Effective Scalar Field Theory Research Articles

A periodic table of effective field theories

We systematically explore the space of scalar effective field theories (EFTs) consistent with a Lorentz invariant and local S-matrix. To do so we define an EFT classification based on four parameters characterizing 1) the number of derivatives per interaction, 2) the soft properties of amplitudes, 3) the leading valency of the interactions, and 4) the spacetime dimension. Carving out the allowed space of EFTs, we prove that exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Using on-shell momentum shifts and recursion relations, we prove that EFTs with arbitrarily soft behavior are forbidden and EFTs with leading valency much greater than the spacetime dimension cannot have enhanced soft behavior. We then enumerate all single scalar EFTs in d < 6 and verify that they correspond to known theories in the literature. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.

Recursion relations from soft theorems

We establish a set of new on-shell recursion relations for amplitudes satisfying soft theorems. The recursion relations can apply to those amplitudes whose additional physical inputs from soft theorems are enough to overcome the bad large-z behaviour. This work is a generalization of the recursion relations recently obtained by Cheung et al for amplitudes in scalar effective field theories with enhanced vanishing soft behaviours, which can be regarded as a special case of those with non-vanishing soft limits. We apply the recursion relations to tree-level amplitudes in various theories, including amplitudes in the Akulov-Volkov theory, amplitudes containing dilatons of spontaneously-broken conformal symmetry.

Effective Field Theories from Soft Limits of Scattering Amplitudes.

We derive scalar effective field theories-Lagrangians, symmetries, and all-from on-shell scattering amplitudes constructed purely from Lorentz invariance, factorization, a fixed power counting order in derivatives, and a fixed order at which amplitudes vanish in the soft limit. These constraints leave free parameters in the amplitude which are the coupling constants of well-known theories: Nambu-Goldstone bosons, Dirac-Born-Infeld scalars, and Galilean internal shift symmetries. Moreover, soft limits imply conditions on the Noether current which can then be inverted to derive Lagrangians for each theory. We propose a natural classification of all scalar effective field theories according to two numbers which encode the derivative power counting and soft behavior of the corresponding amplitudes. In those cases where there is no consistent amplitude, the corresponding theory does not exist.

Explaining the proton radius puzzle with disformal scalars

We analyze the consequences of a disformal interaction between a massless scalar and matter particles in the context of atomic physics. We focus on the displacement of the atomic energy levels that it induces, and in particular the change in the Lamb shift between the 2s and 2p states. We find that the correction to the Lamb shift depends on the mass of the fermion orbiting around the nucleus, implying a larger effect for muonic atoms. Taking the cutoff scale describing the effective scalar field theory close to the QCD scale, we find that the disformal interaction can account for the observed difference in the proton radius of muonic versus electronic hydrogen. Explaining the proton radius puzzle is only possible when the scalar field is embedded in nonlinear theories which alleviate constraints from collider and stellar physics. Short distance properties of the Galileon where nonperturbative effects in vacuum are present ensure that unitarity is preserved in high-energy particle collisions. In matter, the chameleon mechanism alleviates the constraints on disformal interactions coming from the burning rates for stellar objects. We show how to combine these two properties in a single model which renders the proposed explanation of the proton radius puzzle viable.

Random-field-like criticality in glass-forming liquids.

We introduce an approach to derive an effective scalar field theory for the glass transition; the fluctuating field is the overlap between equilibrium configurations. We apply it to the case of constrained liquids for which the introduction of a conjugate source to the overlap field was predicted to lead to an equilibrium critical point. We show that the long-distance physics in the vicinity of this critical point is in the same universality class as that of a paradigmatic disordered model: the random-field Ising model. The quenched disorder is provided here by a reference equilibrium liquid configuration. We discuss to what extent this field-theoretical description and the mapping to the random field Ising model hold in the whole supercooled liquid regime, in particular, near the glass transition.

Theoretical constraints on kinetic k-essence dark energy model in El-Nabulsi fractional action cosmology

In this work, we considered an effective scalar field theory described by a Lagrangian with a noncanonical kinetic term, which leads to accelerated expansion in the present Universe and is known as k-essence in the framework of the fractional action cosmology recently introduced by El-Nabulsi. We have chosen a particular ansatz for the scale factor and the scalar field, in which both are described as a power-law of the time, t. We have studied the behavior of some cosmological quantities in other models to obtain some useful information about the model considered. We observed that the equation of state parameter, w, has decreasing behavior and it never crosses the phantom divide line (i.e., w = –1). Studying the statefinder pair {r, s} and {w, w′}, we observed that the model considered is able to obtain the ΛCDM phase of the Universe.

Equivalence between Born–Infeld tachyon and effective real scalar field theories for brane structures in warped geometry

An equivalence between Born–Infeld and effective real scalar field theories for brane structures is built in some specific warped space–time scenarios. Once the equations of motion for tachyon fields related to the Born–Infeld action are written as first-order equations, a simple analytical connection with a particular class of real scalar field superpotentials can be found. This equivalence leads to the conclusion that, for a certain class of superpotentials, both systems can support identical thick brane solutions as well as brane structures described through localized energy densities, T00(y), in the 5th dimension, y. Our results indicate that thick brane solutions realized by the Born–Infeld cosmology can be connected to real scalar field brane scenarios which can be used to effectively map the tachyon condensation mechanism.

