Ghost Fields Research Articles

Open superstring field theory I: gauge fixing, ghost structure, and propagator

The WZW form of open superstring field theory has linearized gauge invariances associated with the BRST operator Q and the zero mode eta_0 of the picture minus-one fermionic superconformal ghost. We discuss gauge fixing of the free theory in a simple class of gauges using the Faddeev-Popov method. We find that the world-sheet ghost number of ghost and antighost string fields ranges over all integers, except one, and at any fixed ghost number, only a finite number of picture numbers appear. We calculate the propagators in a variety of gauges and determine the field-antifield content and the free master action in the Batalin-Vilkovisky formalism. Unlike the case of bosonic string field theory, the resulting master action is not simply related to the original gauge-invariant action by relaxing the constraint on the ghost and picture numbers.

ON THE ALL ORDER SOLUTIONS OF SEIBERG-WITTEN MAP FOR NONCOMMUTATIVE GAUGE THEORIES

We review the recursive solutions of the Seiberg–Witten map to all orders in θ for gauge, matter and ghost fields. We also present the general structure of the homogeneous solutions of the defining equations. Moreover, we show that the contribution of the first order homogeneous solution to the second order can be written recursively similar to inhomogeneous solutions.

FURTHER GRAVITATIONAL WAVE MODES FROM HIGHER ORDER GRAVITY

It is shown that linearizing higher order theories of gravity, further gravitational massive modes emerge. Besides massless spin-2, also spin-0 and spin-2 massive and ghost fields have to be considered. We investigate the possible detectability of such additional modes on the stochastic cosmic background of gravitational waves by ground-based and space interferometric detectors and calculate the detectable energy density of the spectrum. In conclusion, these massive modes could be of interest for direct detection by the forthcoming LISA experiment.

Homotopy operators and identity-based solutions in cubic superstring field theory

We construct a class of nilpotent operators using the BRST current and ghost fields in superstring theory. The operator can be realized in cubic superstring field theory as a kinetic operator in the background of an identity-based solution. For a particular type of the deformed BRST operators, we find a homotopy operator and discuss its relationship to the cohomology in a similar way to the bosonic case, which has been elaborated by the authors.

A PEDAGOGICAL INTRODUCTION TO THE SLAVNOV FORMULATION OF QUANTUM YANG–MILLS THEORY

Over the last few years, Slavnov has proposed a formulation of quantum Yang–Mills theory in the Coulomb gauge which preserves simultaneously manifest Lorentz invariance and gauge invariance of the ghost field Lagrangian. This paper presents in detail some of the necessary calculations, i.e. those dealing with the functional integral for the S-matrix and its invariance under shifted gauge transformations. The extension of this formalism to quantum gravity in the Prentki gauge deserves consideration.

Multi-loop amplitudes in maximally supersymmetric pure spinor field theory

This paper provides a more detailed background to the results of arXiv:1004.2692 concerning properties of multi-loop amplitudes in a pure spinor formulation of field theories with maximal supersymmetry. This involves the development of a first quantised field theory version of the non-minimal pure spinor formalism originally designed for describing superstring amplitudes. In addition to superspace world-line fields, the formalism involves a set of world-line ghost fields that are required for implementing BRST invariance with a composite b ghost. In particular, we show that BRST invariance requires the presence of certain contact terms. For four-point amplitudes, these are important beyond two loops. We also present an alternative proof of the "no-triangle hypothesis" and the vanishing of amplitudes with fewer than four external particles.

Alternative refined Gribov-Zwanziger Lagrangian

We consider the implications of the condensation of a general local BRST invariant dimension two operator built out of the localizing ghost fields of the Gribov-Zwanziger Lagrangian which is a localized Lagrangian incorporating the Gribov problem in the Landau gauge. For different colour tensor projections of the general operator, the properties of a frozen gluon propagator and unenhanced Faddeev-Popov ghost propagator, which are observed in lattice computations, can be reproduced. The alternative possibilities are distinguished by the infrared structure of the propagators of the spin-1 fields, other than those of the gluon and Faddeev-Popov ghost, for which there is no numerical simulation data to compare with yet.

Loop calculations in the three dimensional Gribov–Zwanziger Lagrangian

The three dimensional Gribov-Zwanziger Lagrangian is analysed at one and two loops. Specifically, the two loop gap equation is evaluated and the Gribov mass is expressed in terms of the coupling constant. The one loop corrections to the propagators of all the fields are determined. It is shown that when the gap equation is satisfied the Faddeev-Popov ghost and both Bose and Grassmann localizing ghosts all enhance in the infrared limit at one loop. This verifies that the Kugo-Ojima confinement criterion holds to this order and we also show that both Grassmann ghosts are enhanced at two loops. For the Bose ghost we determine the full form of the propagator in the zero momentum limit for both the transverse and longitudinal pieces and confirm Zwanziger's recent general analysis for the low energy behaviour. We provide an alternative but equivalent version of the horizon condition expressing it as the vacuum expectation value of an operator involving only the localizing Bose ghost field. The one loop static potential is also determined.

