High Momentum Modes Research Articles

Lagrangian space consistency relation for large scale structure

Consistency relations, which relate the squeezed limit of an (N+1)-point correlation function to an N-point function, are non-perturbative symmetry statements that hold even if the associated high momentum modes are deep in the nonlinear regime and astrophysically complex. Recently, Kehagias & Riotto and Peloso & Pietroni discovered a consistency relation applicable to large scale structure. We show that this can be recast into a simple physical statement in Lagrangian space: that the squeezed correlation function (suitably normalized) vanishes. This holds regardless of whether the correlation observables are at the same time or not, and regardless of whether multiple-streaming is present. The simplicity of this statement suggests that an analytic understanding of large scale structure in the nonlinear regime may be particularly promising in Lagrangian space.

Trapping light into high orbital momentum modes of fiber tapers.

A tapered cylindrical dielectric optical waveguide acts as a high quality factor white-light cavity providing high field concentration as well as long optical group delay. It is possible to optimize shape of a lossless taper to suppress reflection of the input light and to achieve infinitely high field concentration. These tapers can be used in sensing and optoelectronics applications instead of conventional microcavities.

Power spectrum and non-Gaussianities in anisotropic inflation

We study the planar regime of curvature perturbations for single field inflationary models in an axially symmetric Bianchi I background. In a theory with standard scalar field action, the power spectrum for such modes has a pole as the planarity parameter goes to zero. We show that constraints from back reaction lead to a strong lower bound on the planarity parameter for high-momentum planar modes and use this bound to calculate the signal-to-noise ratio of the anisotropic power spectrum in the CMB, which in turn places an upper bound on the Hubble scale during inflation allowed in our model. We find that non-Gaussianities for these planar modes are enhanced for the flattened triangle and the squeezed triangle configurations, but show that the estimated values of the fNL parameters remain well below the experimental bounds from the CMB for generic planar modes (other, more promising signatures are also discussed). For a standard action, fNL from the squeezed configuration turns out to be larger compared to that from the flattened triangle configuration in the planar regime. However, in a theory with higher derivative operators, non-Gaussianities from the flattened triangle can become larger than the squeezed configuration in a certain limit of the planarity parameter.

Revisiting the spectrum of a scalar field in an anisotropic universe

We revisit the issue on signatures of pre-inflationary background anisotropy by considering the quantization of a massless and minimally coupled scalar field in an axially symmetric Kasner background, mimicking cosmological perturbations. We show that the power spectrum of the scalar field fluctuation has a negligible difference from the standard inflation in the non-planar directions, but it has a sharp peak around the symmetry plane. For the non-planar high-momentum modes, we use the WKB approximation for the first period and the asymptotic approximation based on the de Sitter solution for the next period. At the boundary, two mode functions have the same accuracy with error of $O({H_{i}}/k)$. We calculate the approximation up to the order of $({H_{i}}/k)^6$ and show that the power spectrum of the scalar field fails to get corrections until we execute the approximation up to $6^{\rm th}$ order.

Nonperturbative resummation of de Sitter infrared logarithms in the large-Nlimit

We study the O(N) scalar field theory with quartic self-coupling in de Sitter space. When the field is light in units of the expansion rate, perturbative methods break down at very low momenta due to large infrared logarithmic terms. Using the nonperturbative large-N limit, we compute the four-point vertex function in the deep infrared regime. The resummation of an infinite series of perturbative (bubble) diagrams leads to a modified power law which is analogous to the generation of an anomalous dimension in critical phenomena. We discuss in detail the role of high momentum (subhorizon) modes, including the issue of renormalization, and show that they influence the dynamics of infrared (superhorizon) modes only through a constant renormalization factor. This provides an explicit example of effective decoupling between high and low energy physics in an expanding space-time.

Non-Gaussianities in the cosmological perturbation spectrum due to primordial anisotropy II

We continue to investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon well after isotropization. The late time dynamics of these modes is characterized by a non-Bunch Davies vacuum state which encodes all the information about initial anisotropy in the background space-time. We observe that, unlike the non-planar momenta, there exist regimes of planar momenta for which scale invariance of the power spectrum is strongly broken. This regime of planar momenta gives rise to enhanced non-Gaussianity in certain squeezed triangle configurations, although the enhancement of the fNL parameter is limited by the breakdown of linear perturbation theory at ``exact planarity". Finally, we demonstrate that for the range of planar modes for which scale invariance of the power spectrum is preserved, non-Gaussianity in the curvature perturbation spectrum is naturally constrained to be extremely small.