A discussion on Lorentz preserving scalar fields in Lorentz violating theory

Lorentz symmetry can be preserved in effective higher derivative scalar field theories containing a constant vector that breaks Lorentz invariance of flat spacetime, through the choice of special field configurations. These fields do satisfy the equations of motion, yielding cubic dispersion relations analogous to those derived earlier. Moreover, the Lie algebra of the Lorentz group can be realised on these fields.

Power suppression from disparate mass scales in effective scalar field theories of inflation and quintessence

A scalar potential coupled to other fields of large disparate masses will exhibit power suppression of the quantum loop corrections from these massive fields. Quintessence fields in the dark energy regime and inflaton fields during inflation often have a very large background field value. Thus any other field with its mass dependent on the quintessence/inflaton background field value through a moderate coupling will become very massive during the dark energy/inflation phase and its quantum corrections to the scalar effective potential will be suppressed. This concept is developed in this paper using the decoupling theorem. The problem then reduces to a quantitative question of the size of suppression effects within the parameter space of coupling constants, scalar field background value and renormalization scale. Some numerical examples are presented both for inflation and quintessence, but the approach is general and can be applied to any scalar field effective potential. The consequences to dark energy of the decoupling effect developed here is that the quintessence field need not just be an incredibly weakly interacting field, often included as an add-on to generate dark energy and having no other purpose. Instead, this quintessence field could play a central role in the particle physics dynamics at early times and then the other fields simply decouple from it at late times before the onset of the dark energy phase. For inflation a consequence is coupling of the inflaton to other heavy fields can be much larger.

Forces exerted by a correlated fluid on embedded inclusions

We investigate the forces exerted on embedded inclusions by a fluid medium with long-range correlations, described by an effective scalar field theory. Such forces are the basis for the medium-mediated Casimir-like force. To study these forces beyond thermal average, it is necessary to define them in each microstate of the medium. Two different definitions of these forces are currently used in the literature. We study the assumptions underlying them. We show that only the definition that uses the stress tensor of the medium gives the sought-after force exerted by the medium on an embedded inclusion. If a second inclusion is embedded in the medium, the thermal average of this force gives the usual Casimir-like force between the two inclusions. The other definition can be used in the different physical case of an object that interacts with the medium without being embedded in it. We show in a simple example that the two definitions yield different results for the variance of the Casimir-like force.

PARTICLE PRODUCTION AND TRANSPLANCKIAN PROBLEM ON THE NONCOMMUTATIVE PLANE

We consider the coherent state approach to noncommutativity and we derive from it an effective quantum scalar field theory. We show how the noncommutativity can be taken into account by a suitable modification of the Klein–Gordon product, and of the equal-time commutation relations. We prove that, in curved space, the Bogoliubov coefficients are unchanged, hence the number density of the produced particle is the same as for the commutative case. What changes though is the associated energy density, and this offers a simple solution to the transplanckian problem.

Kaon condensation in the color–flavor-locked phase of quark matter, the Goldstone theorem, and the 2PI Hartree approximation

At very high densities, QCD is in the color–flavor-locked phase, which is a color-superconducting phase. The diquark condensates break chiral symmetry in the same way as it is broken in vacuum QCD and gives rise to an octet of pseudo-Goldstone bosons and a superfluid mode. The lightest of these are the charged and neutral kaons. For energies below the superconducting gap, the kaons are described by an O ( 2 ) × O ( 2 ) -symmetric effective scalar field theory with chemical potentials. We use this effective theory to study Bose-condensation of kaons and their properties as functions of the temperature and the chemical potentials. We use the 2-particle irreducible effective action formalism in the Hartree approximation. The renormalization of the gap equations and the effective potential is studied in detail and we show that the counterterms are independent of temperature and chemical potentials. We determine the phase diagram and the medium-dependent quasiparticle masses. It is shown that the Goldstone theorem is satisfied to a very good approximation. The effects of imposing electric charge neutrality is examined as well.

Conformal entropy from horizon states: Solodukhin’s method for spherical, toroidal, and hyperbolic black holes inD-dimensional anti-de Sitter spacetimes

A calculation of the entropy of static, electrically charged, black holes with spherical, toroidal, and hyperbolic-compact and oriented horizons, in $D$ spacetime dimensions, is performed. These black holes live in an anti--de Sitter spacetime, i.e., a spacetime with negative cosmological constant. To find the entropy, the approach developed by Solodukhin is followed. The method consists in a redefinition of the variables in the metric, by considering the radial coordinate as a scalar field. Then one performs a $2+(D\ensuremath{-}2)$ dimensional reduction, where the ($D\ensuremath{-}2$) dimensions are in the angular coordinates, obtaining a 2-dimensional effective scalar field theory. This theory is a conformal theory in an infinitesimally small vicinity of the horizon. The corresponding conformal symmetry will then have conserved charges, associated with its infinitesimal conformal generators, which will generate a classical Poisson algebra of the Virasoro type. Shifting the charges and replacing Poisson brackets by commutators, one recovers the usual form of the Virasoro algebra, obtaining thus the level zero conserved charge eigenvalue ${L}_{0}$, and a nonzero central charge $c$. The entropy is then obtained via the Cardy formula.

