Ghost Fields Research Articles

Ghosts in the matter forms

In this paper we study the matter form of the conformal and super-conformal ghosts action. That is, the ghost fields will be expressed in terms of some scalar and spinor fields. Thus, we obtain a two-dimensional covariant action in the matter form, $i.e.$ $S_g$. The Poincar\'e-like symmetries and various supersymmetries of this covariant action are analyzed. The signatures 10+2 and 11+3 for the total target space of the superstring theory also will be discussed.

Wilson lines in warped space: dynamical symmetry breaking and restoration

The dynamics of Wilson lines integrated along a warped extra dimension has been unknown. We study a five-dimensional SU(N) pure gauge theory with Randall–Sundrum warped compactification on S1/Z2. We clarify the notion of large gauge transformations that are non-periodic on the covering space for this setup. We obtain Kaluza–Klein expansions of gauge and ghost fields for the most general twists and background gauge field configurations, which break the gauge symmetry at classical level in general. We calculate the one-loop effective potential and find that the symmetry corresponding to the subgroup allowing continuous Wilson lines is dynamically restored. The presented method can be directly applied to include extra fields. The connection to dynamical Scherk–Schwarz supersymmetry breaking in warped space is discussed.

A lattice Boltzmann study of non-hydrodynamic effects in shell models of turbulence

A lattice Boltzmann scheme simulating the dynamics of shell models of turbulence is developed. The influence of high-order kinetic modes (ghosts) on the dissipative properties of turbulence dynamics is studied. It is analytically found that when ghost fields relax on the same timescale as the hydrodynamic ones, their major effect is a net enhancement of the fluid viscosity. The bare fluid viscosity is recovered by letting ghost fields evolve on a much longer timescale. Analytical results are borne out by high-resolution numerical simulations. These simulations indicate that the hydrodynamic manifold is very robust towards large fluctuations of non-hydrodynamic fields.

A completely invariant SUSY transform of supersymmetric QED

We study the SUSY breaking of the covariant gauge-fixing term in SUSY QED and consider its correspondence to a breaking of the Lorentz gauge condition by SUSY. Reasoning by analogy with SUSY's violation of the Wess-Zumino gauge, we argue that the SUSY transformation, already modified to preserve the Wess–Zumino gauge, should be further modified by another gauge transformation which restores the Lorentz gauge condition. We derive this modification and use the resulting transformation to derive a Ward identity relating the photon and photino propagators without using ghost fields. Our transformation also fulfils the SUSY algebra, modulo terms that vanish in the Lorentz gauge. We finish with a discussion of how to circumvent our transform's non-local, non-linear nature when deriving higher-order Green's function Ward identities.

Star tracks in the ghost condensate

We consider the infrared modification of gravity by the ghost condensate. Naively, in thisscenario one expects sizable modification of gravity at distances of order 1000 km, providedthat the characteristic timescale of the theory is of the order of the Hubble time. However,we argue that this is not the case. The main physical reason for the masking is the simplefact that the Earth (and any other object in the Universe) has a velocity at least of order10−3c with respect to the rest frame of the ghost condensate. Taken together with strongretardation effects present in the ghost sector, this implies that no observable modificationof the gravitational field of nearby objects occurs. Instead, the physical manifestation ofthe ghost condensate is the presence of ‘star tracks’—narrow regions of spacewith growing gravitational and ghost fields inside—along the trajectory of anymassive object. We briefly discuss the possibilities for observing these tracks.

LINEARIZING N=1 NONLINEAR SUPERSYMMETRY WITH HIGHER DERIVATIVE TERMS OF A NAMBU–GOLDSTONE FERMION

We investigate for N=1 supersymmetry (SUSY) the relation between a scalar supermultiplet of linear SUSY and a nonlinear (NL) SUSY model including apparently pathological higher derivative terms of a Nambu–Goldstone (N-G) fermion besides the Volkov–Akulov (V-A) action. SUSY invariant relations with higher derivative terms of the N-G fermion, which connect the linear and NL–SUSY models, are constructed at leading orders by heuristic arguments. We discuss a higher derivative action of the N-G fermion in the NL–SUSY model, which apparently includes a (Weyl) ghost field. By using this relation, we also explicitly prove an equivalence between the standard NL–SUSY V-A model and our NL–SUSY model with the pathological higher derivatives as an example with respect to the universality of NL–SUSY actions with the N-G fermion.

BRST Symmetry and the Scale Transformation of Ghost Fields in Gauge Theory on NC Spacetime

BRST symmetry is very important to quantize gauge theory and to construct a covariant canonical formulation. It may also be important for gauge theory on noncommutative (NC) spacetime. The BRST symmetry of U(N) gauge theory on NC spacetime has recently been studied by Soroush, who manipulated the component fields of the gauge and fermion fields. We define the BRST transformations of the representation fields of gauge and fermion fields and show its nilpotency in a transparent way. The scale symmetry of ghost fields is also investigated. BRST charge and FP ghost charge are derived and shown to be the generators of the respective symmetries. As a byproduct, it is shown that Noether’s theorem is recovered on NC spacetime by redefining the current.

