Interchange Symmetry Research Articles

A space/time interchange symmetry of rotating AdS black holes in general dimensions

We revisit the previously known local inversion symmetry of the five-dimensional Kerr-AdS metric that relates the over-rotating black hole to the under-rotating one and reinterpret it as an interchanging symmetry between time and the longitudinal angular coordinates. We generalize this to all D dimensions, including D=4, thereby enlarging the trivial linear ZN symmetry of the N=⌊(D−1)/2⌋ longitudinal angular coordinates to the nonlinearly realized ZN+1 symmetry that involves time.

Shrinking the Warm Little Inflaton

We show that warm inflation can be successfully realized in the high temperature regime through dissipative interactions between the inflaton and a single fermionic degree of freedom, provided that the latter’s mass is an oscillatory function of the inflaton field value. We demonstrate, in particular, that despite the consequent large amplitude oscillations of the eta slow-roll parameter, their effect is, on average, sufficiently suppressed to allow for a slow-roll trajectory. In addition, we demonstrate that, even though this also induces a parametric resonance that amplifies inflaton perturbations, this has a negligible effect on CMB scales in the relevant parametric range. Hence, the “Warm Little Inflaton” scenario can be realized with one less fermionic degree of freedom and no need of imposing an additional discrete interchange symmetry.

Non-asymptotic Coqblin–Schrieffer interaction between local f[formula omitted]-states

The magnetism of many cerium-based compounds has been studied considering the hybridization of its local f1 state with itinerant electrons, a mechanism that originates an anisotropic RKKY-type interaction between two neighboring local moments. The orbital degrees of freedom of the f-levels play a fundamental role in this mechanism, as shown in the well-known and broadly used Coqblin–Schrieffer formalism, which, however, is valid only for ions very far apart, yields an effective Hamiltonian that is not hermitian and does not reflect the interchange symmetry when applied for two identical ions. Therefore, the off-diagonal terms of the interaction energy do not exhibit the Friedel oscillations typical of the RKKY interactions. Through an exact evaluation of Ruderman–Kittel-like integrals, we extended such formalism to any ionic separation, corrected the non-hermiticity and the lack of ionic interchange symmetry, which recovered the Friedel oscillations. These improvements strongly impact the contribution of each angular momentum component to the ionic interaction-energy and hence whether ferro- or anti-ferromagnetic alignment is favored. As an example, we calculated the temperature dependence of the magnetic susceptibility for a simple system of Ce-Ce free dimers and show that striking differences exist when compared with the susceptibility evaluated using the original Coqblin–Schrieffer formalism.

A Symmetric Two Higgs Doublet Model

In the light of ongoing experimental search efforts for the dark matter and the post-Higgs Beyond the Standard Model (BSM) null results at the Large Hadron Collider (LHC), the Electroweak sector demands to be investigated for possible new scalar states discoverable at the LHC fulfilling the role of the dark matter. In this work we present a symmetric two Higgs doublet model with a discrete interchange symmetry among the two Higgs doublets (Φ1 ↔ Φ2). Apart from the Standard Model (SM)-like scalar state (h) with mh = 125 GeV, the model has several distinguishing features including the pseudoscalar (A), the charged scalars(H±) and the neutral scalar H, not having any direct coupling to the fermions. The neutral scalar H is assumed to have mass lighter than the 125 GeV SM-like Higgs state h. Due to the presence of a residual Z2 symmetry after the spontaneous symmetry breaking (SSB), the neutral scalar H can emerge as a viable dark matter candidate. We discuss the constraints on such scalar dark matter from the current direct and indirect detection experiments. As a by-product of this construction, the SM-like scalar h ends up having an extra invisible decay mode of h → HH in this model which can also influence the dark matter parameter space. We discuss these model features in detail along with a guideline of relevant phenomenological searches at the LHC for this scenario.

Warm inflation, neutrinos and dark matter: a minimal extension of the Standard Model

We show that warm inflation can be realized within a minimal extension of the Standard Model with three right-handed neutrinos, three complex scalars and a gauged lepton/B-L U(1) symmetry. This simple model can address all the shortcomings of the Standard Model that are not related to fine-tuning, within general relativity, with distinctive experimental signatures that can be probed in the near future. The inflaton field emerges from the collective breaking of the U(1) symmetry, and interacts with two of the right-handed neutrinos, sustaining a high-temperature radiation bath during inflation. The discrete interchange symmetry of the model protects the scalar potential against large thermal corrections and leads to a stable inflaton remnant at late times which can account for dark matter. Consistency of the model and agreement with Cosmic Microwave Background observations naturally yield light neutrino masses below 0.1 eV, while thermal leptogenesis occurs naturally after a smooth exit from inflation into the radiation era.

