Motivated by the FRW-CFT proposal by Freivogel, Sekino, Susskind and Yeh, we compute the three-point function of a scalar field in a Coleman-De Luccia instanton background. We first compute the three-point function of the scalar field making only very mild assumptions about the scalar potential and the instanton background. We obtain the three-point function for points in the FRW patch of the CDL instanton and take two interesting limits; the limit where the three points are near the boundary of the hyperbolic slices of the FRW patch, and the limit where the three points lie on the past lightcone of the FRW patch. We expand the past lightcone three-point function in spherical harmonics. We show that the near boundary limit expansion of the three-point function of a massless scalar field exhibits conformal structure compatible with FRW-CFT when the FRW patch is flat. We also compute the three-point function when the scalar is massive, and explain the obstacles to generalizing the conjectured field-operator correspondence of massless fields to massive fields.
We compute the two-point functions of the scalar and graviton in a Coleman-De Luccia type instanton background in general dimensions. These are analytically continued to Lorentzian signature. We write the correlator in a form convenient for examining the "holographic" properties of this background inspired by the work of Freivogel, Sekino, Susskind and Yeh(FSSY). Based on this, we speculate on what kind of boundary theory we would have on this background if we assume that there exists a holographic duality.
We present a calculation of thick-wall Coleman-de-Luccia (CdL) bounces in the Standard Model effective potential in a de Sitter background. The calculation is performed including the effect of the bounce back-reaction on the metric, which we compare with the case of a fixed de-Sitter background, and with similar full-backreaction calculation in a model polynomial potential. The results show that the Standard Model potential exhibits non-trivial behavior: rather than a single CdL solution, there are multiple (non-oscillating) bounce solutions which may contribute to the decay rate. All the extr…
The String Landscape is a fantasy. We actually have a plausible landscape of minimally supersymmetric $AdS_4$ solutions of supergravity modified by an exponential superpotential. None of these solutions is accessible to world sheet perturbation theory. If they exist as models of quantum gravity, they are defined by conformal field theories, and each is an independent quantum system, which makes no transitions to any of the others. This landscape has nothing to do with CDL tunneling or eternal inflation. A proper understanding of CDL transitions in QFT on a fixed background dS space, shows that…
Simple new relations are presented between the one-loop effective Lagrangians of spinor and scalar particles in constant curvature background fields, both electromagentic and gravitational. These relations go beyond the well-known cases for self-dual background fields.
The stress tensor of a massless scalar field satisfying Robin boundary conditions on two one-dimensional wall in two-dimensional Schwarzschild background is calculated. We show that vacuum expectation value of stress tensor can be obtained explicitly by Casimir effect, trace anomaly and Hawking radiation.
We solve the equations of motion of a complex $ϕ^4$ theory coupled to some given gauge field background. The solutions are given in both cylindrical and spherical coordinates and have finite energy.
Using the Worldline formalism of QED we compute the two-loop effective action induced by a charged scalar, respectively spinor particle in a general constant electromagnetic field.
We consider the complex scalar field coupled to background NC U(1) YM and calculate the correlator of two gauge invariant composite operators. We show how the noncommutative gauge invariance is restored for higher correlators (though the Green's function itself is not invariant). It is interesting that the recently discovered noncommutative solitons appear in the calculation.
Generalizing a previous work concerning cosmological linear tensor perturbations, we show that the lagrangians and hamiltonians of cosmological linear scalar and vector perturbations can be put in simple form through the implementation of canonical transformations and redefinitions of the lapse function, without ever using the background classical equations of motion. In particular, if the matter content of the Universe is a perfect fluid, the hamiltonian of scalar perturbations can be reduced, as usual, to a hamiltonian of a scalar field with variable mass depending on background functions, i…
Path-integral representations for a scalar particle propagator in non-Abelian external backgrounds are derived. To this aim, we generalize the procedure proposed by Gitman and Schvartsman 1993 of path-integral construction to any representation of SU(N) given in terms of antisymmetric generators. And for arbitrary representations of SU(N), we present an alternative construction by means of fermionic coherent states. From the path-integral representations we derive pseudoclassical actions for a scalar particle placed in non-Abelian backgrounds. These actions are classically analyzed and then qu…
The field-theoretic one-loop effective action in a static scalar background depending nontrivially on a single spatial coordinate is related, in the proper-time formalism, to the trace of the evolution kernel (or heat kernel) for an appropriate, one dimensional, quantum-mechanical Hamiltonian. We describe a recursive procedure applicable to these traces for shape-invariant Hamiltonians, resolving subtleties from the continuum mode contributions by utilizing the expression for the regularized Witten index. For some cases which include those of domain-wall-type scalar backgrounds, our recursive …
We consider the evolution of a scalar field coupled to curvature in topological black hole spacetimes. We solve numerically the scalar wave equation with different curvature-coupling constant $ξ$ and show that a rich spectrum of wave propagation is revealed when $ξ$ is introduced. Relations between quasinormal modes and the size of different topological black holes have also been investigated.
