Motivated by ideas obtained from both ghost condensation and gravitational Higgs mechanism, we attempt to find classical solutions in the unitary gauge in general ghost condensation models. It is shown that depending on the form of scalar fields in an action, there are three kinds of exact solutions, which are (anti-) de Sitter space-time, polynomially expanding universes and flat Minkowski space-time. We briefly comment on gravitational Higgs mechanism in these models where we have massive gravitons of 5 degrees of freedom and 1 unitary scalar field (Nambu-Goldstone boson) after spontaneous symmetry breakdown of general coordinate reparametrization invariance. The models at hand are free from the problem associated with the non-unitary propagating mode.
Recent work claimed that the off-diagonal gluons (and ghosts) in pure Yang-Mills theories, with Maximal Abelian gauge fixing (MAG), attain a dynamical mass through an off-diagonal ghost condensate. This condensation takes place due to a quartic ghost interaction, unavoidably present in MAG for renormalizability purposes. The off-diagonal mass can be seen as evidence for Abelian dominance. We discuss why ghost condensation of the type discussed in those works cannot be the reason for the off-diagonal mass and Abelian dominance, since it results in a tachyonic mass. We also point out what the fu…
In the framework of the formalism of Cornwall et all. for composite operators I study the ghost-antighost condensation in SU(2) Yang-Mills theories quantized in the Maximal Abelian Gauge and I derive analytically a condensating effective potential at two ghost loops. I find that in this approximation the one loop pairing ghost-antighost is not destroyed but no mass is generated if the ansatz for the propagator suggested by the tree level Hubbard-Stratonovich transformations is used.
We argue that the BRST and the anti-BRST super symmetries in the four-dimensional Yang-Mills theory can be spontaneously broken in a nonlinear partial gauge due to ghost-anti-ghost condensation. However, we show that the spontaneous BRST symmetry breaking can be avoided if we adopt the modified Maximal Abelian gauge which is an orthosymplectic $OSp(4|2)$ invariant renormalizable gauge proposed by the author to derive quark confinement. We compare the Maximal Abelian gauge with the conventional $OSp(4|2)$ invariant gauge proposed by Delbourgo-Jarvis and Baulieu-Thierry-Mieg. Finally, an implica…
The local action of an SU(2) gauge theory in general covariant Abelian gauges and the associated equivariant BRST symmetry that guarantees the perturbative renormalizability of the model are given. A global SL(2,R) symmetry of the model is spontaneously broken by ghost-antighost condensation at arbitrarily small coupling. This leads to propagators that are finite at Euclidean momenta for all elementary fields except the Abelian ``photon''. Ward Identities show that the symmetry breaking gives rise to massless BRST-quartets with ghost numbers (1,2,-2,-1) and (0,1,-1,0). The latter quartet is in…
NSR superstring theory contains a tower of physical vertex operators (brane-like states) which exist at non-zero pictures only, i.e. are essentially mixed with superconformal ghosts. Some of these states are massless, they are responsible for creating D-branes. Other states are tachyonic (called ghost tachyons) creating a problem for the vacuum stability of the NSR model. In this paper we explore the role played by these tachyonic states in string dynamics. We show that the ghost tachyons condense on D-branes, created by massless brane-like states. Thus the vacuum stability is achieved dynamic…
In this paper we formulate RFDiff invariant f(R) Horava-Lifshitz gravity and we show that it is related to the ghost condensation in the projectable version of Horava-Lifshitz gravity.