Ghost wavefunction renormalization in asymptotically safe quantum gravity

Motivated by Weinberg's asymptotic safety scenario, we investigate the gravitational renormalization group flow in the Einstein–Hilbert truncation supplemented by the wavefunction renormalization of the ghost fields. The latter induces non-trivial corrections to the β-functions for Newton's constant and the cosmological constant. The resulting ghost-improved phase diagram is investigated in detail. In particular, we find a non-trivial ultraviolet fixed point, in agreement with the asymptotic safety conjecture which also survives in the presence of extra dimensions. In four dimensions the ghost anomalous dimension at the fixed point is η*c = −1.8, supporting spacetime being effectively two dimensional at short distances.

The QCD nature of dark energy

The origin of the observed dark energy could be explained entirely within the standard model, with no new fields required. We show how the low-energy sector of the chiral QCD Lagrangian, once embedded in a non-trivial spacetime, gives rise to a cosmological vacuum energy density which can be presented entirely in terms of QCD parameters and the Hubble constant H as ρ Λ ≃ H ⋅ m q 〈 q ¯ q 〉 / m η ′ ∼ ( 4.3 ⋅ 10 − 3 eV ) 4 . In this work we focus on the dynamics of the ghost fields that are essential ingredients of the aforementioned Lagrangian. In particular, we argue that the Veneziano ghost, being unphysical in the usual Minkowski QFT, exhibits important physical effects if the universe is expanding. Such effects are naturally very small as they are proportional to the rate of expansion H / Λ QCD ∼ 10 − 41 . The co-existence of these two drastically different scales ( Λ QCD ∼ 100 MeV and H ∼ 10 − 33 eV ) is a direct consequence of the auxiliary conditions on the physical Hilbert space that are necessary to keep the theory unitary. The exact cancellation taking place in Minkowski space due to this auxiliary condition is slightly violated when the system is upgraded to an expanding background. Nevertheless, this “tiny” effect would in fact the driving force accelerating the universe today. We also derive the time-dependent equation of state w ( t ) for the dark energy component which tracks the dynamics of the Veneziano ghost in a FLRW universe.

Creation/annihilation of wormholes supported by the Sine-Gordon phantom (ghost) field

The possible process of creation/annihilation of traversable wormholes in the model with phantom (ghost) scalar field is described. It is shown that such process can be realized only for some special choice of a potential energy, in particular, for the Sine-Gordon potential.

The one loop $$ \overline {\text{MS}} $$ static potential in the Gribov-Zwanziger lagrangian

We compute the static potential in the Gribov-Zwanziger Lagrangian as a function of the Gribov mass, gamma, in the MSbar scheme in the Landau gauge at one loop. The usual gauge independent one loop perturbative static potential is recovered in the limit as gamma -> 0. By contrast the Gribov-Zwanziger static potential contains the term gamma^2/(p^2)^2. However, the linearly rising potential in coordinate space as a function of the radial variable r does not emerge due to a compensating behaviour as r -> infty. Though in the short distance limit a dipole behaviour is present. We also demonstrate enhancement in the propagator of the bosonic localizing Zwanziger ghost field when the one loop Gribov gap equation is satisfied. The explicit form of the one loop gap equation for the Gribov mass parameter is also computed in the MOM scheme and the zero momentum value of the renormalization group invariant effective coupling constant is shown to be the same value as that in the MSbar scheme.

BRST STRUCTURE OF NONLINEAR SUPERALGEBRAS

In this paper we analyze the structure of the BRST charge of nonlinear superalgebras. We consider quadratic nonlinear superalgebras where a commutator (in terms of (super-)Poisson brackets) of the generators is a quadratic polynomial of the generators. We find the explicit form of the BRST charge up to cubic order in Faddeev–Popov ghost fields for arbitrary quadratic nonlinear superalgebras. We point out the existence of constraints on structure constants of the superalgebra when the nilpotent BRST charge is quadratic in Faddeev–Popov ghost fields. The general results are illustrated by simple examples of superalgebras.

One-loop counterterms in the Yang-Mills theory with a gauge-invariant ghost field Lagrangian

One-loop calculations of renormalization constants in the model with gauge invariant ghost field Lagrangian are performed. It is shown that the model is asymptotically free and the renormalization constants satisfy the same equation as in the ordinary Yang-Mills theory.