Using thermal value of zeta function instead of zero temperature, the partition function of quantized fields in arbitrary stationary backgrounds was found to be independent of undetermined regularization constant in even-dimension and the long drawn problem associated with the trace anomaly effect had been removed. Here, we explicitly calculate the expression for the coincidence limit so that the technique may be applied in some specific problems. A particular problem dealt with here is to calculate the partition function of massless scalar field in Schwarzschild background.
The running of the non-minimal parameter (ξ) of the interaction of the real scalar field and scalar curvature is explored within the non-perturbative setting of the functional renormalization group (RG). We establish the RG flow in curved space-time in the scalar field sector, in particular derive an equation for the non-minimal parameter. The RG trajectory is numerically explored for different sets of initial data.
We construct infinite dimensional symmetries of a complex, free scalar field on curved space-times generated by isometries of the space-time. We use the Anti de-Sitter backgrounds as an example and check that the boundary terms appearing in the Noether current satisfy the requirement of Noether's theorem that they vanish at the boundary.
In the present work we study the propagation of a probe minimally coupled scalar field in Einstein-power-Maxwell charged black hole background in (1+2) dimensions. We find analytical expressions for the reflection coefficient as well as for the absorption cross-section in the low energy regime, and we show graphically their behaviour as functions of the frequency for several values of the free parameters of the theory.
We introduce an approach for calculating the quantum loop corrections in the $ϕ^4$ theory. Differential regularization and background-field method are essential tools and are used to calculate the effective action of the theory to two-loop order. Our approach is considerably simpler than other known methods and can be readily extended to higher-loop calculations and to other models.
We develop a Hamiltonian formalism which can be used to discuss the physics of a massless scalar field in a gravitational background of a Schwarzschild black hole. Using this formalism we show that the time evolution of the system is unitary and yet all known results such as the existence of Hawking radiation can be readily understood. We then point out that the Hamiltonian formalism leads to interesting observations about black hole entropy and the information paradox.
We analyze the problem of the existing ambiguities in the conformal anomaly in theories with external scalar field in curved backgrounds. In particular, we consider the anomaly of self-interacting massive scalar field theory and of Yukawa model in the massless conformal limit. In all cases the ambiguities are related to finite renormalizations of a local non-minimal terms in the effective action. We point out the generic nature of this phenomenon and provide a general method to identify the theories where such an ambiguity can arise.
We compute the graviton two scalar off-shell interaction vertex at tree level in Type IIB superstring theory on the pp-wave background using the light-cone string field theory formalism. We then show that the tree level vertex vanishes when all particles are on-shell and conservation of p_{+} and p_{-} are imposed. We reinforce our claim by calculating the same vertex starting from the corresponding SUGRA action expanded around the pp-wave background in the light-cone gauge.