Extended Hamiltonian Formalism of the Pure Space-Like Axial Gauge Schwinger Model. II

Canonical methods are not sufficient to properly quantize space-like axial gauges. In this paper, we obtain guiding principles which allow the construction of an extended Hamiltonian formalism for pure space-like axial gauge fields. To do so, we clarify the general role residual gauge fields play in the space-like axial gauge Schwinger model. In all the calculations we fix the gauge using a rule, $n{\cdot}A=0$, where $n$ is a space-like constant vector and we refer to its direction as $x_-$. Then, to begin with, we construct a formulation in which the quantization surface is space-like but not parallel to the direction of $n$. The quantization surface has a parameter which allows us to rotate it, but when we do so we keep the direction of the gauge field fixed. In that formulation we can use canonical methods. We bosonize the model to simplify the investigation. We find that the antiderivative, $({\partial}_-)^{-1}$, is ill-defined whatever quantization coordinates we use as long as the direction of $n$ is space-like. We find that the physical part of the dipole ghost field includes infrared divergences. However, we also find that if we introduce residual gauge fields in such a way that the dipole ghost field satisfies the canonical commutation relations, then the residual gauge fields are determined so as to regularize the infrared divergences contained in the physical part. The propagators then take the form prescribed by Mandelstam and Leibbrandt. We make use of these properties to develop guiding principles which allow us to construct consistent operator solutions in the pure space-like case where the quantization surface is parallel to the direction of $n$ and canonical methods do not suffice.

Renormalisability of gauge invariant extensions of the squared gauge potential

We show that gauge invariant extensions of the local functional O=12∫d4xA2 have long range non-localities which can only be “renormalised” with reference to a specific gauge. Consequently, there is no gauge independent way of claiming the perturbative renormalisability of these extensions. In particular, they are not renormalisable in the modern sense of Weinberg and Gomis. Critically, our study does not support the view that ghost fields play an indispensable role in the extension of a local operator into a non-local one as claimed recently in the literature.

Renormalisability of gauge invariant extensions of the squared gauge potential

We show that gauge invariant extensions of the local functional O = 1 2 ∫d 4 x A 2 have long range non-localities which can only be “renormalised” with reference to a specific gauge. Consequently, there is no gauge independent way of claiming the perturbative renormalisability of these extensions. In particular, they are not renormalisable in the modern sense of Weinberg and Gomis. Critically, our study does not support the view that ghost fields play an indispensable role in the extension of a local operator into a non-local one as claimed recently in the literature.

GHOSTS IN A MIRROR

We look at some dynamic geometries produced by scalar fields with both the "right" and the "wrong" signs of the kinetic energy. We start with anisotropic homogeneous universes with closed, open and flat spatial sections. A non-singular solution to the Einstein field equations representing an open anisotropic universe with the ghost field is found. This universe starts collapsing from t→-∞ and then expands to t→∞ without encountering singularities on its way. We further generalize these solutions to those describing inhomogeneous evolution of the ghost fields. Some interesting solutions with the plane symmetry are discussed. These have a property that the same line element solves the Einstein field equations in two mirror regions |t|≥z and |t|≤z, but in one region the solution has the right and in the other, the wrong sign of the kinetic energy. We argue, however, that a physical observer cannot reach the mirror region in a finite proper time. Self-similar collapse/expansion of these fields are also briefly discussed.

Nilpotent symmetries for QED in superfield formalism

In the framework of superfield approach, we derive the local, covariant, continuous and nilpotent (anti-)BRST and (anti-)co-BRST symmetry transformations on the U(1) gauge field (Aμ) and the (anti-)ghost fields ((C̄)C) of the Lagrangian density of the two (1+1)-dimensional QED by exploiting the (dual-)horizontality conditions defined on the four (2+2)-dimensional supermanifold. The long-standing problem of the derivation of the above symmetry transformations for the matter (Dirac) fields (ψ̄,ψ) in the framework of superfield formulation is resolved by a new set of restrictions on the (2+2)-dimensional supermanifold. These new physically interesting restrictions on the supermanifold owe their origin to the invariance of conserved currents of the theory. The geometrical interpretation for all the above transformations is provided in the framework of superfield formalism.

HIDDEN sl(2,R) SYMMETRY IN 2D CFTs AND THE WAVE FUNCTION OF 3D QUANTUM GRAVITY

We show that all two-dimensional conformal field theories possess a hidden sl(2,R) affine symmetry. More precisely, we add appropriate ghost fields to an arbitrary CFT, and we use them to construct the currents of sl(2,R). We then define a BRST operator whose cohomology defines a physical subspace where the extended theory coincides with the original CFT. We use the sl(2,R) algebra to construct candidate wave functions for 3-d quantum gravity coupled to matter, and we discuss their viability.

