Simple Field Theory Research Articles

More asymptotic safety guaranteed

We study interacting fixed points and phase diagrams of simple and semisimple quantum field theories in four dimensions involving non-Abelian gauge fields, fermions and scalars in the Veneziano limit. Particular emphasis is put on new phenomena which arise due to the semisimple nature of the theory. Using matter field multiplicities as free parameters, we find a large variety of interacting conformal fixed points with stable vacua and crossovers inbetween. Highlights include semisimple gauge theories with exact asymptotic safety, theories with one or several interacting fixed points in the IR, theories where one of the gauge sectors is both UV free and IR free, and theories with weakly interacting fixed points in the UV and the IR limits. The phase diagrams for various simple and semisimple settings are also given. Further aspects such as perturbativity beyond the Veneziano limit, conformal windows, and implications for model building are discussed.

General bounds in Hybrid Natural Inflation

Recently we have studied in great detail a model of Hybrid Natural Inflation (HNI) by constructing two simple effective field theories. These two versions of the model allow inflationary energy scales as small as the electroweak scale in one of them or as large as the Grand Unification scale in the other, therefore covering the whole range of possible energy scales. In any case the inflationary sector of the model is of the form V(ϕ)=V0 (1+a cos(ϕ/f)) where 0⩽ a<1 and the end of inflation is triggered by an independent waterfall field. One interesting characteristic of this model is that the slow-roll parameter ϵ(ϕ) is a non-monotonic function of ϕ presenting a maximum close to the inflection point of the potential. Because the scalar spectrum \U0001d4abs(k) of density fluctuations when written in terms of the potential is inversely proportional to ϵ(ϕ) we find that \U0001d4abs(k) presents a minimum at ϕmin. The origin of the HNI potential can be traced to a symmetry breaking phenomenon occurring at some energy scale f which gives rise to a (massless) Goldstone boson. Non-perturbative physics at some temperature T<f might occur which provides a potential (and a small mass) to the originally massless boson to become the inflaton (a pseudo-Nambu-Goldstone boson). Thus the inflaton energy scale Δ is bounded by the symmetry breaking scale, Δ≡ VH1/4 <f. To have such a well defined origin and hierarchy of scales in inflationary models is not common. We use this property of HNI to determine bounds for the inflationary energy scale Δ and for the tensor-to-scalar ratio r.

Three-Body Halo States in Effective Field Theory: Renormalization and Three-Body Interactions in the Helium-6 System

In this paper we study the renormalization of Halo effective field theory applied to the Helium-6 halo nucleus seen as an alpha –neutron–neutron three-body state. We include the 0^+ dineutron channel together with both the 3/2^- and 1/2^- neutron–alpha channels into the field theory and study all of the six lowest-order three-body interactions that are present. Furthermore, we discuss three different prescriptions to handle the unphysical poles in the P-wave two-body sector. In the simpler field theory without the 1/2^- channel present we find that the bound-state spectrum of the field theory is renormalized by the inclusion of a single three-body interaction. However, in the field theory with both the 3/2^- and 1/2^- included, the system can not be renormalized by only one three-body operator.

MOLECULAR STRUCTURE OF MANGANESE TRIS-ACETYLACETONATE IN DIFFERENT SPIN STATES

Quantum chemical calculations of the geometric structure, force fields and harmonic vibration frequencies of the molecule Mn(acac)3 for electronic states with multiplicities M = 1, 3 and 5 were performed using the GAUSSIAN 09 program in the framework of density functional theory (DFT/UB3LYP) with correlation-consistent valence three-exponential basis functions cc-pVTZ. The structure with high-spin state S=2 (symmetry of electronic state 5B) possesses the lowest energy and it is characterized by C2 symmetry. The coordination polyhedron MnO6 possesses the shape of “elongated octahedron”. The high-spin state 5A is characterized by structure of compressed octahedron. The distortion of octahedral structure of coordination polyhedron in the states 5A and 5B is significant, and this fact testifies to the strong Jahn-Teller effect, or vibronic effect, in 5E electronic state. The calculations for low-spin state S=0 are notable for some specifics. The optimization resulted in C2 symmetry of molecule having the symmetry of electronic state 1B. The bond distances Mn-O within 0.001 Å were equal to values obtained for structure with D3 symmetry with S=1. This result corresponds to the situation if two electrons occupy different 1e orbitals possessing opposite spins. The spin states 3A2 and 1B lie higher than the high-spin state by 5.2 and 17.3 kcal/mol, respectively. The structural features are explained well in a framework of simple crystal field theory indicating that d-orbitals of Mn3+ ion undergo the significant influence of ligand field.Forcitation:Berger R.J.F., Girichev G.V., Giricheva N.I., Petrova A.A., Sliznev V.V., Tverdova N.V. Molecular structure of manganese tris-acetylacetonate in different spin states. Izv. Vyssh. Uchebn. Zaved. Khim. Khim. Tekhnol. 2017. V. 60. N 4. P. 47-53.

