Quartic Interaction Term Research Articles

Critical analysis of Goldberger-Wise stabilization of the Randall-Sundrum braneworld scenario

The Goldberger-Wise mechanism of stabilizing modulus in the Randall-Sundrum braneworld, by introducing a bulk scalar field with quartic interaction terms localized at the 3-branes, has been extremely popular as a stabilizing mechanism when the backreaction of the scalar field on the geometry is negligibly small. In this paper we reexamine the mechanism by an exact analysis without resorting to the approximations adopted by Goldberger and Wise. An exact calculation of the stabilization condition indicates the existence of closely spaced minimum and a maximum for the potential and also brings out some new features involved in the context of the stabilization of such braneworld models.

Asymptotic Bethe ansatzS-matrix and Landau–Lifshitz-type effective 2d actions

Motivated by the desire to relate Bethe ansatz equations for anomalous dimensions found on the gauge theory side of the AdS/CFT correspondence to superstring theory on AdS_5 x S5 we explore a connection between the asymptotic S-matrix that enters the Bethe ansatz and an effective two-dimensional quantum field theory. The latter generalizes the standard ``non-relativistic'' Landau-Lifshitz (LL) model describing low-energy modes of ferromagnetic Heisenberg spin chain and should be related to a limit of superstring effective action. We find the exact form of the quartic interaction terms in the generalized LL type action whose quantum S-matrix matches the low-energy limit of the asymptotic S-matrix of the spin chain of Beisert, Dippel and Staudacher (BDS). This generalises to all orders in the `t Hooft coupling an earlier computation of Klose and Zarembo of the S-matrix of the standard LL model. We also consider a generalization to the case when the spin chain S-matrix contains an extra ``string'' phase and determine the exact form of the LL 4-vertex corresponding to the low-energy limit of the ansatz of Arutyunov, Frolov and Staudacher (AFS). We explain the relation between the resulting ``non-relativistic'' non-local action and the second-derivative string sigma model. We comment on modifications introduced by strong-coupling corrections to the AFS phase. We mostly discuss the SU(2) sector but also present generalizations to the SL(2) and SU(1|1) sectors, confirming universality of the dressing phase contribution by matching the low-energy limit of the AFS-type spin chain S-matrix with tree-level string-theory S-matrix.

Sigma model Lagrangian for the Heisenberg group

We study the Lagrangian for a sigma model based on the non-compact Heisenberg group. A unique feature of this model—unlike the case for compact Lie groups—is that the Lagrangian has to be regulated since the trace over the Heisenberg group is otherwise divergent. The resulting theory is a real Lagrangian with a quartic interaction term. In particular, in D=2 space–time dimensions, after a few non-trivial transformations, the Lagrangian is shown to be equivalent, at the classical level, to a complex cubic Lagrangian. A one-loop computation confirms that the quartic and cubic Lagrangians are equivalent at the quantum level as well.The complex Lagrangian is known to be classically equivalent to the SU(2) sigma model, with the equivalence breaking down at the quantum level. An explanation of this well-known results emerges from the properties of the Heisenberg sigma model.

CLOSED STRING TACHYONS ON C/ZN

We analyze the condensation of closed string tachyons on the C/ZN orbifold. We construct the potential for the tachyons up to the quartic interaction term in the large N limit. In this limit there are near marginal tachyons. The quartic coupling for these tachyons is calculated by subtracting from the string theory amplitude for the tachyons, the contributions from the massless exchanges, computed from the effective field theory. We argue that higher point interaction terms are also of the same order in 1/N as the quartic term and are necessary for existence of the minimum of the tachyon potential that is consistent with earlier analysis.

Replica Symmetry Breaking in Critical Phenomena in Long-Range Disordered Ferromagnets

The replica symmetry breaking (RSB) is investigated in -component ferromagnetic spin systems with a long-range disorder, with a correlation function obeying a power law . The Landau–Ginzburg Hamiltonian with an RSB quartic interaction term is studied, with the renormalization-group expansion in and , where is the spatial dimension. It is shown that the long-range disorder fixed point found previously is unstable under the perturbation of RSB for and stable for . The RSB fixed points are calculated and there is no physical stable fixed point for .

