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Register a new userLattice effective potential of massless $(lambdaPhi^4)_4$: `triviality and spontaneous symmetry breaking
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We present a precise lattice computation of the slope of the effective potential for massless $(lambdaPhi^4)_4$ theory in the region of bare parameters indicated by the Brahms analysis of lattice data. Our results confirm the existence on the lattice of a remarkable phase of $(lambdaPhi^4)_4$ where Spontaneous Symmetry Breaking is generated through ``dimensional transmutation. The resulting effective potential shows no evidence for residual self-interaction effects of the shifted `Higgs field $h(x)=Phi(x)-langlePhirangle$, as predicted by ``triviality, and cannot be reproduced in perturbation theory. Accordingly the mass of the Higgs particle, by itself, does not represent a measure of any observable interaction.
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We compute numerically the effective potential for the $(lambda Phi^4)_4$ theory on the lattice. Three different methods were used to determine the critical bare mass for the chosen bare coupling value. Two different methods for obtaining the effective potential were used as a control on the results. We compare our numerical results with three theoretical descriptions. Our lattice data are in quite good agreement with the ``Triviality and Spontaneous Symmetry Breaking picture.
Interacting quantum scalar field theories in $dS_Dtimes M_d$ spacetime can be reduced to Euclidean field theories in $M_d$ space in the vicinity of $I_+$ infinity of $dS_D$ spacetime. Using this non-perturbative mapping, we analyze the critical behavior of Euclidean $lambdaphi_4^4$ theory in the symmetric phase and find the asymptotic behavior $beta(lambda)sim lambda$ of the beta function at strong coupling. Scaling violating contributions to the beta function are also estimated in this regime.
A formulation of $mathcal{N} = 2$ supersymmetric Yang-Mills theory with a spacetime-dependent gauge coupling allows to study the breaking of conformal symmetry at the quantum level. The theory has an energy-momentum tensor that is only conserved if an equation of motion for the coupling is imposed. It admits non-trivial solitons, among which the Wu-Yang monopole that can be regularized and turns out to be massless. On the other hand, the ordinary BPS monopole is only a solution in the large $N_c$ limit.
Using the well-known low-energy effective Lagrangian of QCD --valid for small (non-vanishing) quark masses and a large number of colors-- we study in detail the regions of parameter space where $CP$ is spontaneously broken/unbroken for a vacuum angle $theta= pi$. In the $CP$-broken region there are first order phase transitions as one crosses $theta=pi$, while on the (hyper)surface separating the two regions, there are second order phase transitions signaled by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a divergent QCD topological susceptibility. The second order point sits at the end of a first order line associated with the $CP$ spontaneous breaking, in the appropriate complex parameter plane. When the effective Lagrangian is extended by the inclusion of an axion these features of QCD imply that standard calculations of the axion potential have to be revised when the QCD parameters fall in the above mentioned $CP$-broken region, in spite of the fact that the axion solves the strong-$CP$ problem. These latter results could be of interest for axionic dark matter calculations if the topological susceptibility of pure Yang-Mills theory falls off sufficiently fast when temperature is increased towards the QCD deconfining transition.
We investigate non-linear extensions of the holographic soft wall model proposed by Karch, Katz, Son and Stephanov [1] including non-minimal couplings in the five-dimensional action. The non-minimal couplings bring a new parameter $a_0$ which controls the transition between spontaneous and explicit symmetry breaking near the limit of massless quarks (the chiral limit). In the physical region (positive quark mass), we show that above a critical value of the parameter $a_0$ the chiral condensate $langle bar{q} q rangle$ is finite in the chiral limit, signifying spontaneous chiral symmetry breaking. This result is supported by the lightest states arising in the spectrum of the pseudoscalar mesons, which become massless in the chiral limit and are therefore intrepreted as Nambu-Goldstone bosons. Moreover, the decay constants of the pseudoscalar mesons also support this conclusion, as well as the Gell-Mann-Oakes-Renner (GOR) relation satisfied by the lightest states. We also calculate the spectrum of scalar, vector, and axial-vector mesons with their corresponding decay constants. We describe the evolution of masses and decay constants with the increasing of the quark mass and for the physical mass we compare our results against available experimental data. Finally, we do not find instabilities in our model for the physical region (positive quark mass).
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