Quartic Interaction Research Articles

Spontaneous scalarization in (A)dS gravity at zero temperature

We study spontaneous scalarization of electrically charged extremal black holes in D ≥ 4 spacetime dimensions. Such a phenomenon is caused by the symmetry breaking due to quartic interactions of the scalar — Higgs potential and Stueckelberg interaction with electromagnetic and gravitational fields, characterized by the couplings a and b, respectively. We use the entropy representation of the states in the vicinity of the horizon, apply the inverse attractor mechanism for the scalar field, and analyze analytically the thermodynamic stability of the system using the laws of thermodynamics. As a result, we obtain that the scalar field condensates on the horizon only in spacetimes which are asymptotically non-flat, Λ ≠ 0 (dS or AdS), and whose extremal black holes have non-planar horizons k = ±1, provided that the mass m of the scalar field belongs to a mass interval (area code) different for each set of the boundary conditions specified by (Λ, k). A process of scalarization describes a second order phase transition of the black hole, from the extremal Reissner-Nordström (A)dS one, to the corresponding extremal hairy one. Furthermore, for the transition to happen, the interaction has to be strong enough, and all physical quantities on the horizon depend at most on the effective Higgs-Stueckelberg interaction am2− 2b. Most of our results are general, valid for any parameter and any spacetime dimension.

UV divergences, RG equations and high energy behaviour of the amplitudes in the Wess-Zumino model with quartic interaction

We analyse the UV divergences for the scattering amplitudes in the Wess-Zumino SUSY model with the quartic superpotential. We argue that the only divergent amplitudes are those with four external legs. Within the superfield formalism, we calculate the corresponding Feynman diagrams and evaluate their leading divergences up to 4 loop order of PT. Then we construct recurrence relations that connect the leading UV divergences in subsequent orders of perturbation theory. These recurrence relations allow us to calculate the leading divergences in a pure algebraic way starting from the one loop contribution. We check that the obtained relations correctly reproduce the lower order diagrams evaluated explicitly. At last, we convert the recurrence relations into the RG equations that have integro-differential form. Solving these equations for a particular sequence of diagrams, we find out the high energy behaviour of the amplitude. We then argue that the full amplitude has a similar behaviour with the key feature of the existence of a pole in the s-channel corresponding to a state with a mass ∼ 1/g, where g is the original dimensionfull coupling of the theory. We find out the this state is actually a ghost one similar to the Landau pole in scalar theory.

Renormalization in TT¯ -deformed nonintegrable theories

That the exact quantum S-matrix of $\text{T}\bar{\text{T}}$-deformed field theories is known has interesting consequences for their perturbative renormalisation. Recent investigations into the interplay between renormalisation and integrable deformations have focused on those cases where the (undeformed) seed theories are integrable. In this paper, we study the perturbative renormalisation of non-integrable $\text{T}\bar{\text{T}}$-deformed field theories, focusing on a theory of scalars with a quartic interaction. We show that in this theory, the 4-point 1-loop S-matrix exhibits features similar to its integrable cousins. We also carry out a similar analysis for the case of an integrable quantum field theory comprising a pair of chiral bosons. Our discussion of this latter theory supplies the first explicit example of a perturbative field theory computation in the formalism due to Sen.

Color-flavor reflection in the continuum limit of two-dimensional lattice gauge theories with scalar fields.

We address the interplay between local and global symmetries in determining the continuum limit of two-dimensional lattice scalar theories characterized by SO(N_{c}) gauge symmetry and non-Abelian O(N_{f}) global invariance. We argue that, when a quartic interaction is present, the continuum limit of these models corresponds in some cases to the gauged nonlinear σ model field theory associated with the real Grassmannian manifold SO(N_{f})/(SO(N_{c})×SO(N_{f}-N_{c})), which is characterized by the invariance under the color-flavor reflection N_{c}↔N_{f}-N_{c}. Monte Carlo simulations and finite-size scaling analyses, performed for N_{f}=7 and several values of N_{c}, confirm the emergence of the color-flavor reflection symmetry in the scaling limit and support the identification of the continuum limit.