Replica symmetry breaking in the critical behavior in the m-component ferromagnetic spin systems with a short-range disorder

We investigate the replica symmetry breaking (RSB) in m-component ferromagnetic spin systems with a short-range disorder. Using ε-expansion the Landau–Ginzburg Hamiltonian with a RSB quartic interaction term is studied, where ε=4− d, d is the spatial dimension. The differential recursion relations of renormalization group (RG) are derived to the second order of ε. The replicon eigenvalue, which is a simple way to investigate the stability with respect to the continuous RSB modes, is defined. The fixed points and their eigenvalues are obtained. For m< m c =4 there is no stable fixed point. For m> m c , we find a stable fixed point, which is not only stable in the one-step RSB subspace but also stable with respect to the continuous RSB. However, it is unphysical. For m> m c only the pure fixed point is physical and stable.

Transport theory of massless fields

Using the Schwinger-Keldysh technique we discuss how to derive the transport equations for the system of massless quantum fields. We analyze the scalar field models with quartic and cubic interaction terms. In the ${\ensuremath{\varphi}}^{4}$ model the massive quasiparticles appear due to the self-interaction of massless bare fields. Therefore, the derivation of the transport equations strongly resembles one of the massive fields, but the subset of diagrams which provides the quasiparticle mass has to be resummed. The kinetic equation for the finite width quasiparticles is found, where, except for the mean-field and collision terms, there are terms which are absent in the standard Boltzmann equation. The structure of these terms is discussed. In the massless ${\ensuremath{\varphi}}^{3}$ model the massive quasiparticles do not emerge and presumably there is no transport theory corresponding to this model. It is not surprising since the ${\ensuremath{\varphi}}^{3}$ model is, in any case, ill defined.

BLACK HOLES IN TWO-DIMENSIONAL DILATON GRAVITY AND NONLINEAR KLEIN-GORDON SOLITON

Two-dimensional dilaton gravity coupled to a Klein-Gordon matter field with a quartic interaction term is considered. The theory has a classical solution which exhibits black hole formation by a soliton. The geometry of a black hole induced by a soliton is investigated.

Effective action for high-energy scattering in gravity.

The multi-Regge effective action is derived directly from the linearized gravity action. After excluding the redundant field components we separate the fields into momentum modes and integrate over modes which correspond neither to the kinematics of scattering nor to that of exchanged particles. The effective vertices of scattering and of particle production are obtained as sums of the contributions from the triple and quartic interaction terms and the fields in the effective action are defined in terms of the two physical components of the metric fluctuation.

Effective hamiltonians for 1/ N expansion in two-dimensional QCD

We discuss the general structure of effective hamiltonians for systematic 1/ N expansion in QCD using the light-cone quantization. These are second-quantized hamiltonians acting on the Fock space of mesons and glueballs defined by the solution of the N = ∞ problem. In the two-dimensional case we find only cubic and quartic interaction terms, and give explicit expressions for the vertex functions as integrals of solutions of 't Hooft equation. As examples of possible applications of our formalism, we study 1/ N corrections to meson mass and form factors for decays of Q q ̄ states, recently discussed by Grinstein and Mende in the large- N limit. We find that 1/ N is a good small expansion parameter.

New contributions to the cosmological constant.

We show that the quantized gravitino sector of N=1, D=11 supergravity theory leads to new contributions to the four-dimensional cosmological constant in addition to the one coming from the field strength of the three-index totally antisymmetric tensor field. These new contributions arise from the vacuum expectation values of the different auxiliary fields introduced in order to eliminate the quartic gravitino interaction terms.

Manifestly covariant field theory of interacting string II

Abstract A manifestly covariant field theory is constructed for the interacting bosonic open string. A very simple string action is presented which is invariant under an inhomogeneous nilpotent BRS transformation. The on-shell scattering amplitudes in this theory reproduce the Koba-Nielsen amplitudes at the tree level, aside from a contributions from a necessary quartic interaction term.