G-Strands on symmetric spaces.

We study the G-strand equations that are extensions of the classical chiral model of particle physics in the particular setting of broken symmetries described by symmetric spaces. These equations are simple field theory models whose configuration space is a Lie group, or in this case a symmetric space. In this class of systems, we derive several models that are completely integrable on finite dimensional Lie group G, and we treat in more detail examples with symmetric space SU(2)/S1 and SO(4)/SO(3). The latter model simplifies to an apparently new integrable nine-dimensional system. We also study the G-strands on the infinite dimensional group of diffeomorphisms, which gives, together with the Sobolev norm, systems of 1+2 Camassa-Holm equations. The solutions of these equations on the complementary space related to the Witt algebra decomposition are the odd function solutions.

Polarizable polymer chain under external electric field: Effects of many-body electrostatic dipole correlations.

We present a new simple self-consistent field theory of a polarizable flexible polymer chain under an external constant electric field with account for the many-body electrostatic dipole correlations. We show the effects of electrostatic dipole correlations on the electric-field-induced globule-coil transition. We demonstrate that only when the polymer chain is in the coil conformation, the electrostatic dipole correlations of monomers can be considered as pairwise. However, when the polymer chain is in a collapsed state, the dipole correlations have to be considered at the many-body level.

LHC future prospects of the 750 GeV resonance

A quantitative discussion on the future prospects of the 750 GeV resonance at the LHC experiment is given using a simple effective field theory analysis. The relative size of two effective operators relevant to diphoton decays can be probed by ratios of diboson signals in a robust way. We obtain the future sensitivities of $Z\gamma $, $ZZ$ and $WW$ resonance searches at the high luminosity LHC, rescaling from the current sensitivities at $\sqrt{s}=13$ TeV. Then, we show that a large fraction of parameter space in the effective field theory will be covered with 300 fb$^{-1}$ and almost the whole parameter space will be tested with 3000 fb$^{-1}$. This discussion is independent of production processes, other decay modes and total decay width.

Hybrid Natural Inflation

We construct two simple effective field theory versions of {\it Hybrid Natural Inflation (HNI)} that illustrate the range of its phenomenological implications. The resulting inflationary sector potential, $V=\Delta^4(1+a\cos(\phi/f))$, arises naturally, with the inflaton field a pseudo-Nambu-Goldstone boson. The end of inflation is triggered by a waterfall field and the conditions for this to happen are determined. Also of interest is the fact that the slow-roll parameter $\epsilon$ (and hence the tensor $r$) is a non-monotonic function of the field with a maximum where observables take universal values that determines the maximum possible tensor to scalar ratio $r$. In one of the models the inflationary scale can be as low as the electroweak scale. We explore in detail the associated HNI phenomenology, taking account of the constraints from Black Hole production, and perform a detailed fit to the Planck 2015 temperature and polarisation data.

Asymmetric condensed dark matter

We explore the viability of a boson dark matter candidate with an asymmetry between the number densities of particles and antiparticles. A simple thermal field theory analysis confirms that, under certain general conditions, this component would develop a Bose-Einstein condensate in the early universe that, for appropriate model parameters, could survive the ensuing cosmological evolution until now. The condensation of a dark matter component in equilibrium with the thermal plasma is a relativistic process, hence the amount of matter dictated by the charge asymmetry is complemented by a hot relic density frozen out at the time of decoupling. Contrary to the case of ordinary WIMPs, dark matter particles in a condensate must be lighter than a few tens of eV so that the density from thermal relics is not too large. Big-Bang nucleosynthesis constrains the temperature of decoupling to the scale of the QCD phase transition or above. This requires large dark matter-to-photon ratios and very weak interactions with standard model particles.