We calculate the zero point energy of a massive scalar field in the background of an infinitely thin spherical shell given by a potential of the delta function type. We use zeta functional regularization and express the regularized ground state energy in terms of the Jost function of the related scattering problem. Then we find the corresponding heat kernel coefficients and perform the renormalization, imposing the normalization condition that the ground state energy vanishes when the mass of the quantum field becomes large. Finally the ground state energy is calculated numerically. Correspond…
We consider (0+1) and (1+1) dimensional Yukawa theory in various scalar field backgrounds, which are solving classical equations of motion: $\ddotϕ_{cl} = 0$ or $\Box ϕ_{cl} = 0$, correspondingly. The (0+1)--dimensional theory we solve exactly. In (1+1)--dimensions we consider background fields of the form $ϕ_{cl} = E\, t$ and $ϕ_{cl} = E\, x$, which are inspired by the constant electric field. Here $E$ is a constant. We study the backreaction problem by various methods, including the dynamics of a coherent state. We also calculate loop corrections to the correlation functions in the theory us…
We study interacting scalar field theory non-minimally coupled to gravity in the FRW background. We show that for a specific choice of interaction terms, the energy-momentum tensor of the scalar field vanishes, and as a result the scalar field does not gravitate. The naive space dependent solution to equations of motion gives rise to singular field profile. We carefully analyze the energy-momentum tensor for such a solution and show that the singularity of the solution gives a subtle contribution to the energy-momentum tensor. The space dependent solution therefore is not non-gravitating. Our …
We investigate the dynamics of gauge and scalar fields on unstable D-branes with rolling tachyons. Assuming an FRW metric on the brane, we find a solution of the tachyon equation of motion which is valid for arbitrary tachyon potentials and scale factors. The equations of motion for a U(1) gauge field and a scalar field in this background are derived. These fields see an effective metric which differs from the original FRW metric. The field equations receive large corrections due to the curvature of the effective metric as well as the time variation of the gauge coupling. The equations of stat…
We consider the proposal that predicts holographic duality between certain 2D minimal models at large central charge and Vasiliev 3D higher spin gravity with a single complex field. We compute the scalar correlator in the background of a higher spin black hole at order $\mathcal O(α^{5})$ in the chemical potential $α$ associated with the spin-3 charge. The calculation is performed at generic values of the symmetry algebra $\mbox{hs}[λ]$ parameter $λ$ and for the scalar in three different representations. We then study the perturbative data in the large $λ$ limit and discover remarkable regular…
It has recently been shown that the equation of motion of a massless scalar field in the background of some specific p branes can be reduced to a modified Mathieu equation. In the following the absorption rate of the scalar by a D3 brane in ten dimensions is calculated in terms of modified Mathieu functions of the first kind, using standard Mathieu coefficients. The relation of the latter to Dougall coefficients (used by others) is investigated. The S-matrix obtained in terms of modified Mathieu functions of the first kind is easily evaluated if known rapidly convergent low energy expansions o…
We studied the massive scalar wave propagation in the background of Reissner-Nordström black hole by using numerical simulations. We learned that the value $Mm$ plays an important role in determining the properties of the relaxation of the perturbation. For $Mm << 1$ the relaxation process depends only on the field parameter and does not depend on the spacetime parameters. For $Mm >> 1$, the dependence of the relaxation on the black hole parameters appears. The bigger mass of the black hole, the faster the perturbation decays. The difference of the relaxation process caused by the black hole c…
We study deformations of the Klebanov-Strassler background parametrized by the size of a dim-6 VEV. In the UV, these solutions describe the usual duality cascade of Klebanov-Strassler; however below the scale rho* set by the dim-6 VEV they exhibit hyperscaling violation over a range of the radial coordinate. Focusing on the spectrum of scalar glueballs, we find a parametrically light state, the mass of which is suppressed by rho*, becoming massless in the limit of rho* -> infinity. Along the way, we clarify the choice of IR and UV boundary conditions for the fluctuations in the bulk, and find …
We consider flat solutions in the brane background with a massless scalar field appearing in 5D $H^2_{MNPQ}$. Since there exist bulk singularities or arises the divergent 4D Planck mass, we should introduce a compact extra dimension, the size of which is then fixed by brane tension(s) and a bulk cosmological constant. Inspecting scalar perturbations around the flat solutions, we find that the flat solutions are stable vacua from the positive mass spectrum of radion. We show that the massless radion mode is projected out by the boundary condition arising in cutting off the extra dimension. Thus…
