Presence Of Spontaneous Symmetry Breaking Research Articles

Numerical RG-time integration of the effective potential: Analysis and benchmark

We investigate the renormalization group (RG)-time integration of the effective potential in the functional renormalization group in the presence of spontaneous symmetry breaking and its subsequent convexity restoration on the example of a scalar theory in $d=3$. The features of this setup are common to many physical models and our results are, therefore, directly applicable to a variety of situations. We provide exhaustive work-precision benchmarks and numerical stability analyses by considering the combination of different discrete formulations of the flow equation and a large collection of different algorithms. The results are explained by using the different components entering the RG-time integration process and the eigenvalue structure of the discrete system. Particularly, the combination of Rosenbrock methods, implicit multistep methods, or certain (diagonally) implicit Runge-Kutta methods with exact or automatic differentiation Jacobians proves to be very potent. Furthermore, a reformulation in a logarithmic variable circumvents issues related to the singularity bound in the flat regime of the potential.

Probing Many-Body Systems near Spectral Degeneracies

The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially decaying part. This separation is strongly affected when spectral degeneracies occur, for instance, in the presence of spontaneous symmetry breaking. Moreover, the slowest decay rate is determined by the smallest energy level spacing, and this decay rate diverges at the spectral degeneracies. Probing the quantum evolution with the diagonal elements of the time correlation matrix is discussed as a general concept and tested in the case of a bosonic Josephson junction. It reveals for the latter characteristic properties at the transition to Hilbert-space localization.

Minimal submanifolds asymptotic to AdS 4 × S 2 in AdS 5 × S 5

In this work, as an attempt in understanding the interplay between deformations of the external and internal spaces associated with the probe-brane embedding submanifold, we construct the zero-temperature phase diagram for the coupled phase between two two-dimensional defects stacked parallel in a four-dimensional ambient spacetime. Different UV parameters are turned on for different defects. We study the system in the quenched strong coupling limit, using holography with probe brane approximation, realized explicitly through the D3/D5 system. This coupled phase is holographic dual to the presence of spontaneous symmetry breaking of the individual ultraviolet flavor symmetries associated with the double heterostructure of the defect layers. We characterize this solution by its infrared geometric data, and present the numerical result showing a first-order phase transition between the asymmetrically coupled phase and the more mundane decoupled phase.

Towards next-to-leading order transport coefficients from the four-particle irreducible effective action

Transport coefficients can be obtained from 2-point correlators using the Kubo formulae. It has been shown that the full leading order result for electrical conductivity and (QCD) shear viscosity is contained in the re-summed 2-point function that is obtained from the 3-loop 3PI re-summed effective action. The theory produces all leading order contributions without the necessity for power counting, and in this sense it provides a natural framework for the calculation. In this article we study the 4-loop 4PI effective action for a scalar theory with cubic and quartic interactions in the presence of spontaneous symmetry breaking. We obtain a set of integral equations that determine the re-summed 2-point vertex function. A next-to-leading order contribution to the viscosity could be obtained from this set of coupled equations.

(Reverse) engineering vacuum alignment

In the presence of spontaneous symmetry breaking, the alignment of the vacuum with respect to the gauge group is often controlled by quadratically divergent operators in the low energy non-linear sigma model. In principle the magnitudes and signs of these operators can be changed by making different assumptions about the ultraviolet physics, but in practice all known ways of regulating these theories preserve the naive vacuum alignment. We show that by "integrating in" different sets of heavy spin-one fields, it is possible to UV extend certain non-linear sigma models into two distinct UV insensitive theories. These UV extensions have identical low energy degrees of freedom but different radiative potentials, making it possible to engineer two different vacuum alignments for the original non-linear sigma model. Our construction employs "non-square" theory spaces which generically violate the common lore that the preferred vacuum alignment preserves the maximal gauge symmetry. By UV extending the SO(9)/(SO(4) X SO(5)) little Higgs model, we find a radiative potential that deviates from the naive expectation but does not stabilize the correct vacuum for proper electroweak symmetry breaking.

Spontaneous symmetry breaking for scalar QED with nonminimal Chern-Simons coupling

We investigate the two-loop effective potential for both minimally and non-minimally coupled Maxwell-Chern-Simons theories. The non-minimal gauge interaction represents the magnetic moment interaction between a charged scalar and the electromagnetic field. In a previous paper we have shown that the two loop effective potential for this model is renormalizable with an appropriate choice of the non-minimal coupling constant. We carry out a detailed analysis of the spontaneous symmetry breaking induced by radiative corrections. As long as the renormalization point for all couplings is chosen to be the true minimum of the effective potential, both models predict the presence of spontaneous symmetry breaking. Two loop corrections are small compared to the one loop result, and thus the symmetry breaking is perturbatively stable.

Collective aspects of protein folding illustrated by a toy model.

A simple toy model for polypeptides serves as a testbed to illuminate some nonlocal, or collective, aspects of protein folding phenomena. The model is two dimensional and has only two amino acids, but involves a continuous range of backbone bend angles. Global potential energy minima and their folding structures have been determined for leading members of two special and contrasting polypeptide sequences, center doped and Fibonacci, named descriptively for their primary structures. The results display the presence of spontaneous symmetry breaking, elastic strain, and substantial conformational variation for specific embedded amino acid strings. We conclude that collective variables generated by the primary amino acid structure may be required for fully effective protein folding predictors, including those based on neural networks.

(Infinite) boundary corrections for the LMBW-equations and the TZ-formula of surface tension in the presence of spontaneous symmetry breaking

Abstract We investigate on a broad scale the so-called LMBW-hierarchy and various consequences thereof in the presence of spontaneous symmetry breaking and long-range correlations. We show, by carefully performing the thermodynamic limit, that in general additional boundary terms will survive which are usually brushed under the carpet and which, in some applications, may even be infinite. We discuss the necessary modifications and make some (sketchy) remarks as to the relevance of our observations for the melting (freezing) problem. The bulk of the practical applications consists, however, in a detailed analysis of the various derivations of the Triezenberg-Zwanzig form of surface tension and its equivalence with the older Kirkwood-Buff expression. We show that, in general, γTZ is only one contribution occurring in γKB, the others being boundary terms which in some cases happen to be infinite. It turns out that in that situation γTZ is ill defined and singular as well, with the infinites of γTZ and the boundary contributions just cancelling each other, yielding a well defined γKB.

On the solution of the Schwinger-Dyson equation in the presence of spontaneous symmetry breaking

On presente une approche possible pour resoudre l'equation de Schwinger-Dyson pour la partie auto-energie d'un propagateur en presence de rupture de symetrie