Manifestly covariant field theory of interacting string I

A manifestly covariant field theory is constructed for the interacting bosonic open string. A very simple string action is presented which is invariant under an inhomogeneous nilpotent BRS transformation. The on-shell scattering amplitudes in this theory reproduce the Koba-Nielsen amplitudes at the tree level, aside from a contributions from a necessary quartic interaction term.

On the continuum limit of D = 4 lattice φ4 theory

The renormalization group structure of d = 4, φ 4 theory is studied in real space. The theory is simulated by MC techniques on a 16 4 lattice for various positive values of the bare φ 4 coupling at the corresponding critical point. Block-spin transformations to size 8 4 and 4 4 are performed and the resulting flow of couplings is determined in a space of 6 quadratic and 18 quartic interaction terms. The results demonstrate that the quartic couplings are not relevant for the long distance behaviour. The RG trajectories on the critical surface all move towards a common fixed point depending only on the type of block-spin transformation applied. The critical exponents are compatible with gaussian values, the continuum limit is that of a non-interacting boson theory.

Renormalization of Yang-Mills theory in the Abelian gauge.

Renormalization of pure Yang-Mills theory is studied in the so-called Abelian gauge, a special bilinear gauge with a favored role given to a certain Abelian subgroup from the full non-Abelian gauge group. Renormalization in this gauge exhibits some unusual features---notably, different wave-function renormalizations are necessary for gauge fields with different ``Abelian'' charges and quartic ghost interaction terms are generated as renormalization counterterms. Despite these difficulties we show, through a careful analysis of the Becchi-Rouet-Stora transformation properties of the effective action, that Yang-Mills theory can be consistently renormalized in this gauge. Possible physical applications of this type of gauge (and its generalization which renders a favored role to a certain non-Abelian subgroup from the given gauge group) are noted briefly.

Critical dynamics of inhomogeneous superconducting films

The Gaussian-random model for the critical dynamics in inhomogeneous superconducting films is augmented by including the quartic interaction term in the free-energy functional. Within the Hartree approximation a self-consistent calculation of the order-parameter relaxation rate $\ensuremath{\Gamma}$ is presented. The temperature dependence of $\ensuremath{\Gamma}$ exhibits a pronounced change for various values of the Ginzburg critical width. A comparison with an experiment on Al-${\mathrm{Al}}_{2}$${\mathrm{O}}_{3}$-Pb junction is presented and the validity of the Gaussian-random model for this specific experiment is demonstrated.

Higgs model and supersymmetry

The Higgs model can be made supersymmetric, provided a Dirac spinor is added, and the quartic interaction term in the Lagrangian density is —(e2/2)(ϕ†φ)2, wheree is the gauge coupling constant. The model describes a vector, a Dirac spinor and a real scalar; it depends only on two arbitrary parameters,m ande. As a gauge-invariant model, it can be studied in a Wess-Zumino gauge, or in a supersymmetric gauge. It can also be obtained as a theory of a self-interacting vector multiplet. Finally, it is suggested that a scalar particle may be associated with the photon and the two neutrinos in the theory of weak and electromagnetic interactions.

Renormalization group approach to structural phase transition

Structural phase transitions of second order which are driven by a soft optic mode are studied by means of a normalization group approach on a lagrangian with a quartic interaction term. An effective lagrangian for the propagation of the soft modes is derived which incorporates the effect of the acoustic modes in temperature-dependent bare coupling constants and a series of n-point interaction terms. The theory describes phase transitions which are driven by Brillouin centre and corner modes. It is shown that the strongest infrared divergences result from the quartic interaction of Leff. This leads to a Heisenberg-type problem with a finite coupling constant the critical coefficients of which are gamma =1.375 and eta =0.043. The results are discussed for the cubic-tetragonal (para-antiferroelectric) phase transition of SrTiO3. Good agreement with recent EPR linewidth measurements is obtained.