Edge counts for the auxiliary pair graph within the graphical unitary group approach

Closed-form expressions are presented for the numbers of edges in the auxiliary pair graphs (APGs) associated with non spin–orbit and spin–orbit Shavitt graphs for full configuration interaction expansions. A Shavitt graph is a visual representation of a configuration state function expansion space constructed via the graphical unitary group approach (GUGA). An APG is an organisational aid and a programmatic tool generated from a Shavitt graph. The number of edges in an APG determines bounds on the computational scaling as a function of the total numbers of electrons, orbitals, and spin multiplicities. The edge counts extend a suite of Shavitt graph statistics based on these functional parameters. The derivation and the presentation of the formulas for the edge counts has been assisted by the bra–ket interchange symmetry and the particle-hole interchange symmetry in the GUGA formalism. These symmetry operators produce one-to-one correspondences between various sets of edges, and this yields identities among some edge count formulas. There are 208 possible edge types. Of these, some do not contribute to two-electron operators, some are related by bra–ket interchange symmetry, and some are related by particle-hole interchange symmetry. For the remaining unique edge types, explicit expressions are derived for the numbers of edges.

Supersymmetric ν-inflaton Dark Matter

We present the supersymmetric extension of the unified model for inflation and Dark Matter studied in ref. [1]. The scenario is based on the incomplete decay of the inflaton field into right-handed (s)neutrino pairs. By imposing a discrete interchange symmetry on the inflaton and the right-handed (s)neutrinos, one can ensure the stability of the inflaton field at the global minimum today, while still allowing it to partially decay and reheat the Universe after inflation. Compatibility of inflationary predictions, BBN bounds and obtaining the right DM abundance for the inflaton Dark Matter candidate typically requires large values of its coupling to the neutrino sector, and we use supersymmetry to protect the inflaton from potentially dangerous large radiative corrections which may spoil the required flatness of its potential. In addition, the inflaton will decay now predominantly into sneutrinos during reheating, which in turn give rise both to the thermal bath made of Standard Model particles, and inflaton particles. We have performed a thorough analysis of the reheating process following the evolution of all the partners involved, identifying the different regimes in the parameter space for the final Dark Matter candidate. This as usual can be a WIMP-like inflaton particle or an oscillating condensate, but we find a novel regime for a FIMP-like candidate.

Towards a reliable effective field theory of inflation

We present the first quantum field theory model of inflation that is renormalizable in the matter sector, with a super-Hubble inflaton mass and sub-Planckian field excursions, which is thus technically natural and consistent with a high-energy completion within a theory of quantum gravity. This is done in the framework of warm inflation, where we show, for the first time, that strong dissipation can fully sustain a slow-roll trajectory with slow-roll parameters larger than unity in a way that is both theoretically and observationally consistent. The inflaton field corresponds to the relative phase between two complex scalar fields that collectively break a U(1) gauge symmetry, and dissipates its energy into scalar degrees of freedom in the warm cosmic heat bath. A discrete interchange symmetry protects the inflaton mass from large thermal corrections. We further show that the dissipation coefficient decreases with temperature in certain parametric regimes, which prevents a large growth of thermal inflaton fluctuations. We find, in particular, a very good agreement with the Planck legacy data for a simple quadratic inflaton potential, predicting a low tensor-to-scalar ratio r≲10−5.

Partitioned second derivative methods for separable Hamiltonian problems

In this paper, the partitioned second derivative general linear methods for solving separable Hamiltonian problems are derived which are G-symplectic, interchange symmetry and have zero parasitic growth factors. Order conditions for such methods based on the theory of rooted trees are provided and examples of partitioned pairs of order 2 and 3 are given. The experiments have been performed on some separable problems and no drift in the variation of the Hamiltonian is observed in numerical experiments for long time intervals. Also, the results of numerical experiments demonstrate the efficiency of our new methods in comparison with some symplectic and G-symplectic methods.

Importance of generalized \u03bc\u03c4 symmetry and its CP extension on neutrino mixing and leptogenesis

Within the framework of residual symmetry, two ℤ2 type associate μτ inter- change symmetries robustly constrain the Dirac CP phase δ in a model independent way. Both of them predict simultaneous maximality of δ and the atmospheric mixing angle θ23. We show how these well known correlations will be changed if we generalize the μτ in- terchange symmetry to a μτ mixing symmetry. In particular, we show that the stringent condition of simultaneous maximality could be relaxed even with a very small departure from the exact μτ interchange. In addition, the present neutrino data on δ and θ23 can be explained better by the mixing symmetry. After discussing the impact of the μτ mix- ing in some realistic neutrino mass models, we show how the proposed mixing could be realized with two simultaneous CP transformations which also lead to novel and testable correlations between δ and the mixing angles θij . Next we discuss in particular, the ‘three flavour regime’ of leptogenesis within the CP extended framework and show, unlike the ordinary CP extended μτ interchange symmetry, a resonant leptogenesis is possible due the generalization of μτ interchange to the μτ mixing and the resulting baryon asymmetry always requires a nonmaximal θ23 owing to the fact that the baryon to photon ratio ηB vanishes in the exact limit of θ23 = π/4. This is one of the robust predictions of this frame- work. The CP extended μτ mixing is also a novel example of a low energy effective model that provides an important insight to the off-diagonal terms of the flavour coupling matrix which have usually been neglected in literature to compute the final baryon asymmetry, in particular in the models with flavour symmetries.