Boundedness from below of SU(n) potentials

Vacuum stability requires that the scalar potential is bounded from below. Whether or not this is true depends on the scalar quartic interactions alone, but even so the analysis is arduous and has only been carried out for a limited set of models. Complementing the existing literature, this work contains the necessary and sufficient conditions for two SU(n) invariant potentials to be bounded from below. In particular, expressions are given for models with the fundamental and the 2-index (anti)symmetric representations of this group. A sufficient condition for vacuum stability is also provided for models with the fundamental and the adjoint representations. Finally, some considerations are made concerning the model with the gauge group SU(2) and the scalar representations $\boldsymbol{1}$, $\boldsymbol{2}$ and $\boldsymbol{3}$; such a setup is particularly important for neutrino mass generation and lepton number violation.

A wavelet-based set of constructive masses for the Minkowskian Feynman propagator

We continue our pursuit of Minkowskian quantum field theory—specifically, a nonperturbative analysis of the characteristic functional generating the time-ordered Wightman distributions for the quartic scalar field interaction. As in a previous paper, our starting point is the Minkowskian Feynman propagator for the free scalar field theory analyzed by a system of expansion functions in space-time. Here, we choose a significantly different system of expansion functions. We start with an L2-orthonormal wavelet basis {Ψw:w∈W}, where each Ψw has the properties of a Daubechies wavelet in the temporal coordinate and the properties of a Meyer wavelet in the spatial coordinates. We consider the matrix elements Gww′(m) of the mass-m Feynman propagator based on the expansion functions vw=Lw−1Ψw, where Lw denotes the length scale of w∈W. For every finite Λ⊂W, we let GΛ(m) denote the Λ × Λ matrix of such elements. We define a constructive mass to be any value of m such that GΛ(m) is nonsingular for each finite Λ⊂W. We prove that the set of such masses is at least co-countable (although we expect every mass value to be constructive). For an arbitrary constructive mass m and an arbitrary finite Λ⊂W, we rigorously construct the interacting characteristic functional as an integral in amplitudes, where the Λ-cutoff on the quartic interaction is supplemented by a cutoff on the free-field action defined by GΛ(m)−1.

Considerations on anomalous photon and Z-boson self-couplings from the Born–Infeld weak hypercharge action

We investigate the effects of the Born–Infeld action on the Abelian sector of the electroweak model. The consequence of this approach is the emergence of anomalous couplings in the neutral sector of the Z-gauge boson and photon. These new couplings consist of quartic interactions of the photon with the Z-particle, as for example, three-photon-and-one-Z vertex. With that, we obtain the decay width of Z rightarrow 3,gamma from which we impose a bound on the Born–Infeld parameter. Other bounds are also obtained from the photon quartic couplings. Subsequently, we consider the presence of an external uniform magnetic field in connection with this Born–Infeld weak hypercharge model. The magnetic background field yields new kinematic effects, like the kinetic mixing between the photon and the Z-boson, and we obtain thereby the corresponding dispersion relations for the mixed photon-Z-particle system. Finally, we calculate the lowest-order modifications to the interaction energy for the anomalous coupling 3gamma -Z, within the framework of the gauge-invariant but path-dependent variables formalism. Our results show that the interaction energy contains a linear term leading to the confinement of static probe charges. With the help of the potential that comes out, interparticle forces are estimated.

Asymmetric Nuclear Matter in Relativistic Mean-field Models with Isoscalar- and Isovector-meson Mixing

Using the relativistic mean-field model with nonlinear couplings between the isoscalar and isovector mesons, we study the properties of isospin-asymmetric nuclear matter. Not only the vector mixing, ω μ ω μ ρ ν ρ ν , but also the quartic interaction due to the scalar mesons, σ 2 δ 2, is taken into account to investigate the density dependence of nuclear symmetry energy, E sym, and the neutron star properties. It is found that the δ meson increases E sym at high densities, whereas the σ–δ mixing makes E sym soft above the saturation density. Furthermore, the δ meson and its mixing have a large influence on the radius and tidal deformability of a neutron star. In particular, the σ–δ mixing reduces the neutron star radius; thus, the present calculation can simultaneously reproduce the dimensionless tidal deformabilities of a canonical 1.4 M ⊙ neutron star observed from the binary neutron star merger GW170817 and the compact binary coalescence GW190814.

Fast Diffusion leads to partial mass concentration in Keller–Segel type stationary solutions

We show that partial mass concentration can happen for stationary solutions of aggregation–diffusion equations with homogeneous attractive kernels in the fast diffusion range. More precisely, we prove that the free energy admits a radial global minimizer in the set of probability measures which may have part of its mass concentrated in a Dirac delta at a given point. In the case of the quartic interaction potential, we find the exact range of the diffusion exponent where concentration occurs in space dimensions [Formula: see text]. We then provide numerical computations which suggest the occurrence of mass concentration in all dimensions [Formula: see text], for homogeneous interaction potentials with higher power.