Non-gaussianities in the cosmological perturbation spectrum due to primordial anisotropy

We investigate possible signatures of a pre-inflationary anisotropic phase in two-point and three-point correlation functions of the curvature perturbation for high-momentum modes which exit the horizon well after isotropization. In this momentum regime, the early time dynamics admits a WKB description and the late time dynamics can be described in terms of a non-Bunch Davies vacuum state which encodes the information of initial anisotropy in the background spacetime. We compute the bi-spectrum for curvature perturbation in a canonical single-field action with and without higher derivative operators. We show that the bi-spectrum at late times, in either case, is enhanced for a flattened triangle configuration as well as a squeezed triangle configuration and compute the corresponding fNL parameters. The angular dependence and the particular momentum dependence of the fNL parameter appear as distinctive features of background anisotropy at early times.

An analytic approach to perturbations from an initially anisotropic universe

We present the analytic forms for the spectra of the cosmological perturbations from an initially anisotropic universe for the high momentum modes in the context of WKB approximations, as the continuation of the work [29]. We consider the Einstein gravity coupled to a light scalar field. We then assume that the scalar field has the zero velocity initially and then slowly rolls down on the potential toward the origin. In the slow-roll approximations, the Kasner-de Sitter universe with a planar symmetry is a good approximation as the background evolution. Quantization of the perturbations in the adiabatic vacuum, which we call the anisotropic vacuum, is carried out. For non-planar high momentum modes whose comoving momentum component orthogonal to the plane is bigger than the Hubble parameter at the inflationary phase, the WKB approximation is valid for the whole stage of the isotropization. On the other hand, the planar modes whose comoving momentum component orthogonal to the plane is comparable to the Hubble parameter, is amplified during the process of the anisotropic expansion. In the final gravitational wave spectra, we find that there is an asymmetry between the two polarizations of the gravitational wave because the initial mode mixing does not vanish.

Confinement from semiclassical gluon fields in [formula omitted] gauge theory

The infrared structure of SU ( 2 ) Yang–Mills theory is studied by means of lattice gauge simulations using a new constrained cooling technique. This method reduces the action while all Polyakov lines on the lattice remain unchanged. In contrast to unconstrained cooling, quark confinement remains intact. A study of the Hessian of the Yang–Mills action shows that low action (semi-)classical configurations can be achieved, with a characteristic splitting between collective modes and higher momentum modes. Besides confinement, the semiclassical configurations also support the topological susceptibility and generate spontaneous breakdown of chiral symmetry. We show that they possess a cluster structure of locally mainly (anti-)selfdual objects. By contrast to an instanton or a meron medium, the topological charge of individual clusters is smoothly distributed.

Decoupling in the similarity renormalization group for nucleon-nucleon forces

Decoupling via the similarity renormalization group (SRG) of low-energy nuclear physics from high-energy details of the nucleon-nucleon interaction is examined for two-body observables and few-body binding energies. The universal nature of this decoupling is illustrated and errors from suppressing high-momentum modes above the decoupling scale are shown to be perturbatively small.

The fermion spectrum in braneworld collisions

In braneworld collisions fermions originally localised on one brane can be transferred to another brane, or to a space-time boundary. By modelling branes as scalar field kinks we bounce them off boundaries and study resulting effects according to a braneworld observer. Extending on our previous work, we numerically compute the spectrum of excitations of fermion modes localised on the brane and boundary, in terms of the momentum k along the brane dimensions. We find that the spectrum depends strongly on collision velocity and fermion-scalar coupling. Also, high-momentum modes tend to ``fall off'' the kinks and become delocalised radiation.

Non-abelian plasma instabilities for strong anisotropy

We numerically investigate gauge field instabilities in anisotropic SU(2) plasmas using weak field initial conditions. The growth of unstable modes is stopped by non-abelian effects for moderate anisotropy. If we increase the anisotropy the growth continues beyond the non-abelian saturation bound. We find strong indications that the continued growth is not due to over-saturation of infrared field modes, but instead due to very rapid growth of high momentum modes which are not unstable in the weak field limit. The saturation amplitude strongly depends on the initial conditions. For strong initial fields we do not observe the sustained growth.

Nonperturbative renormalization group and momentum dependence ofn-point functions. I

We present an approximation scheme to solve the nonperturbative renormalization group equations and obtain the full momentum dependence of the n-point functions. It is based on an iterative procedure where, in a first step, an initial ansatz for the n-point functions is constructed by solving approximate flow equations derived from well motivated approximations. These approximations exploit the derivative expansion and the decoupling of high momentum modes. The method is applied to the O(N) model. In leading order, the self-energy is already accurate both in the perturbative and the scaling regimes. A stringent test is provided by the calculation of the shift DeltaTc in the transition temperature of the weakly repulsive Bose gas, a quantity which is particularly sensitive to all momentum scales. The leading order result is in agreement with lattice calculations, albeit with a theoretical uncertainty of about 25%.