Using the background field method, we, in the large $N_f$ approximation, calculate the beta function of scalar quantum electrodynamics at the first nontrivial order in $1/N_f$ by two different ways. In the first way, we get the result by summing all the graphs contributing directly. In the second way, we begin with the Borel transform of the related two point Green's function. The main results are that the beta function is fully determined by a simple function and can be expressed as an analytic expression with a finite radius of convergence, and the scheme-dependent renormalized Borel transfo…
We discuss massive scalar field with conformal coupling in Friedmann-Robertson-Walker (FRW) Universe of special type with constant electromagnetic field. Treating an external gravitational-electromagnetic background exactly, at first time the proper-time representations for out-in, in-in, and out-out scalar Green functions are explicitly constructed as proper-time integrals over the corresponding (complex) contours. The vacuum-to-vacuum transition amplitudes and number of created particles are found and vacuum instability is discussed. The mean values of the current and energy-momentum tensor …
The quantum dynamics of quarks, gluons and the scalar degrees of freedom associated with the non-linear regime of the non-linear gauge is derived. We discuss the subtleties in quantizing in a stochastic background. Then we show in detail that the stochastic average of the Yang-Mills action is only dependent on the gluon and not on the scalars thus proving that the scalars are non-propagating. Integrating out the scalars from the stochastically averaged fermion action leads to fermions that decline exponentially. Finally, we derive the effective action of the gluons and fermions resulting from …
We consider 2D Yukawa theory in the strong scalar wave background. We use operator and functional formalisms. In the latter the Schwinger--Keldysh diagrammatic technique is used to calculate retarded, advanced and Keldysh propagators. We use simplest states in the two formalisms in question, which appear to be different from each other. As the result two Keldysh propagators found in different formalisms do not coincide, while the retarded and advanced ones do coincide. We use these propagators to calculate physical quantities. Such as the fermion stress energy flux and the scalar current. The …
The scalar background field and its consequences are discussed for the Friedmann type cosmological solutions of the scalar-tensor theory of gravity with the Higgs field of the Standard Model as the scalar gravitational field.
We study scalar radiation spectra from a particle in circular orbit, in the background of the Janis-Newman-Winicour (JNW) naked singularity. The differences in the nature of the spectra, from what one obtains with a Schwarzschild black hole, is established. We also compute the angular distribution of the spectra.
We consider two--dimensional Yukawa theory in the scalar wave background $ϕ(t-x)$. If one takes as initial state in such a background the scalar vacuum corresponding to $ϕ=0$, then loop corrections to a certain part of the Keldysh propagator, corresponding to the anomalous expectation value, grow with time. That is a signal to the fact that under the kick of the $ϕ(t-x)$ wave the scalar field rolls down the effective potential from the $ϕ=0$ position to the proper ground state. We show the evidence supporting these observations.
We discuss what is light-cone quantization on a curved spacetime also without a null Killing vector. Then we consider as an example the light-cone quantization of a scalar field on a background with a Killing vector and the connection with the second quantization of the particle in the same background. It turns out that the proper way to define the light-cone quantization is to require that the constant light-cone time hypersurface is null or, equivalently, that the particle Hamiltonian is free of square roots. Moreover, in order to quantize the scalar theory it is necessary to use not the ori…
In this paper it is shown how to obtain, without ever using the background classical equations of motion, a simple second order Hamiltonian involving the Mukhanov-Sasaki variable describing quantum linear scalar perturbations for the case of scalar fields with arbitrary potentials and arbitrary spacelike hyper-surfaces. It is a generalization of previous works, where the scalar field potential was absent and the spacelike hypersurfaces were flat. This was possible due to the implementation of a new method, together with the Faddeev-Jackiw procedure for the constraint reduction. The resulting H…
We invesigate analytically both the intermediate and late-time behaviour of the massive scalar field in the background of static spherically symmetric black hole solution in dilaton gravity with arbitrary coupling constant. The intermediate asymptotic behaviour of scalar field depends on the field's parameter mass as well as the multiple number l. On its turn, the late-time behaviour has the power law decay rate independent on coupling constant in the theory under consideration.
We show that a {\it massless} scalar field in a gravitational wave background can develop a non-zero vacuum expectation value. We draw comparisons to the generation of a non-zero vacuum expectation value for a scalar field in the Higgs mechanism and with the dynamical Casimir vacuum. We propose that this vacuum expectation value, generated by a gravitational wave, can be connected with particle production from gravitational waves and may have consequences for the early Universe where scalar fields are thought to play an important role.