We analyze the ghost condensates <f^{abc}c^{b}c^{c}>, <f^{abc}\oc^{b}\oc^{c}> and <f^{abc}\oc^{b}c^{c}> in Yang-Mills theory in the Curci-Ferrari gauge. By combining the local composite operator formalism with the algebraic renormalization technique, we are able to give a simultaneous discussion of <f^{abc}c^{b}c^{c}>, <f^{abc}\oc^{b}\oc^{c}> and <f^{abc}\oc^{b}c^{c}>, which can be seen as playing the role of the BCS, respectively Overhauser effect in ordinary superconductivity. The Curci-Ferrari gauge exhibits a global continuous symmetry generated by the Nakanishi-Ojima (NO) algebra. This al…
Motivated by the ghost condensate model, we study the Randall-Sundrum (RS) brane-world with an arbitrary function of the higher derivative kinetic terms, $\mathcal{P}(X)$, where $X=-(\nabla ϕ)^{2}$. The five-dimensional Einstein equations reduce to two equations of motion with a constraint between $\mathcal{P}(X)$ and the five-dimensional cosmological constant on the brane. For a static extra dimension, $\mathcal{P}(X)$ has solutions for both a negative kinetic scalar (so called {\textit{ghost}}) as well as an ordinary scalar field. However ghost condensation cannot take place. We show that sm…
We show a new class of interaction terms with higher derivatives that can be added to every low derivative real scalar, such that the theory is degenerate, and the equation of motion remains of second order. In contrast to previous setups, the necessary constraints that eliminate the ghosts also have a clear physical motivation: they impose and preserve at all times the low derivative dynamics of the real scalar as a background, on top of which, the fluctuations induced by these higher derivative terms are degenerate, and ghost-free. We summarize the setup for these constrained ghost-free real…
Assuming the existence of a scalar field which undergoes "ghost condensation" and which has a suitably chosen potential, it is possible to obtain a non-singular bouncing cosmology in the presence of regular matter and radiation. The potential for the ghost condensate field can be chosen such that the cosmological bounce is stable against the presence of anisotropic stress. Cosmological fluctuations on long wavelengths relevant to current cosmological observations pass through the bounce unaffected by the new physics which yields the bounce. Thus, this model allows for the realization of the "m…
A tachyon is considered to be sick in the context of particle mechanics, but in field theory just indicates instability of a background. We consider a similar possibility that a ghost in field theory might be just an indication of instability of a background and that it can condense to form a different background around which there is no ghost. We construct a low energy effective field theory based on the derivative expansion around the stable background. Possible applications are discussed, including dark energy, dark matter, inflation and black hole.
Euclidean $SU(2)$ gauge theory is studied in a nonlinear gauge. In this theory, ghost condensation happens and gauge fields acquire tachyonic masses. It is shown that these tachyonic masses are removed by a gauge field condensate $\langle A_μ^+A_μ^-\rangle$. Because of the ghost condensation, monopole solutions are included naturally. We find the condensate $\langle A_μ^+A_μ^-\rangle$ makes the magnetic potential massive.
The phase structure and the infrared behaviour of the Euclidean 3-dimensional $O(2)$ symmetric ghost scalar field model with higher-order derivative term has been investigated in Wegner and Houghton's renormalization group framework. The symmetric phase in which no ghost condensation occurs and the phase with restored symmetry but with a transient presence of a ghost condensate have been identified. Finiteness of the correlation length at the phase boundary hints to a phase transition of first order. The results are compared with those for the ordinary $O(2)$ symmetric scalar field model.
We propose a theoretically consistent modification of gravity in the infrared, which is compatible with all current experimental observations. This is an analog of Higgs mechanism in general relativity, and can be thought of as arising from ghost condensation--a background where a scalar field ϕhas a constant velocity, <\dotϕ> = M^2. The ghost condensate is a new kind of fluid that can fill the universe, which has the same equation of state, ρ= -p, as a cosmological constant, and can hence drive de Sitter expansion of the universe. However, unlike a cosmological constant, it is a physical flui…
We perform a numerical study of ghost condensation -- in the so-called Overhauser channel -- for SU(2) lattice gauge theory in minimal Landau gauge. The off-diagonal components of the momentum-space ghost propagator G^{cd}(p) are evaluated for lattice volumes V = 8^4, 12^4, 16^4, 20^4, 24^4 and for three values of the lattice coupling: β= 2.2, 2.3, 2.4. Our data show that the quantity ϕ^b(p) = ε^{bcd} G^{cd}(p) / 2 is zero within error bars, being characterized by very large statistical fluctuations. On the contrary, |ϕ^b(p)| has relatively small error bars and behaves at small momenta as L^{-…
In the setup of ghost condensation model the generalized second law of black hole thermodynamics can be respected under a radiatively stable assumption that couplings between the field responsible for ghost condensate and matter fields such as those in the Standard Model are suppressed by the Planck scale. Since not only black holes but also cosmology are expected to play important roles towards our better understanding of gravity, we consider a cosmological setup to test the theory of ghost condensation. In particular we shall show that the de Sitter entropy bound proposed by Arkani-Hamed, et…
We show that cosmological acceleration, Dark Energy (DE) effect is a consequence of the zero rest mass, conformal non-invariance of gravitons, and 1-loop finiteness of quantum gravity (QG). The effect is due to graviton-ghost condensates arising from the interference of quantum coherent states. The theory is constructed as follows: Faddeev-Popov-De Witt gauged path integral -> factorization of classical and quantum variables -> transition to the 1-loop approximation -> choice of ghost sector, satisfying 1-loop finiteness of the theory off the mass shell. The Bogolyubov-Born-Green-Kirckwood-Yvo…
A ghost D-brane has been proposed as an object that cancels the effects of a D-branes. We construct a classical solution with an arbitrary number of D-branes and ghost D-branes in the context of open string field theory. Cancellation of BRST cohomolgy between D-branes and ghost D-branes is shown.