Erratum

This paper proves that it is possible to build a Lagrangian for quantum electrodynamics which makes it explicit that the photon mass is eventually set to zero in the physical part on observational ground. Gauge independence is achieved upon considering the joint effect of gauge-averaging term and ghost fields. It remains possible to obtain a counterterm Lagrangian where the only non-gauge-invariant term is proportional to the squared divergence of the potential, while the photon propagator in momentum space falls off like 1 over (k-squared) at large k, which indeed agrees with perturbative renormalizability. The resulting radiative corrections to the Coulomb potential in QED are also shown to be gauge-independent. The experience acquired with quantum electrodynamics is used to investigate properties and problems of the extension of such ideas to non-Abelian gauge theories.

On brane-induced gravity in warped backgrounds

We study whether modification of gravity at large distances is possible in warped backgrounds with two branes and a brane-induced term localized on one of the branes. We find that there are three large regions in the parameter space where the theory is weakly coupled up to high energies. In one of these regions gravity on the brane is four-dimensional at arbitrarily large distances, and the induced Einstein term results merely in the renormalization of the 4d Planck mass. In the other two regions the behavior of gravity changes at ultra-large distances; however, radion becomes a ghost. In parts of these regions, both branes have positive tensions, so the only reason for the appearance of the ghost field is the brane-induced term. In between these three regions, there are domains in the parameter space where gravity is strongly coupled at phenomenologically unacceptable low energy scale.

ON PROBLEMS OF THE LAGRANGIAN QUANTIZATION OF W3-GRAVITY

We consider the two-dimensional model of W3-gravity within Lagrangian quantization methods for general gauge theories. We use the Batalin–Vilkovisky formalism to study the arbitrariness in the realization of the gauge algebra. We obtain a one-parametric nonanalytic extension of the gauge algebra, and a corresponding solution of the classical master equation, related via an anticanonical transformation to a solution corresponding to an analytic realization. We investigate the possibility of closed solutions of the classical master equation in the Sp (2)-covariant formalism and show that such solutions do not exist in the approximation up to the third order in ghost and auxiliary fields.

Nucleation of liquid bridges and bubbles in nanoscale capillaries

Nucleation of liquid bridges and bubbles during condensation and evaporation of Lennard-Jones fluid in cylindrical pores is explored by Monte Carlo simulation. The isotherm of constrained critical nuclei is constructed using the gauge cell method. We confirm the Everett–Haynes scenario of bridging through the formation of a bump/undulation on the adsorption film. The molecular structure of growing bridges and cavitating bubbles is revealed. A new simulation approach is introduced to calculate the nucleation energy barriers. The method is based on the introduction and subsequent removal of a virtual “ghost” potential field with a tunable magnitude. Two computation schemes for determining the free energy of nuclei are elaborated based on the thermodynamic integration along a trajectory of states generated in the tunable ghost field and on the umbrella sampling. The methods developed are applicable to study various nucleation phenomena.

Perturbative analysis of gauged matrix models

We analyze perturbative aspects of gauged matrix models, including those where classically the gauge symmetry is partially broken. Ghost fields play a crucial role in the Feynman rules for these vacua. We use this formalism to elucidate the fact that non-perturbative aspects of N=1 gauge theories can be computed systematically using perturbative techniques of matrix models, even if we do not possess an exact solution for the matrix model. As examples we show how the Seiberg-Witten solution for N=2 gauge theory, the Montonen-Olive modular invariance for N=1*, and the superpotential for the Leigh-Strassler deformation of N=4 can be systematically computed in perturbation theory of the matrix model/gauge theory (even though in some of these cases the exact answer can also be obtained by summing up planar diagrams of matrix models).

Brane-induced gravity in more than one extra dimension: Violation of equivalence principle and ghost

We consider brane-induced gravity model in more than one extra dimensions, regularized by assuming that the bulk gravity is soft in ultraviolet. We study linear theory about flat multi-dimensional space-time and flat brane. We first find that this model allows for violation of equivalence between gravitational and inertial masses of brane matter. We then observe that the model has a scalar ghost field localized near the brane, as well as quasi-localized massive graviton. Pure tensor structure of four-dimensional gravity on the brane at intermediate distances is due to the cancellation between the extra polarization of the massive graviton, and the ghost. This is completely analogous to the situation in the GRS model.

GINZBURG–LANDAU EQUATION FROM SU(2) GAUGE FIELD THEORY

The dual superconductor picture of the QCD vacuum is thought to describe the various aspects of the strong interaction including confinement. Ordinary superconductivity is described by the Ginzburg–Landau (GL) equation. In the present work we show that it is possible to arrive at a GL-like equation from pure SU(2) gauge theory. This is accomplished by using Abelian projection to split the SU(2) gauge fields into an Abelian subgroup and its coset. The two gauge field components of the coset part act as the effective, complex, scalar field of the GL equation. The Abelian part of the SU(2) gauge field is then analogous to the electromagnetic potential in the GL equation. An important feature of the dual superconducting model is for the GL Lagrangian to have a spontaneous symmetry breaking potential, and the existence of Nielsen–Olesen flux tube solutions. Both of these require a tachyonic mass for the effective scalar field. Such a tachyonic mass term is obtained from the condensation of ghost fields.