UV/IR MIXING IN NONCOMMUTATIVE FIELD THEORIES AND OPEN–CLOSED STRING DUALITY

In this paper we study the phenomenon of UV/IR mixing in noncommutative field theories from the point of view of worldsheet open–closed duality in string theory. New infrared divergences in noncommutative field theories arise as a result of integrating over high momentum modes in the loops. These are believed to come from integrating out additional bulk closed string modes. We analyze this issue in detail for the bosonic theory and further for the supersymmetric theory on the C2/Z2 orbifold. We elucidate on the exact role played by the constant background B-field in this correspondence.

Aspects of open-closed duality in a background B-field, II

It was shown in [hep-th/0503009], in the context of bosonic theory that the IR singular terms that arise as a result of integrating out high momentum modes in nonplanar diagrams of noncommutative gauge theory can be recovered from low lying tree-level closed string exchanges. This follows as a natural consequence of world-sheet open-closed string duality. Here using the same setup we study the phenomenon for noncommutative ${\cal N}=2$ gauge theory realised on a $D_3$ fractional brane localised at the fixed point of $C^2/Z_2$. The IR singularities from the massless closed string exchanges are exactly equal to those coming from one-loop gauge theory. This is as a result of cancellation of all contributions from the massive modes.

Lattice QCD with suppressed high momentum modes of the Dirac operator

Lattice fermions in five Euclidean dimensions and the corresponding effective theory in four dimensions are defined. The main properties of these theories include the suppression of high momentum modes of the lattice Dirac operator and their ability to continuously interpolate between quenched and dynamical fermions. In particular, the standard formulation of lattice QCD can be viewed as a limiting case of the theory.

Symmetry breaking and false vacuum decay after hybrid inflation

We discuss the onset of symmetry breaking from the false vacuum in generic scenarios in which the mass squared of the symmetry breaking (Higgs) field depends linearly with time, as it occurs, via the evolution of the inflaton, in models of hybrid inflation. We show that the Higgs fluctuations evolve from quantum to classical during the initial stages. This justifies the subsequent use of real-time lattice simulations to describe the fully nonperturbative and nonlinear process of symmetry breaking. The early distribution of the Higgs field is that of a smooth classical Gaussian random field, and consists of lumps whose shape and distribution is well understood analytically. The lumps grow with time and develop into ``bubbles'' which eventually collide among themselves, thus populating the high momentum modes, in their way towards thermalization at the true vacuum. With the help of some approximations we are able to provide a quasianalytic understanding of this process.

Computational methods for UV-suppressed fermions

Lattice fermions with suppressed high momentum modes solve the ultraviolet slowing down problem in lattice QCD. This paper describes a stochastic evaluation of the effective action of such fermions. The method is a based on the Lanczos algorithm and it is shown to have the same complexity as in the case of standard fermions.

The structure of nuclear systems derived from low momentum nucleon–nucleon potentials

Various nuclear structure observables are evaluated employing low-momentum nucleon–nucleon (NN) potentials V low- k derived from the CD-Bonn and Nijmegen NN interactions V NN. By construction, the high momentum modes of the original V NN are integrated out in V low- k , with the requirement that the deuteron binding energy and low energy phase shifts of V NN are exactly reproduced. Using this interaction, we evaluate the bulk properties (binding energy and saturation density) of nuclear matter and finite nuclei, in particular their dependence on the cut-off parameter. We also study the pairing gap and the residual interaction in nuclear matter in terms of the Landau parametrization. At low and medium densities, the HF and BHF binding energies for nuclear matter calculated with the V low- k 's derived from the CD-Bonn and Nijmegen potentials are nearly identical. The pairing gaps and Landau parameters derived from V low- k are remarkably close to those given by the full-space V NN. The V low- k interactions, however, fail to reproduce the saturation property of nuclear matter at higher densities if the cut-off for the high momentum modes is assumed density independent.

DC and microwave fluctuational conductivity of anisotropic superconductors

We present measurements of the dc and microwave excess conductivity above Tc in anisotropic superconducting cuprates and MgB2. When temperature raises well above Tc, both the dc and microwave excess conductivities drop much faster than predicted by the well-established Gaussian theory. We introduce a spectral cutoff in the calculation of the finite-frequency fluctuational conductivity in order to suppress the contribution of high-momentum modes at high temperatures. We find that our data are well described by the model for appropriate dimensionalities.