On 1D, mathcal{N} = 4 supersymmetric SYK-type models. Part II

This paper is an extension of our last 1D, mathcal{N} = 4 supersymmetric SYK paper [1]. In this paper we introduced the complex linear supermultiplet (CLS), which is “usefully inequivalent” to the chiral supermultiplet. We construct three types of models based on the complex linear supermultiplet containing quartic interactions from modified CLS kinetic term, quartic interactions from 3-pt vertices integrated over the whole superspace, and 2(q − 1)-pt interactions generated via superpotentials respectively. A strong evidence for the inevitability of dynamical bosons for 1D, mathcal{N} = 4 SYK is also presented.

Scaling dimensions at large charge for cubic ϕ3 theory in six dimensions

The $O(N)$ model with scalar quartic interactions at its ultraviolet fixed point, and the $O(N)$ model with scalar cubic interactions at its infra-red fixed point are conjectured to be equivalent. This has been checked by comparing various features of the two models at their respective fixed points. Recently, the scaling dimensions of a family of operators of fixed charge $Q$ have been shown to match at the FPs up to $\cal{O}\left(\frac{1}{N^2}\right)$at leading order (LO) and next-to-leading order (NLO) in $Q$ using a semiclassical computation which is valid to all orders in the coupling. Here we perform a complementary but overlapping comparison using a perturbative calculation in six dimensions, up to three-loop order in the coupling, to compare these critical scaling dimensions beyond NLO in $Q$, in fact to all relevant orders in $Q$. We also obtain the corresponding results at $\cal{O}\left(\frac{1}{N^3}\right)$ for the cubic theory.

Ab initio theory of magnetism in two-dimensional 1T−TaS2

We investigate, using a first-principles density-functional methodology, the nature of magnetism in monolayer $1T$-phase of tantalum disulfide ($1T$-TaS$_2$ ). Magnetism in the insulating phase of TaS$_2$ is a longstanding puzzle and has led to a variety of theoretical proposals including notably the realization of a two-dimensional quantum-spin-liquid phase. By means of non-collinear spin calculations, we derive $\textit{ab initio}$ spin Hamiltonians including two-spin bilinear Heisenberg exchange, as well as biquadratic and four-spin ring-exchange couplings. We find that both quadratic and quartic interactions are consistently ferromagnetic, for all the functionals considered. Relativistic calculations predict substantial magnetocrystalline anisotropy. Altogether, our results suggest that this material may realize an easy-plane XXZ quantum ferromagnet with large anisotropy.

Convexity, large charge and the large-N phase diagram of the φ4 theory

In this note we discuss the phase space of the O(2N) vector model in the presence of a quadratic and a quartic interaction by writing the large-N effective potential using large charge methods in dimensions 2 < D < 4 and 4 < D < 6. Based on a simple discussion of the convexity properties of the grand potential, we find very different behavior in the two regimes: while in 2 < D < 4, the theory is well-behaved, the model in 4 < D < 6 leads to a complex CFT in the UV, consistently with earlier results. We also find a new metastable massive phase in the high-energy regime for the theory on the cylinder.

Melonic Large N Limit of 5-Index Irreducible Random Tensors

We demonstrate that random tensors transforming under rank-5 irreducible representations of mathrm {O}(N) can support melonic large N expansions. Our construction is based on models with sextic (5-simplex) interaction, which generalize previously studied rank-3 models with quartic (tetrahedral) interaction (Benedetti et al. in Commun Math Phys 371:55, 2019. arXiv:1712.00249; Carrozza in JHEP 06:039, 2018. arXiv:1803.02496). Beyond the irreducible character of the representations, our proof relies on recursive bounds derived from a detailed combinatorial analysis of the Feynman graphs. Our results provide further evidence that the melonic limit is a universal feature of irreducible tensor models in arbitrary rank.

Phenomenology of a Born-Infeld extension of the U(1)Y sector at lepton colliders

In this work we perform a non-linear extension of the $U(1)_{\rm Y}$ sector of the Standard Model leading to novel quartic effective interactions between the neutral gauge bosons. We study the induced effects through high-energy processes resulting in three photons, namely, Z-boson decay and electron-positron annihilation. Available experimental data on these processes do not yield viable lower bounds on the mass parameter $\sqrt{\beta}$, but we estimate that the range $\sqrt{\beta} \lesssim m_Z$ could be reliably excluded with better statistics in future $e^- e^+$ colliders. We also discuss neutral gauge-boson scatterings, contextualizing our findings with recent results on anomalous quartic gauge couplings.