We study the physical spectrum of cubic open string field theory around universal solutions, which are constructed using the matter Virasoro operators and the ghost and anti-ghost fields. We find the cohomology of the new BRS charge around the solutions, which appear with a ghost number that differs from that of the original theory. Considering the gauge-unfixed string field theory, we conclude that open string excitations perturbatively disappear after the condensation of the string field to the solutions.
We discuss a special class of quantum gravity phenomena that occur on the scale of the Universe as a whole at any stage of its evolution. These phenomena are a direct consequence of the zero rest mass of gravitons, conformal non-invariance of the graviton field, and one-loop finiteness of quantum gravity. The effects are due to graviton-ghost condensates arising from the interference of quantum coherent states. Each of coherent states is a state of gravitons and ghosts of a wavelength of the order of the horizon scale and of different occupation numbers. The state vector of the Universe is a c…
We describe the ghost sector of cubic string field theory in terms of degrees of freedom on the two halves of a split string. In particular, we represent a class of pure ghost BRST operators as operators on the space of half-string functionals. These BRST operators were postulated by Rastelli, Sen, and Zwiebach to give a description of cubic string field theory in the closed string vacuum arising from condensation of a D25-brane in the original tachyonic theory. We find a class of solutions for the ghost equations of motion using the pure ghost BRST operators. We find a vanishing action for th…
SU(3) gauge theory in the nonlinear gauge of the Curci--Ferrari type is studied. In the low-energy region, ghost condensation and subsequent gauge field condensation can happen. The latter condensation makes classical gauge fields massive. If the color electric potential with string is chosen as the classical gauge field, it produces the static potential with the linear potential. We apply this static potential to the three-quark system, and show, different from the $Y$-type potential, infrared divergence remains in the $Δ$-type potential. The color electric flux is also studied, and show that…
We investigate a non-perturbative vacuum in open string field theory expanded around the analytic classical solution which has been found in the universal Fock space generated by matter Virasoro generators and ghost oscillators. We carry out level-truncation analyses up to level (6,18) in the theory around one-parameter families of the solution. We observe that the value of the vacuum energy cancels the D-brane tension as the approximation level is increased, but this non-perturbative vacuum disappears at the boundary of the parameter space. These results provide strong evidence for the conjec…
SU(2) gauge theory in the nonlinear gauge of the Curci-Ferrari type is studied in low-energy region. We give a classical solution that connects color electric charges. Its dual solution, which has a configuration of monopole, is also presented. Due to the gluon condensation subsequent to the ghost condensation, these classical fields become massive. The massive Lagrangian with the classical solution and that with the dual solution are derived. We show that these Lagrangians produce a linear potential between a quark and an antiquark. This is the mechanism of quark confinement that is different…
We give a simple discussion of ghosts, unitarity violation, negative norm states and quantum vs classical behavior in the simplest model with four derivative action - the Pais-Uhlenbeck oscillator. We also point out that the normalizable "vacuum state" (in the sense defined below) of this model can be understood as spontaneous breaking of the emergent conformal symmetry. We provide an example of an interacting system that couples the "particle" and "ghost" degrees of freedom and nevertheless remains unitary on both classical and quantum level.