Self-stabilization of extra dimensions

We show that the problem of stabilization of extra dimensions in Kaluza-Klein type cosmology may be solved in a theory of gravity involving high-order curvature invariants. The method suggested (employing a slow-change approximation) can work with rather a general form of the gravitational action. As examples, we consider pure gravity with Lagrangians quadratic and cubic in the scalar curvature and some more complex ones in a simple Kaluza-Klein framework. After a transition to the 4D Einstein conformal frame, this results in effective scalar field theories with certain effective potentials, which in many cases possess positive minima providing stable small-size extra dimensions. Estimates made in the original (Jordan) conformal frame show that the problem of a small value of the cosmological constant in the present Universe is softened in this framework but is not solved completely.}

Effective field theory forHe4

We introduce an effective scalar field theory to describe the $^{4}\mathrm{He}$ phase diagram, which can be considered as a generalization of the $XY$ model which gives the usual $\ensuremath{\lambda}$ transition. This theory results from a Ginzburg-Landau Hamiltonian with higher order derivatives, which allow one to produce transitions between the superfluid, normal liquid, and solid phases of $^{4}\mathrm{He}$. Mean field and Monte Carlo analyses suggest that this model is able to reproduce the main qualitative features of $^{4}\mathrm{He}$ phase transitions.

Alpha matter on a lattice

We obtain the equation of state of interacting alpha matter and the critical temperature of Bose–Einstein condensation of alpha particles within an effective scalar field theory. We start from a non-relativistic model of uniform alpha matter interacting with attractive two-body and repulsive three-body potentials and reformulate this model as a O ( 2 ) symmetric scalar ϕ 6 field theory with negative quartic and positive sextic interactions. Upon restricting the Matsubara sums, near the temperature of Bose–Einstein condensation, to the zeroth order modes we further obtain an effective classical theory in three spatial dimensions. The phase diagram of the alpha matter is obtained from simulations of this effective field theory on a lattice using local Monte Carlo algorithms.

On the Landau–Ginzburg theory of MAG projected SU(2) lattice gauge theory

Maximal Abelian gauge fixing and subsequent Abelian projection of SU(2) lattice gauge theory defines closed trajectories of magnetic monopoles. These trajectories can be interpreted in terms of an effective scalar field theory of the MAG monopoles using the world line representation of the functional determinants. Employing the monopole world lines detected in the numerical simulation, we show that a scalar bound state exists. The screening mass m of this state properly scales towards the continuum limit. We find m≈1.4 GeV when the string tension σ=440 MeV is used as reference scale.

Construction of an effective Hamiltonian for a three-dimensional Ising universality class.

The asymptotic and preasymptotic critical behavior in fluids, mixtures, and uniaxial magnets is believed to be described by an effective straight phi(4) scalar field theory with suitable, nonuniversal, coupling constants. The critical parameters as well as the extent of crossovers and corrections to the leading critical behavior in physical systems, crucially depends on the choice of these couplings. Here we propose a new method for deriving the effective scalar field theory appropriate to a microscopic model in this universality class. Use is made of the hierarchical reference theory, which implements the basic ideas of Wilson momentum space renormalization group to microscopic Hamiltonians. The effective low-energy field theory is then analyzed by the minimal subtraction scheme of Schloms and Dohm. We discuss the application of this method to the three-dimensional Ising model and to the liquid-vapor phase transition. We make comparison with high-temperature expansion results and with experimental data for rare gas.

New physics and the Landau pole

In scalar field theories the Landau pole is an ultraviolet singularity in the running coupling constant that indicates a mass scale at which the theory breaks down and new physics must intervene. However, new physics at the pole will in general affect the running of the low energy coupling constant, which will in turn affect the location of the pole and the related upper limit (``triviality'' bound) on the low energy coupling constant. If the new physics is strongly coupled to the scalar fields these effects can be significant even though they are power suppressed. We explore the possible range of such effects by deriving the one loop renormalization group equations for an effective scalar field theory with a dimension 6 operator representing the low energy effects of the new physics. As an independent check we also consider a renormalizable model of the high-scale physics constructed so that its low energy limit coincides with the effective theory.

Asymptotic Stability in Geometric σ–models

Geometric σ–models have been defined as purely geometric theories of scalar fields in interaction with gravity. By construction, these theories possess soliton solutions with topologically nontrivial scalar sectors. We perform a detailed analysis of the stability of the effective scalar field theory far from the soliton core. It is shown that the requirement for the asymptotic stability is consistent with the existence of massive, static, spherically symmetric soliton solutions.