EPR spectroscopic characterization of a monomeric PtIII species produced via electrochemical oxidation of the anticancer compound trans-[PtII{(p-HC6F4)NCH2CH2NEt2}Cl(py)

The bulk oxidative electrolysis of a 2mM solution of trans-[PtII{(p-HC6F4)NCH2CH2NEt2}Cl(py)] in highly non-coordinating dichloromethane (0.05M [Bu4N][B(C6F5)]) media leads to the formation of about 14% of the PtIII species trans-[PtIII{(p-HC6F4)NCH2CH2NEt2}Cl(py)]+. The EPR spectrum of this electro-synthesized formally PtIII species shows Pt-hyperfine coupling with gx~gy>gz~ge, and is broadly consistent with the simple crystal field theory prediction for 5d7 PtIII in an elongated tetragonal environment where the unpaired electron is in a 5d(z2) orbital. The crystal field calculations lead to an estimate of the 5d(z2) character of around 37% and indicate partial delocalization of the unpaired electron onto the orbitals of the surrounding ligands. Transient cyclic voltammetric and steady-state microelectrode studies in the same media as used for bulk electrolysis exhibit a chemically reversible one electron oxidation process under their shorter time scale conditions. Analysis of X-ray diffraction data obtained from a single crystal of trans-[PtII{(p-HC6F4)NCH2CH2NEt2}Cl(py)] shows the square planar geometry of the ligands around the Pt metal center and the ‘W’ arrangement of the ethyl groups on the ligand is explained in terms of agostic interactions.

Spectrum-doubled heavy vector bosons at the LHC

We study a simple effective field theory incorporating six heavy vector bosons together with the standard-model field content. The new particles preserve custodial symmetry as well as an approximate left-right parity symmetry. The enhanced symmetry of the model allows it to satisfy precision electroweak constraints and bounds from Higgs physics in a regime where all the couplings are perturbative and where the amount of fine-tuning is comparable to that in the standard model itself. We find that the model could explain the recently observed excesses in di-boson processes at invariant mass close to 2 TeV from LHC Run 1 for a range of allowed parameter space. The masses of all the particles differ by no more than roughly 10%. In a portion of the allowed parameter space only one of the new particles has a production cross section large enough to be detectable with the energy and luminosity of Run 1, both via its decay to WZ and to Wh, while the others have suppressed production rates. The model can be tested at the higher-energy and higher-luminosity run of the LHC even for an overall scale of the new particles higher than 3 TeV.

Diagrammatic computation of multi-Higgs processes at very high energies: Scalinglogσnwith MadGraph

At very high energies scattering amplitudes in a spontaneously broken gauge theory into multi-particle final states are known to grow factorially with the number of particles produced. Using simple scalar field theory models with and without the VEV, we compute total cross-sections with up to 7 particles in the final state at the leading order in perturbation theory with MadGraph. By exploring the known scaling properties of the multi-particle rates with the number of particles, we determine from these the general $n$-point cross-sections in the large-$n$ limit. In the high-multiplicity regime we are considering, n>>1 and lambda n=fixed, the perturbation theory becomes strongly coupled with the higher-order loop effects contributing increasing powers of lambda n. In the approximation where only the leading loop effects are included, we show that the corresponding perturbative cross-sections grow exponentially and ultimately violate perturbative unitarity. This occurs at surprisingly low energy scales ~50 TeV with multiplicities above ~130. It is expected that a repair mechanism or an extension of the theory has to set-in before these scales are reached, possibly involving a novel non-perturbative dynamics in the a priori weakly coupled theory.