A U-spin prediction for the CP-forbidden transition e+e−→ D0D̄0 → (K+K−)D(π+π−)D

The LHCb Collaboration has recently reported the discovery of direct CP violation in combined [Formula: see text] and [Formula: see text] decay modes at the [Formula: see text] level. Assuming U-spin symmetry (i.e. [Formula: see text] interchange symmetry) for the strong-interaction parts of these two channels, we find that their corresponding direct CP-violating asymmetries are [Formula: see text] and [Formula: see text]. The CP-forbidden transition [Formula: see text] on the [Formula: see text] resonance is therefore expected to have a branching fraction of [Formula: see text] or smaller under U-spin symmetry, and it can be observed at a high-luminosity super-[Formula: see text]-charm factory if at least [Formula: see text] pairs of coherent [Formula: see text] and [Formula: see text] events are accumulated.

Correlated Electronic Properties of a Graphene Nanoflake: Coronene.

We report studies of the correlated excited states of coronene and substituted coronene within the Pariser–Parr–Pople (PPP) correlated -electron model employing the symmetry-adapted density matrix renormalization group technique. These polynuclear aromatic hydrocarbons can be considered as graphene nanoflakes. We review their electronic structures utilizing a new symmetry adaptation scheme that exploits electron-hole symmetry, spin-inversion symmetry, and end-to-end interchange symmetry. The study of the electronic structures sheds light on the electron correlation effects in these finite-size graphene analogues, which diminishes going from one-dimensional to higher-dimensional systems, yet is significant within these finite graphene derivatives.

\u03bd-inflaton dark matter

We present a unified model where the same scalar field can drive inflation and account for the present dark matter abundance. This scenario is based on the incomplete decay of the inflaton field into right-handed neutrino pairs, which is accomplished by imposing a discrete interchange symmetry on the inflaton and on two of the right-handed neutrinos. We show that this can lead to a successful reheating of the Universe after inflation, while leaving a stable inflaton remnant at late times. This remnant may be in the form of WIMP-like inflaton particles or of an oscillating inflaton condensate, depending on whether or not the latter evaporates and reaches thermal equilibrium with the cosmic plasma. We further show that this scenario is compatible with generating light neutrino masses and mixings through the seesaw mechanism, predicting at least one massless neutrino, and also the observed baryon asymmetry via thermal leptogenesis.

Symmetrized density matrix renormalization group algorithm for low-lying excited states of conjugated carbon systems: Application to 1,12-benzoperylene and polychrysene

The symmetry adapted density matrix renormalization group (SDMRG) technique has been an efficient method for studying low-lying eigenstates in one- and quasi-one-dimensional electronic systems. However, the SDMRG method had bottlenecks involving the construction of linearly independent symmetry adapted basis states as the symmetry matrices in the DMRG basis were not sparse. We have developed a modified algorithm to overcome this bottleneck. The new method incorporates end-to-end interchange symmetry $({C}_{2})$, electron-hole symmetry $(J)$, and parity or spin-flip symmetry $(P)$ in these calculations. The one-to-one correspondence between direct-product basis states in the DMRG Hilbert space for these symmetry operations renders the symmetry matrices in the new basis with maximum sparseness, just one nonzero matrix element per row. Using methods similar to those employed in the exact diagonalization technique for Pariser-Parr-Pople (PPP) models, developed in the 1980s, it is possible to construct orthogonal SDMRG basis states while bypassing the slow step of the Gram-Schmidt orthonormalization procedure. The method together with the PPP model which incorporates long-range electronic correlations is employed to study the correlated excited-state spectra of 1,12-benzoperylene and a narrow mixed graphene nanoribbon with a chrysene molecule as the building unit, comprising both zigzag and cove-edge structures.

Partitioned general linear methods for separable Hamiltonian problems

Partitioned general linear methods possessing the G-symplecticity property are introduced. These are intended for the numerical solution of separable Hamiltonian problems and, as for multivalue methods in general, there is a potential for loss of accuracy because of parasitic solution growth. The solution of mechanical problems over extended time intervals often benefits from interchange symmetry as well as from symplectic behaviour. A special type of symmetry, known as interchange symmetry, is developed from a model Runge–Kutta case to a full multivalue case. Criteria are found for eliminating parasitic behaviour and order conditions are explored.