We study radiation emitted by a time-dependent source of a scalar massless field in the framework of the ghost-free modifications of the theory. We consider a simple model of the emitter: namely,we assume that it is point-like and monochromatic. We focused on the most common versions of the ghost-free theory, where the propagator $\Box^{-1}$ is modified as follows $\exp(-(\Box/μ^2)^N) \Box^{-1}$, where $μ$ is the characteristic mass-scale of such $GF_N$-theory. We demonstrated that far from the source, in the wave-zone, the radiation asymptotically converges to its "classical" value for any $N…
Ghost fields have reemerged in a handful of phenomenologically motivated cosmological and particle physics scenarios, and most recently in a cyclic mechanism to address the fine-tuning of gauge couplings in the standard model. We study the classical and quantum stability of a ghost-dilaton system coupled to a gauge sector and find that this system is classically stable due to the existence of limit cycles in phase space. We also analyze the coupled gauge invariant classical perturbations and find a range of phenomenologically viable parameters where the system is stable. We also discuss ways t…
Interacting theories with higher derivatives involve ghosts. They correspond to instabilities that display themselves at the classical level. We notice that comparatively "benign" mechanical higher-derivative systems exist where the classical vacuum is stable with respect to small perturbations and the problems appear only at the nonperturbative level. We argue that benign higher-derivative field theories exist which are stable with respect to small fluctuations with nonzero momenta. A particular example is the 6D N=2 higher-derivative SYM theory, which is finite and unitary at the perturbativ…
A brief review of the physics of systems including higher derivatives in the Lagrangian is given. All such systems involve ghosts, i.e. the spectrum of the Hamiltonian is not bounded from below and the vacuum ground state is absent. Usually this leads to collapse and loss of unitarity. In certain special cases, this does not happen, however: ghosts are benign. We speculate that the Theory of Everything is a higher-derivative field theory, characterized by the presence of such benign ghosts and defined in a higher-dimensional bulk. Our Universe represents then a classical solution in this theor…
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…
We present a classical analysis on the issue of vector superluminality in the decoupling limit ghost-free massive gravity with a Minkowski reference metric. We show explicitly in the Lorenz gauge that the theory is free of superluminal vector excitations around a nontrivial solution at the cubic order in the fields. In the same gauge, we demonstrate that superluminal vector modes arise at the quartic order and compute some superluminal propagating solutions. We then generalize our findings to all orders in a gauge-independent way. We check the physical consistency of the vector superluminaliti…
In the simplest Higgs phase of gravity called ghost condensation, an accelerating universe with a phantom era (w<-1) can be realized without ghost or any other instabilities. In this paper we show how to reconstruct the potential in the Higgs sector Lagrangian from a given cosmological history (H(t), ρ(t)). This in principle allows us to constrain the potential by geometrical information of the universe such as supernova distance-redshift relation. We also derive the evolution equation for cosmological perturbations in the Higgs phase of gravity by employing a systematic low energy expansion. …
In a recently proposed model of ``ghost condensation'', spatially homogeneous states may mix, via tunneling, with inhomogeneous states which are somewhat similar to bubbles in the theory of false vacuum decay, the corresponding bubble nucleation rate being exponentially sensitive to the ultraviolet completion of the model. The conservation of energy and charge requires that the energy density is negative and the field is strongly unstable in a part of the nucleated bubble. Unlike in the theory of false vacuum decay, this region does not expand during subsequent real-time evolution. In the oute…
A condensed introduction to quantum gauge theories is given in the perturbative S-matrix framework; path integral methods are used nowhere. This approach emphasizes the fact that it is not necessary to start from classical gauge theories which are then subject to quantization, but it is also possible to recover the classical group structure and coupling properties from purely quantum mechanical principles. As a main tool we use a free field version of the Becchi-Rouet-Stora-Tyutin gauge transformation, which contains no interaction terms related to a coupling constant. This free gauge transfor…
Using a supergeometric interpretation of field functionals, we show that for a class of classical field models used for realistic quantum field theoretic models, an infinite-dimensional supermanifold (smf) of classical solutions in Minkowski space can be constructed. That is, we show that the smf of smooth Cauchy data with compact support is isomorphic with an smf of corresponding classical solutions of the model.
