice spacings is presented. Our numerical simulations show that the above perturbative result is applicable in the phenomenologically interesting parameter region.Comment: 3 pages, Latex, 3 figures, Talk presented at LATTICE96(electroweak) by Z. Fodo

On the multiplicity of arrangements of congruent zones on the sphere

Consider an arrangement of $n$ congruent zones on the $d$-dimensional unit sphere $S^{d-1}$, where a zone is the intersection of an origin symmetric Euclidean plank with $S^{d-1}$. We prove that, for sufficiently large $n$, it is possible to arrange $n$ congruent zones of suitable width on $S^{d-1}$ such that no point belongs to more than a constant number of zones, where the constant depends only on the dimension and the width of the zones. Furthermore, we also show that it is possible to cover $S^{d-1}$ by $n$ congruent zones such that each point of $S^{d-1}$ belongs to at most $A_d\ln n$ zones, where the $A_d$ is a constant that depends only on $d$. This extends the corresponding $3$-dimensional result of Frankl, Nagy and Nasz\'odi (2016). Moreover, we also examine coverings of $S^{d-1}$ with congruent zones under the condition that each point of the sphere belongs to the interior of at most $d-1$ zones

Chiral properties of SU(3) sextet fermions

SU(3) gauge theory with overlap fermions in the 2-index symmetric (sextet) and fundamental representations is considered. A priori it is not known what the pattern of chiral symmetry breaking is in a higher dimensional representation although the general expectation is that if two representations are both complex, the breaking pattern will be the same. This expectation is verified for the sextet at N_f = 0 in several exact zero mode sectors. It is shown that if the volume is large enough the same random matrix ensemble describes both the sextet and fundamental Dirac eigenvalues. The number of zero modes for the sextet increases approximately 5-fold relative to the fundamental in accordance with the index theorem for small lattice spacing but zero modes which do not correspond to integer topological charge do exist at larger lattice spacings. The zero mode number dependence of the random matrix model predictions correctly match the simulations in each sector and each representation.Comment: 38 pages (12 pages text and gazillion tables/figures), minor modification, references adde