Examination of pairs in neutrino mixing matrix

We exam the pairs of neutrino mixing matrix and suggest pairs that can be used in the construction of new mixing patterns, with "pair" denoting the equality of the modulus of a pair of matrix elements. The results show that the tri-maximal mixing in $\nu_2$ and the $\mu$-$\tau$ interchange symmetry are good choices under current experimental results. The two cases of bi-pair mixing pattern depend on the mass hierarchy of neutrinos. We also derive constraints on the CP-phase by the pairs. The results are compatible with the maximal CP-violation in most cases that are both self-consistent and consistent with experimental results.

Generalized μ–τ symmetry and discrete subgroups of [formula omitted

The generalized μ–τ interchange symmetry in the leptonic mixing matrix U corresponds to the relations: |Uμi|=|Uτi| with i=1,2,3. It predicts maximal atmospheric mixing and maximal Dirac CP violation given θ13≠0. We show that the generalized μ–τ symmetry can arise if the charged lepton and neutrino mass matrices are invariant under specific residual symmetries contained in the finite discrete subgroups of O(3). The groups A4, S4 and A5 are the only such groups which can entirely fix U at the leading order. The neutrinos can be (a) non-degenerate or (b) partially degenerate depending on the choice of their residual symmetries. One obtains either vanishing or very large θ13 in case of (a) while only A5 can provide θ13 close to its experimental value in the case (b). We provide an explicit model based on A5 and discuss a class of perturbations which can generate fully realistic neutrino masses and mixing maintaining the generalized μ–τ symmetry in U. Our approach provides generalization of some of the ideas proposed earlier in order to obtain the predictions, θ23=π/4 and δCP=±π/2.

Neutrino mixing and CP phase correlations

A special form of the 3×3 Majorana neutrino mass matrix derivable from μ–τ interchange symmetry accompanied by a generalized CP transformation was obtained many years ago. It predicts θ23=π/4 as well as δCP=±π/2, with θ13≠0. Whereas this is consistent with present data, we explore a deviation of this result which occurs naturally in a recent proposed model of radiative inverse seesaw neutrino mass.

Symmetries and pattern formation in hyperbolic versus parabolic models of self-organised aggregation.

The study of self-organised collective animal behaviour, such as swarms of insects or schools of fish, has become over the last decade a very active research area in mathematical biology. Parabolic and hyperbolic models have been used intensively to describe the formation and movement of various aggregative behaviours. While both types of models can exhibit aggregation-type patterns, studies on hyperbolic models suggest that these models can display a larger variety of spatial and spatio-temporal patterns compared to their parabolic counterparts. Here we use stability, symmetry and bifurcation theory to investigate this observation more rigorously, an approach not attempted before to compare and contrast aggregation patterns in models for collective animal behaviors. To this end, we consider a class of nonlocal hyperbolic models for self-organised aggregations that incorporate various inter-individual communication mechanisms, and take the formal parabolic limit to transform them into nonlocal parabolic models. We then discuss the symmetry of these nonlocal hyperbolic and parabolic models, and the types of bifurcations present or lost when taking the parabolic limit. We show that the parabolic limit leads to a homogenisation of the inter-individual communication, and to a loss of bifurcation dynamics (in particular loss of Hopf bifurcations). This explains the less rich patterns exhibited by the nonlocal parabolic models. However, for multiple interacting populations, by breaking the population interchange symmetry of the model, one can preserve the Hopf bifurcations that lead to the formation of complex spatio-temporal patterns that describe moving aggregations.

Neutrino mass textures and partialμ–τsymmetry

We discuss the viability of the $\ensuremath{\mu}--\ensuremath{\tau}$ interchange symmetry imposed on the neutrino mass matrix in the flavor space. Whereas the exact symmetry is shown to lead to textures of a completely degenerate spectrum, which is incompatible with the neutrino oscillation data, introducing small perturbations into the preceding textures, inserted in a minimal way, leads, however, to four deformed textures representing an approximate $\ensuremath{\mu}$--$\ensuremath{\tau}$ symmetry. We motivate the form of these ``minimal'' textures, which disentangle the effects of the perturbations, and present some concrete realizations assuming exact $\ensuremath{\mu}--\ensuremath{\tau}$ at the Lagrangian level but at the expense of adding new symmetries and matter fields. We find that all of these deformed textures are capable of accommodating the experimental data, and in all types of neutrino mass hierarchies, particularly the nonvanishing value for the smallest mixing angle.