We discuss classical solutions of a graviton-dilaton-B_{μν}-tachyon system. Both constant tachyon solutions, including AdS_3 solutions, and space-dependent tachyon solutions are investigated, and their possible implications to closed string tachyon condensation are argued. The stability issue of the AdS_3 solutions is also discussed.
Using a supergeometric interpretation of field functionals developed in previous papers, we show that for quite a large class of systems of nonlinear field equations with anticommuting fields, infinite-dimensional supermanifolds (smf) of classical solutions can be constructed. Such systems arise in classical field models used for realistic quantum field theoretic models. In particular, we show that under suitable conditions, the smf of smooth Cauchy data with compact support is isomorphic with an smf of corresponding classical solutions of the model.
The local covariant continuum action of an SU(2) gauge theory in covariant Abelian gauges is investigated. It describes the critical limit of an Abelian Lattice Gauge Theory (LGT) with an equivariant BRST-symmetry. This Abelian LGT has previously been proven to be physically equivalent to the SU(2)-LGT. Renormalizability requires a quartic ghost interaction in these nonlinear gauges (also in maximal Abelian gauge). Arguments that a certain global SL(2,R) symmetry is dynamically broken by ghost-antighost condensation in a BCS-like mechanism are presented. The scenario can be viewed as a dynamic…
We develop an approach based on the Noether method to construct nilpotent BRST charges and BRST-invariant actions. We apply this approach first to the holomorphic part of the flat-space covariant superstring, and we find that the ghosts b, c_z which we introduced by hand in our earlier work, are needed to fix gauge symmetries of the ghost action. Then we apply this technique to the superparticle and determine its cohomology. Finally, we extend our results to the combined left- and right-moving sectors of the superstring.
The aim of these notes is to provide a self-contained review of why it is generically a problem when a solution of a theory possesses ghost fields among the perturbation modes. We define what a ghost field is and we show that its presence is associated to a classical instability whenever the ghost field interacts with standard fields. We then show that the instability is more severe at quantum level, and that perturbative ghosts can exist only in low energy effective theories. However, if we don't consider very ad-hoc choices, compatibility with observational constraints implies that low energ…
We explicitly show that general local higher-derivative theories with only complex conjugate ghosts and normal real particles are unitary at any perturbative order in the loop expansion. The proof presented here relies on integrating the loop energies on complex paths resulting from the deformation of the purely imaginary paths, when the external energies are continued from imaginary to real values. Contrary to the case of nonlocal theories, where the same integration path was first proposed, for the classes of theories studied here the same procedure is not analytic, but the resulting theory …
We review the fate of the Ostrogradsky ghost in higher-order theories. We start by recalling the original Ostrogradsky theorem and illustrate, in the context of classical mechanics, how higher-derivatives Lagrangians lead to unbounded Hamiltonians and then lead to (classical and quantum) instabilities. Then, we extend the Ostrogradsky theorem to higher-derivatives theories of several dynamical variables and show the possibility to evade the Ostrogradsky instability when the Lagrangian is "degenerate", still in the context of classical mechanics. In particular, we explain why higher-derivatives…
We construct a supersymmetric (1+1)-dimensional field theory involving extra derivatives and associated ghosts: the spectrum of the Hamiltonian is not bounded from below, neither from above. In spite of that, there is neither classical, nor quantum collapse and unitarity is preserved.