Lightlike limit of entanglement entropy

We study certain classes of $g_{++}$ deformations of theories arising in gauge/string realizations of nonrelativistic holography, some of which pertain to $z=2$ Lifshitz theories while others (pertaining to hyperscaling violation) comprise certain classes of excited states. Building on previous work, we consider holographic entanglement entropy for spacelike strip subsystems in a highly boosted (lightlike) limit, where the strip is stretched along the null $x^+$-plane. The leading divergence in entanglement in this null limit for these excited states is milder than the usual area law for spacelike subsystems in ground states. For ground states, the entanglement vanishes, perhaps consistent with ultralocality. We discuss this briefly from a field theory perspective. We also present some simple free lightfront field theory examples in excited states where correlators are nonvanishing.

Spin-1 Blume–Capel model in a transverse crystal field: An improved variational approach

We examine the phase diagram of the spin-1 Blume–Capel model in a transverse crystal field. Using an improved pair approximation within the framework of Bogoliubov variational approach for the free energy, we go beyond the simple mean-field approximation (MFA) and effective field theory (EFT) at investigating the phase diagram of this model. The present results may clarify important points with respect to the multicritical phenomena in the phase diagram, which are not yet fully resolved, since MFA and EFT yield conflicting results. Phase diagrams in one, two and three dimensions are investigated, and compared with previous ones obtained by employing MFA and EFT. We show how the nature of the phase transition changes as both longitudinal and transverse crystal fields are varied. In addition, the spin-1 Ising model in a transverse crystal field is obtained as a limiting case of zero longitudinal crystal field, and its phase diagram is also analysed carefully. We show analytical expressions for the critical equation at finite as well as at absolute zero temperatures. By means of a Landau expansion of the free energy, we locate tricritical points besides critical ones. Remarkably, quantum tricritical points are found in two and three dimensions. We also study the behaviour of the thermodynamic quantities, namely magnetisation and quadrupole moment, which turn out to be important to define the order and nature of the transitions.

Electromagnetic gauge field interpolation between the instant form and the front form of the Hamiltonian dynamics

We present the electromagnetic gauge field interpolation between the instant form and the front form of the relativistic Hamiltonian dynamics and extend our interpolation of the scattering amplitude presented in the simple scalar field theory to the case of the electromagnetic gauge field theory with the scalar fermion fields known as the sQED theory. We find that the Coulomb gauge in the instant form dynamics (IFD) and the light-front gauge in the front form dynamics, or the light-front dynamics (LFD), are naturally linked by the unified general physical gauge that interpolates between these two forms of dynamics and derive the spin-1 polarization vector for the photon that can be generally applicable for any interpolation angle. Corresponding photon propagator for an arbitrary interpolation angle is found and examined in terms of the gauge field polarization and the interpolating time ordering. Using these results, we calculate the lowest-order scattering processes for an arbitrary interpolation angle in sQED. We provide an example of breaking the reflection symmetry under the longitudinal boost, $P^z \leftrightarrow -P^z$, for the time-ordered scattering amplitude in any interpolating dynamics except the LFD and clarify the confusion in the prevailing notion of the equivalence between the infinite momentum frame (IMF) and the LFD. The particular correlation found in our previous analysis of the scattering amplitude in the simple scalar field theory, coined as the J-shaped correlation, between the total momentum of the system and the interpolation angle persists in the present analysis of the sQED scattering amplitude. We discuss the singular behavior of this correlation in conjunction with the zero-mode issue in the LFD.

The Eynard–Orantin recursion for simple singularities

According to (9) and (19), the ancestor correlators of any semi- simple cohomological field theory satisfy local Eynard-Orantin recursion. In this paper, we prove that for simple singularities, the loca l recursion can be extended to a global one. The spectral curve of the global recursion is an interesting family of Riemann surfaces defined by the invari ant polynomials of the corresponding Weyl group. We also prove that for genus 0 and 1, the free energies introduced in (10) coincide up to some constant factors with respectively the genus 0 and 1 primary potentials of the simple singularity.