HOL-Boogie—An Interactive Prover-Backend for the Verifying C Compiler

Boogie is a verification condition generator for an imperative core language. It has front-ends for the programming languages C# and C enriched by annotations in first-order logic, i.e. pre- and postconditions, assertions, and loop invariants. Moreover, concepts like ghost fields, ghost variables, ghost code and specification functions have been introduced to support a specific modeling methodology. Boogie's verification conditions--constructed via a wp calculus from annotated programs--are usually transferred to automated theorem provers such as Simplify or Z3. This also comprises the expansion of language-specific modeling constructs in terms of a theory describing memory and elementary operations on it; this theory is called a machine/memory model. In this paper, we present a proof environment, HOL-Boogie, that combines Boogie with the interactive theorem prover Isabelle/HOL, for a specific C front-end and a machine/memory model. In particular, we present specific techniques combining automated and interactive proof methods for code verification. The main goal of our environment is to help program verification engineers in their task to "debug" annotations and to find combined proofs where purely automatic proof attempts fail.

Cosmological BCS mechanism and the big bang singularity

We provide a novel mechanism that resolves the big bang singularity present in Friedman-Lemaitre-Robertson-Walker space-times without the need for ghost fields. Building on the fact that a four-fermion interaction arises in general relativity when fermions are covariantly coupled, we show that at early times the decrease in scale factor enhances the correlation between pairs of fermions. This enhancement leads to a BCS-like condensation of the fermions and opens a gap dynamically driving the Hubble parameter $H$ to zero and results in a nonsingular bounce, at least in some special cases.

No Lee-Wick fields out of gravity

We investigate the gravitational one-loop divergences of the standard model in large extra dimensions, with gravitons propagating in the ($4+\ensuremath{\delta}$)-dimensional bulk and gauge fields as well as scalar and fermionic multiplets confined to a three-brane. To determine the divergences we establish a cutoff regularization which allows us to extract gauge-invariant counterterms. In contrast to the claim of a recent paper [F. Wu and M. Zhong, Phys. Rev. D 78, 085010 (2008).], we show that the fermionic and scalar higher derivative counterterms do not coincide with the higher derivative terms in the Lee-Wick standard model. We argue that even if the exact Lee-Wick higher derivative terms were found, as in the case of the pure gauge sector, this would not allow to conclude the existence of the massive ghost fields corresponding to these higher derivative terms in the Lee-Wick standard model.

Aspects of U-duality in BLG models with Lorentzian metric 3-algebras

In [1], it was shown that BLG model based on a Lorentzian metric 3-algebra gives Dp-brane action whose worldvolume is compactified on torus Td (d = p−2). Here the 3-algebra was a generalized one with d+1 pairs of Lorentzian metric generators and expressed in terms of a loop algebra with central extensions. In this paper, we derive the precise relation of the coupling constant of the super Yang-Mills, the moduli of Td and some R-R flux to VEV's of ghost fields associated with Lorentzian metric generators. In particular, for d = 1, we derive the Yang-Mills action with θ term and show that SL(2,Z) Montonen-Olive duality is realized as the rotation of two VEV's. Furthermore, some moduli parameters such as NS-NS 2-form flux are identified as the deformation parameters of the 3-algebras. By combining them, we recover most of the moduli parameters which are required by U-duality symmetry.

PERTURBATIVE EXPANSION FOR THE t-J MODEL CONSTRUCTED FROM THE GENERATORS OF THE SUPERSYMMETRIC HUBBARD ALGEBRA

By using the Hubbard [Formula: see text]-operators as field variables along with the supersymmetric version of the Faddeev–Jackiw symplectic formalism, a family of first-order constrained Lagrangians for the t-J model is found. In order to satisfy the Hubbard [Formula: see text]-operator commutation rules satisfying the graded algebra spl(2,1), the number and kind of constraints that must be included in a classical first-order Lagrangian formalism for this model are presented. The model is also analyzed via path-integral formalism, where the correlation-generating functional and the effective Lagrangian are constructed. In this context, the introduction of a proper ghost field is needed to render the model renormalizable. The perturbative Lagrangian formalism is developed and it is shown how propagators and vertices can be renormalized to each order. In particular, the renormalized ferromagnetic magnon propagator arising in the present formalism is discussed. As an example, the thermal softening of the magnon frequency is computed.

Nonquadratic gauge fixing and global gauge invariance in the effective action

The possibility of having a gauge fixing term in the effective Lagrangian that is not a quadratic expression has been explored in spin-two theories so as to have a propagator that is both traceless and transverse. We first show how this same approach can be used in spontaneously broken gauge theories as an alternate to the 't Hooft gauge fixing which avoids terms quadratic in the scalar fields. This "non-quadratic" gauge fixing in the effective action results in there being two complex Fermionic and one real Bosonic ghost fields. A global gauge invariance involving a Fermionic gauge parameter, analogous to the usual BRST invariance, is present in this effective action.