Signatures of quartic asymmetric exchange in a class of two-dimensional magnets

Indirect quartic interaction of spins is suggested to play an important role in two dimensional magnets with trigonal prismatic symmetry such as Fe$_3$GeTe$_2$ monolayer. The proposed interaction is described by terms in micromagnetic energy that are linear in magnetization gradients. Such terms enable the stability of non-collinear magnetic textures. We investigate signatures of the quartic interaction in magnon spectra in the presence of anisotropy and external magnetic field. We also show how magnetic spirals, which are induced by the proposed interaction, can be manipulated by external field. Our analysis is based on symmetry considerations and can be used to quantify the quartic interaction strength in experiments with magnetic monolayers.

First order ferroelectric phase transition phenomenon in alkali-phosphate crystal by using Green’s function approach

In this paper, first order phase transition phenomenon in CsH2AsO4 crystal has been theoretically investigated. With the help of a simple PLCM modified model presently Hamiltonian, with the consideration of four body interaction SizSjzSkzSlz, cubic, and quartic phonon anharmonic interactions, and another all possible interactions are added into it. The contribution of pseudo spin parameter <Sz> and <Sx> are also introduced here which accounts for the spontaneous polarisation. It is shown that soft mode frequency, and phase transition phenomenon such as, permittivity, loss tangent, and Cochran’s mode frequency in the vicinity of Curie’s temperature at about 145.5K due to anharmonicity within the crystal. Observed the obtained theoretical consequences of above parameters are in well resembles with the experimental results of earlier authors.

4D effective action from the non-Abelian DBI action with a magnetic flux background

We study a systematic derivation of four dimensional $\mathcal{N}=1$ supersymmetric effective theory from ten dimensional non-Abelian Dirac-Born-Infeld action compactified on a six dimensional torus with magnetic fluxes on the D-branes. We find a new type of matter K\"{a}hler metric while gauge kinetic function and superpotential are consistent with previous studies. For the ten dimensional action, we use a symmetrized trace prescription and focus on the bosonic part up to $\mathcal{O}(F^4)$. In the presence of the supersymmetry, four dimensional chiral fermions can be obtained via index theorem. The new matter K\"{a}hler metric is independent of flavor but depends on the fluxes, 4D dilaton, K\"{a}hler moduli and complex structure moduli, and will be always positive definite if an induced Ramond-Ramond charge of the D-branes on which matters are living are positive. We read the superpotential from an F-term scalar quartic interaction derived from the ten dimensional action and the contribution of the new matter K\"{a}hler metric to the scalar potential which we derive turns out to be consistent with the supergravity formulation.

Mapping between Witten and lightcone string field theories

We propose a transformation between the off-shell field variables of Witten’s open bosonic string field theory and the traditional lightcone string field theory of Kaku and Kikkawa, based on Mandelstam’s interacting string picture. This is accomplished by deforming the Witten vertex into lightcone cubic and quartic vertices, followed by integrating out the ghost and lightcone oscillator excitations from the string field. Surprisingly, the last step does not alter the cubic and quartic interactions and does not generate effective vertices, and leads precisely to Kaku and Kikkawa’s lightcone string field theory.

Modulational stability brought by cubic–quartic interactions of the nearest-neighbor in FK model subjected in a parametrized on-site potential

This work extends to higher-order interactions the results of Nguetcho (2017), in which we discussed only on modulational instability in one-dimensional chain made of atoms, harmonically coupled to their nearest neighbors and subjected to an external on-site potential. Here we investigate the competition between cubic–quartic nonlinearities interactions of the nearest-neighbor and substrate’s deformability, and mainly discuss its impact on the modulational instability of the system. This makes it possible to adapt the theoretical model to a real physical system such as atomic chains or DNA lattices. The governing equation, derived from the modified Frenkel–Kontorova model, is an extended nonlinear Schrödinger equation (eNLS) containing a new higher-order nonlinear term. By employing linear stability analysis, the generic properties of the MI gain spectra of the system are demonstrated. In the presence of the new quartic nonlinearity, the combinations of the system’s parameters open a large variety of gain profiles and instability domains that cannot be explored without the quartic nonlinearity. Direct numerical simulations are performed to support our analytical results, and an excellent agreement is found.