Dynamical Generation of Hadronic Resonances

One type of dynamical generation consists in the formation of multiple hadronic resonances from single seed states by incorporating hadronic loop contributions on the level of $s$-wave propagators. Along this line, we study the propagator poles within two models of scalar resonances and report on the status of our work: (i) Using a simple quantum field theory describing the decay of $f_{0}(500)$ into two pions, we may obtain a second, additional pole on the first Riemann sheet below the pion-pion threshold (i.e., a stable state can emerge). (ii) We perform a numerical study of the pole(s) of $a_{0}(1450)$ by using as an input the results obtained in the extended Linear Sigma Model (eLSM). Here, we do not find any additional pole besides the original one, thus we cannot obtain $a_{0}(980)$ as an emerging state. (iii) We finally demonstrate that, although the coupling constants in typical effective models might be large, the next-to-leading-order contribution to the decay amplitude is usually small and can be neglected.

Non-empirical Prediction of the Photophysical and Magnetic Properties of Systems with Open d- and f-Shells Based on Combined Ligand Field and Density Functional Theory (LFDFT)

Despite the important growth of ab initio and computational techniques, ligand field theory in molecular science or crystal field theory in condensed matter offers the most intuitive way to calculate multiplet energy levels arising from systems with open shells d and/or f electrons. Over the past decade we have developed a ligand field treatment of inorganic molecular modelling taking advantage of the dominant localization of the frontier orbitals within the metal-sphere. This feature, which is observed in any inorganic coordination compound, especially if treated by Density Functional Theory calculation, allows the determination of the electronic structure and properties with a surprising good accuracy. In ligand field theory, the theoretical concepts consider only a single atom center; and treat its interaction with the chemical environment essentially as a perturbation. Therefore success in the simple ligand field theory is no longer questionable, while the more accurate molecular orbital theory does in general over-estimate the metal-ligand covalence, thus yields wave functions that are too delocalized. Although LF theory has always been popular as a semi-empirical method when dealing with molecules of high symmetry e.g. cubic symmetry where the number of parameters needed is reasonably small (3 or 5), this is no more the case for molecules without symmetry and involving both an open d- and f-shell (# parameters ∼90). However, the combination of LF theory and Density Functional (DF) theory that we introduced twenty years ago can easily deal with complex molecules of any symmetry with two and more open shells. The accuracy of these predictions from 1(st) principles achieves quite a high accuracy (<5%) in terms of states energies. Hence, this approach is well suited to predict the magnetic and photo-physical properties arbitrary molecules and materials prior to their synthesis, which is the ultimate goal of each computational chemist. We will illustrate the performance of LFDFT for the design of phosphors that produces light similar to our sun and predict the magnetic anisotropy energy of single ion magnets.

Interpolating from Bianchi attractors to Lifshitz and AdS spacetimes

We construct classes of smooth metrics which interpolate from Bianchi attractor geometries of Types II, III, VI and IX in the IR to Lifshitz or $AdS_2 \times S^3$ geometries in the UV. While we do not obtain these metrics as solutions of Einstein gravity coupled to a simple matter field theory, we show that the matter sector stress-energy required to support these geometries (via the Einstein equations) does satisfy the weak, and therefore also the null, energy condition. Since Lifshitz or $AdS_2 \times S^3$ geometries can in turn be connected to $AdS_5$ spacetime, our results show that there is no barrier, at least at the level of the energy conditions, for solutions to arise connecting these Bianchi attractor geometries to $AdS_5$ spacetime. The asymptotic $AdS_5$ spacetime has no non-normalizable metric deformation turned on, which suggests that furthermore, the Bianchi attractor geometries can be the IR geometries dual to field theories living in flat space, with the breaking of symmetries being either spontaneous or due to sources for other fields. Finally, we show that for a large class of flows which connect two Bianchi attractors, a C-function can be defined which is monotonically decreasing from the UV to the IR as long as the null energy condition is satisfied. However, except for special examples of Bianchi attractors (including AdS space), this function does not attain a finite and non-vanishing constant value at the end points.

Analytic approach to nuclear rotational states and the role of spin: A minimal model

We use a simple field theory model to investigate the role of the nucleon spin for the magnetic sum rules associated with the low-lying collective scissors mode in deformed nuclei. Various constraints from rotational symmetry are elucidated and discussed. We put special emphasis on the coupling of the spin part of the M1 operator to the low lying collective modes, and investigate how this coupling changes the sum rules.