Physical Tuning and Naturalness

We present a radically new proposal for the solution of the naturalness/hierarchy problem, where the fine-tuning of the Higgs mass finds its physical explanation and the well-known multiplicative renormalization of the usual perturbative approach emerges as an IR property of the non-perturbative running of the mass.Comment: 7 pages, 4 figure

Renormalization Group in Quantum Mechanics

We establish the renormalization group equation for the running action in the context of a one quantum particle system. This equation is deduced by integrating each fourier mode after the other in the path integral formalism. It is free of the well known pathologies which appear in quantum field theory due to the sharp cutoff. We show that for an arbitrary background path the usual local form of the action is not preserved by the flow. To cure this problem we consider a more general action than usual which is stable by the renormalization group flow. It allows us to obtain a new consistent renormalization group equation for the action.Comment: 20 page

Finite-momentum Bose-Einstein condensates in shaken 2D square optical lattices

We consider ultracold bosons in a 2D square optical lattice described by the Bose-Hubbard model. In addition, an external time-dependent sinusoidal force is applied to the system, which shakes the lattice along one of the diagonals. The effect of the shaking is to renormalize the nearest-neighbor hopping coefficients, which can be arbitrarily reduced, can vanish, or can even change sign, depending on the shaking parameter. It is therefore necessary to account for higher-order hopping terms, which are renormalized differently by the shaking, and introduce anisotropy into the problem. We show that the competition between these different hopping terms leads to finite-momentum condensates, with a momentum that may be tuned via the strength of the shaking. We calculate the boundaries between the Mott-insulator and the different superfluid phases, and present the time-of-flight images expected to be observed experimentally. Our results open up new possibilities for the realization of bosonic analogs of the FFLO phase describing inhomogeneous superconductivity.Comment: 7 pages, 7 figure

The antiferromagnetic phi4 Model, II. The one-loop renormalization

It is shown that the four dimensional antiferromagnetic lattice phi4 model has the usual non-asymptotically free scaling law in the UV regime around the chiral symmetrical critical point. The theory describes a scalar and a pseudoscalar particle. A continuum effective theory is derived for low energies. A possibility of constructing a model with a single chiral boson is mentioned.Comment: To appear in Phys. Rev.

Ordinary versus PT-symmetric ϕ3\phi^3 quantum field theory

A quantum-mechanical theory is PT-symmetric if it is described by a Hamiltonian that commutes with PT, where the operator P performs space reflection and the operator T performs time reversal. A PT-symmetric Hamiltonian often has a parametric region of unbroken PT symmetry in which the energy eigenvalues are all real. There may also be a region of broken PT symmetry in which some of the eigenvalues are complex. These regions are separated by a phase transition that has been repeatedly observed in laboratory experiments. This paper focuses on the properties of a PT-symmetric $ig\phi^3$ quantum field theory. This quantum field theory is the analog of the PT-symmetric quantum-mechanical theory described by the Hamiltonian $H=p^2+ix^3$, whose eigenvalues have been rigorously shown to be all real. This paper compares the renormalization-group properties of a conventional Hermitian $g\phi^3$ quantum field theory with those of the PT-symmetric $ig\phi^3$ quantum field theory. It is shown that while the conventional $g\phi^3$ theory in $d=6$ dimensions is asymptotically free, the $ig\phi^3$ theory is like a $g\phi^4$ theory in $d=4$ dimensions; it is energetically stable, perturbatively renormalizable, and trivial.Comment: 13 pages, 2 figure

Effective potential and vacuum stability

By following previous work on this subject, we investigate the issue of the instability of the electroweak vacuum against the top loop corrections by performing an accurate analysis of a Higgs-Yukawa model. We find that, when the physical cutoff is properly implemented in the theory, the potential does not exhibit any instability. Moreover, contrary to recent claims, we show that this instability cannot be understood in terms of the very insightful work of Wu and Weinberg on the non-convexity of the one-loop effective potential of a scalar theory. Some of the theoretical and phenomenological consequences of our results are briefly discussed.Comment: 10 pages, 4 figure

Wegner-Houghton equation and derivative expansion

We study the derivative expansion for the effective action in the framework of the Exact Renormalization Group for a single component scalar theory. By truncating the expansion to the first two terms, the potential $U_k$ and the kinetic coefficient $Z_k$, our analysis suggests that a set of coupled differential equations for these two functions can be established under certain smoothness conditions for the background field and that sharp and smooth cut-off give the same result. In addition we find that, differently from the case of the potential, a further expansion is needed to obtain the differential equation for $Z_k$, according to the relative weight between the kinetic and the potential terms. As a result, two different approximations to the $Z_k$ equation are obtained. Finally a numerical analysis of the coupled equations for $U_k$ and $Z_k$ is performed at the non-gaussian fixed point in $D<4$ dimensions to determine the anomalous dimension of the field.Comment: 15 pages, 3 figure

Flow Equations for U_k and Z_k

By considering the gradient expansion for the wilsonian effective action S_k of a single component scalar field theory truncated to the first two terms, the potential U_k and the kinetic term Z_k, I show that the recent claim that different expansion of the fluctuation determinant give rise to different renormalization group equations for Z_k is incorrect. The correct procedure to derive this equation is presented and the set of coupled differential equations for U_k and Z_k is definitely established.Comment: 5 page

Spin Liquid Phases in 2D Frustrated XY Model

In this paper we consider the $J_1-J_2-J_3$ classical and quantum 2D XY model. Spin wave calculations show that a spin liquid phase still exists in the quantum case as for Heisenberg models. We formulate a semiclassical approach of these models based on spin wave action and use a variational method to study the role played by vortices. Liquid and crystal phases of vortex could emerge in this description. These phases seem to be directly correlated with the spin liquid one and to its crystalline interpretation.Comment: 16 pages, Latex, 4 figures. To be published in Phys. Rev.

The antiferromagnetic phi4 Model, I. The Mean-field Solution

Certain higher dimensional operators of the lagrangian may render the vacuum inhomogeneous. A rather rich phase structure of the phi4 scalar model in four dimensions is presented by means of the mean-field approximation. One finds para- ferro- ferri- and antiferromagnetic phases and commensurate-incommensurate transitions. There are several particles described by the same quantum field in a manner similar to the species doubling of the lattice fermions. It is pointed out that chiral bosons can be introduced in the lattice regularized theory.Comment: To appear in Phys. Rev.