Ordinary QED formulated in the Feynman's space-time picture is equivalent to a one dimensional field theory. In the large N limit there is no phase transition in such a theory. In this letter, we show a phase transition does exist in a generalization of QED characterized by the addition of the curvature of the world line (rigidity) to the Feynman's space-time action. The large distance scale of the disordered phase essentially coincides with ordinary QED, while the ordered phase is strongly coupled. Although rigid QED exhibits the typical pathologies of higher derivative theories at the classi…
In the context of Lorentz-invariant massive gravity we show that classical solutions around heavy sources are plagued by ghost instabilities. The ghost shows up in the effective field theory at huge distances from the source, much bigger than the Vainshtein radius. Its presence is independent of the choice of the non-linear terms added to the Fierz-Pauli Lagrangian. At the Vainshtein radius the mass of the ghost is of order of the inverse radius, so that the theory cannot be trusted inside this region, not even at the classical level.
In this paper we will show all the linearized curvature tensors in the infinite derivative ghost and singularity free theory of gravity in the static limit. We have found that in the region of non-locality, in the ultraviolet regime (at short distance from the source), the Ricci tensor and the Ricci scalar are not vanishing, meaning that we do not have a vacuum solution anymore due to the smearing of the source induced by the presence of non-local gravitational interactions. It also follows that, unlike in Einstein's gravity, the Riemann tensor is not traceless and it does not coincide with th…
We perform a Hamiltonian analysis and prove that a large class of scalar-tensor theories whose Lagrangian is given by a generic function $F\left(K_{ab},N,R_{ab},h^{ab},\nabla_a,t\right)$ is free from the Ostrogradsky ghost, and thus these theories contain at most 3 degrees of freedom at classical level.
Theories that spontaneously break Lorentz invariance also violate diffeomorphism symmetries, implying the existence of extra degrees of freedom and modifications of gravity. In the minimal model (``ghost condensation'') with only a single extra degree of freedom at low energies, the scale of Lorentz violation cannot be larger than about M ~ 100GeV due to an infrared instability in the gravity sector. We show that Lorentz symmetry can be broken at much higher scales in a non-minimal theory with additional degrees of freedom, in particular if Lorentz symmetry is broken by the vacuum expectation …
We investigate the nature of correlations in Gaussian light sources used for ghost imaging. We adopt methods from quantum information theory to distinguish genuinely quantum from classical correlations. Combining a microscopic analysis of speckle-speckle correlations with an effective coarse-grained description of the beams, we show that quantum correlations exist even in `classical'-like thermal light sources, and appear relevant for the implementation of ghost imaging in the regime of low illumination. We further demonstrate that the total correlations in the thermal source beams effectively…
We consider a class of abstract nonlinear evolution equations in supermanifolds (smf's) modelled over Z_2-graded locally convex spaces. We show uniqueness, local existence, smoothness, and an abstract version of causal propagation of the solutions. If an a-priori estimate prevents the solutions from blowing-up then an infinite-dimensional smf of "all" solutions can be constructed. We apply our results to a class of systems of nonlinear field equations with anticommuting fields which arise in classical field models used for realistic quantum field theoretic models. In particular, we show that u…
In cosmological context, classical scalar fields are important ingredients for inflation models, many candidate models of dark energy, symmetry breaking and phase transition epochs, and their consequences such as baryo and lepto-genesis. We investigate the formation of these fields by studying the production of a light quantum scalar field during the decay of a heavy particle. For simplicity it is assumed to be a scalar too. We discuss the effects of the decay mode, the thermodynamical state of the decaying field, boundary conditions, and related physical parameters on the production and evolu…
We explore the possibility that theories with negative kinetic energy (ghosts) can be meta-stable up to cosmologically long times. In classical mechanics, ghosts undergo spontaneous lockdown rather than run-away if weakly-coupled and non-resonant. Physical examples of this phenomenon are shown. In quantum mechanics this leads to meta-stability similar to vacuum decay. In classical field theory, lockdown is broken by resonances and ghosts behave statistically, drifting towards infinite entropy as no thermal equilibrium exists. We analytically and numerically compute the run-away rate finding th…
Understanding the role of higher derivatives is probably one of the most relevant questions in quantum gravity theory. Already at the semiclassical level, when gravity is a classical background for quantum matter fields, the action of gravity should include fourth derivative terms to provide renormalizability in the vacuum sector. The same situation holds in the quantum theory of metric. At the same time, including the fourth derivative terms means the presence of massive ghosts, which are gauge-independent massive states with negative kinetic energy. At both classical and quantum level such g…
