Double-Scaling Limit of the O(N)-Symmetric Anharmonic Oscillator

In an earlier paper it was argued that the conventional double-scaling limit of an O(N)-symmetric quartic quantum field theory is inconsistent because the critical coupling constant is negative and thus the integral representing the partition function of the critical theory does not exist. In this earlier paper it was shown that for an O(N)-symmetric quantum field theory in zero-dimensional spacetime one can avoid this difficulty if one replaces the original quartic theory by its PT-symmetric analog. In the current paper an O(N)-symmetric quartic quantum field theory in one-dimensional spacetime [that is, O(N)-symmetric quantum mechanics] is studied using the Schroedinger equation. It is shown that the global PT-symmetric formulation of this differential equation provides a consistent way to perform the double-scaling limit of the O(N)-symmetric anharmonic oscillator. The physical nature of the critical behavior is explained by studying the PT-symmetric quantum theory and the corresponding and equivalent Hermitian quantum theory.Comment: ten pages, 4 figure

Nodal Liquids in Extended t-J Models and Dynamical Supersymmetry

In the context of extended t-J models, with intersite Coulomb interactions of the form $-V\sum\limits_{} {n_in_j}$, with n_i denoting the electron number operator at site i, nodal liquids are discussed. We use the spin-charge separation ansatz as applied to the nodes of a d-wave superconducting gap.Such a situation may be of relevance to the physics of high-temperature superconductivity. We point out the possibility of existence of certain points in the parameter space of the model characterized by dynamical supersymmetries between the spinon and holon degrees of freedom, which are quite different from the symmetries in conventional supersymmetric t-J models. Such symmetries pertain to the continuum effective field theory of the nodal liquid, and one's hope is that the ancestor lattice model may differ from the continuum theory only by renormalization-group irrelevant operators in the infrared. We give plausible arguments that nodal liquids at such supersymmetric points are characterized by superconductivity of Kosterlitz-Thouless type. The fact that quantum fluctuations around such points can be studied in a controlled way, probably makes such systems of special importance for an eventual non-perturbative understanding of the complex phase diagram of the associated high-temperature superconducting materials.Comment: 39 pages latex, one eps, 2 latex figures incorporate

Comments on Extended t-J Models, Nodal Liquids and Supersymmetry

In the context of extended t-J models, with intersite Coulomb interactions, nodal liquids are discussed. We use the spin-charge separation ansatz as applied to the nodes of a d-wave superconducting gap. Such a situation may be of relevance to the physics of high-temperature superconductivity. We point out the possibility that at certain points of the parameter space supersymmetric points may occur, characterized by dynamical supersymmetries between the spinon and holon degrees of freedom, which are quite different from the symmetries in conventional supersymmetric t-J models. Such symmetries pertain to the continuum effective field theory of the nodal liquid, and one's hope is that the ancestor lattice model may differ from the continuum theory only by renormalization-group irrelevant operators in the infrared. We give plausible arguments that nodal liquids at such supersymmetric points are characterized by superconductivity of Kosterlitz-Thouless type.Comment: 18 pages latex, one eps figure incorporated (minor typos corrected). Presented by N.E.M. at the Workshop ``Common Trends in Particle and Condensed Matter Physics'', September 24-28 1999, Corfu (Greece

CPT-Violating Leptogenesis induced by Gravitational Defects

We explore leptogenesis induced by the propagation of neutrinos in gravitational backgrounds that may occur in string theory. The first background is due to linear dilatons and the associated Kalb-Ramond field (axion) in four non-compact space-time dimensions of the string, and can be described within the framework of local effective lagrangians. The axion is linear in the time coordinate of the Einstein frame and gives rise to a constant torsion which couples to the fermion spin through a gravitational covariant derivative. This leads to different energy-momentum dispersion relations for fermions and anti-fermions and hence leptogenesis. The next two backgrounds go beyond the local effective lagrangian framework. One is a stochastic (Lorentz Violating) Finsler metric which again leads to different dispersion relations between fermions and antifermions. The third background of primary interest is the one due to populations of stochastically fluctuating point-like space-time defects that can be encountered in string/brane theory (D0 branes). Only neutral matter interacts non-trivially with these defects, as a consequence of charge conservation. Hence, such a background singles out neutrinos among the Standard Model excitations as the ones interacting predominantly with the defects. The back-reaction of the defects on the space-time due to their interaction with neutral matter results in stochastic Finsler-like metrics (similar to our second background). On average, the stochastic fluctuations of the D0 brane defects preserve Lorentz symmetry, but their variance is non-zero. Interestingly, the particle/antiparticle asymmetry comes out naturally to favour matter over antimatter in this third background, once the effects of the kinematics of the scattering of the D branes with matter is incorporated.Comment: 22 pages revtex 4-1, one eps figure incorporate

Fingerprints of Classical Instability in Open Quantum Dynamics

The dynamics near a hyperbolic point in phase space is modelled by an inverted harmonic oscillator. We investigate the effect of the classical instability on the open quantum dynamics of the oscillator, introduced through the interaction with a thermal bath, using both the survival probability function and the rate of von Neumann entropy increase, for large times. In this parameter range we prove, using influence functional techniques, that the survival probability function decreases exponentially at a rate, K', depending not only on the measure of instability in the model but also on the strength of interaction with the environment. We also show that K' determines the rate of von Neumann entropy increase and that this result is independent of the temperature of the environment. This generalises earlier results which are valid in the limit of vanishing dissipation. The validity of inferring similar rates of survival probability decrease and entropy increase for quantum chaotic systems is also discussed.Comment: 13 pages, to be published in Physical Review

Spontaneous CPT Violation and Quantum Anomalies in a Model for Matter-Antimatter Asymmetry in the Cosmos

We review scenarios of baryogenesis through leptogenesis at early epochs of the universe, in string-inspired minimal extensions of the Standard Model (SM), involving heavy right-handed Majorana neutrinos. Spontaneous violation of CPT symmetry is induced by appropriate (in general, temperature-dependent) backgrounds of the Kalb-Ramond (KR) axion field, which has its origins in the (bosonic) massless string multiplet. As interesting features of the model, we also discuss two issues associated with quantum (chiral) anomalies: (i) the non-contribution of the KR axion background to the (anomalous) chiral magnetic effect, which arises in the presence of external electromagnetic fields and non-zero chiral chemical potentials of charged fermions and (ii) the potential r\^ole of quantum fluctuations of the KR axion on the (anomalous) radiative generation of a Majorana mass for the right-handed neutrinos themselves.Comment: 18 pages rev tex. Plenary talk (by N.E.M.) at the 7th International Conference of New Frontiers in Physics 2018, 4-12 July 2018, Kolymbari (Greece); review with possible text overlap with: arXiv:1209.6387 [hep-ph], arXiv:1403.7684 [hep-ph], arXiv:1412.7077 [hep-ph], arXiv:1712.03312 [hep-ph], arXiv:1810.13384 [hep-ph