We extend to curved backgrounds all flat-space scalar field models that obey purely second-order equations, while maintaining their second-order dependence on both field and metric. This extension simultaneously restores to second order the, originally higher derivative, stress tensors as well. The process is transparent and uniform for all dimensions.
We consider scalar fields which are coupled to Einstein gravity with a negative cosmological constant, and construct periodic solutions perturbatively. In particular, we study tachyonic scalar fields whose mass is at or above the Breitenlohner-Freedman bound in four, five, and seven spacetime dimensions. The critical amplitude of the leading order perturbation, for which the perturbative expansion breaks down, increases as we consider less massive fields. We present various examples including a model with a self-interacting scalar field which is derived from a consistent truncation of IIB supe…
We show that a suitable deformation of the algebra $h_k(1)$ of the creation and annihilation operators for a complex scalar field, initially quantized in Minkowski space--time, induces the canonical quantization of the same field in a generic gravitational background. This discloses the physical meaning of the deformation parameter $q$ which turns out to be related to the gravitational field. The thermal properties are re-obtained in this formalism, and the application to Schwarzschild and Rindler space-times are carried out.
We study the scalar perturbation on the background of a Kerr black hole in the dynamical Chern-Simons modified gravity with a quadratic coupling between the scalar field and Chern-Simons term. In particular, the late-time tails of scalar perturbations are investigated numerically in time domain by using the hyperboloidal foliation method. It is found that the Kerr black hole becomes unstable under linear perturbations in a certain region of the parameter space, which depends on the harmonic azimuthal index $m$ of the perturbation's mode. This may indicate that some Kerr black holes in this the…
Behaviour of a weekly self-interacting scalar field with a small mass in the de Sitter background is investigated using the stochastic approach (including the case of a double-well interaction potential). Existence of the de Sitter invariant equilibrium quantum state of the scalar field in the presence of interaction is shown for any sign of the mass term. The stochastic approach is further developed to produce a method of calculation of an arbitrary anomalously large correlation function of the scalar field in the de Sitter background, and expressions for the two-point correlation function in…
The propagator of a scalar field on a stationary slowly varying in space gravitational background is derived retaining only the second derivatives of the metric. The corresponding one-loop effective action is constructed. The propagator and the effective action turn out to depend nontrivially on the Killing vector defining the vacuum state and the Hamiltonian of a scalar field. The Hawking particle production is described in the quasiclassical approximation and the quasiclassical formula for the Hawking temperature is derived. The behaviour of the Unruh detector on a curved background is consi…
We discuss the possible detection of a stochastic background of massive, non-relativistic scalar particles, through the cross correlation of the two LIGO interferometers in the initial, enhanced and advanced configuration. If the frequency corresponding to the mass of the scalar field lies in the detector sensitivity band, and the non-relativistic branch of the spectrum gives a significant contribution to energy density required to close the Universe, we find that the scalar background can induce a non-negligible signal, in competition with a possible signal produced by a stochastic background…
General-relativistic stable spacetimes can be made unstable under the presence of certain nonminimally coupled free scalar fields. In this paper, we analyze the evolution of linear scalar-field perturbations in spherically symmetric spacetimes and compare the classical stability analysis with a recently discussed quantum field one. In particular, it is shown that vacuum fluctuations lead to natural seeds for the unstable phase, whereas in the classical framework the presence of such seeds in the initial conditions must be assumed.
We study spatially localized, time-periodic solutions (breathers) of scalar field theories with various self-interacting potentials on Anti-de Sitter (AdS) spacetimes in $D$ dimensions. A detailed numerical study of spherically symmetric configurations in $D=3$ dimensions is carried out, revealing a rich and complex structure of the phase-space (bifurcations, resonances). Scalar breather solutions form one-parameter families parametrized by their amplitude, $\varepsilon$, while their frequency, $ω=ω(\varepsilon)$, is a function of the amplitude. The scalar breathers on AdS we find have a small…
A large mass expansion of the one-loop effective action of a scalar field on the two-dimensional Minkowski spacetime is found in the system of coordinates, where the metric $g_{μν}(t,x)\neqη_{μν}=diag(1,-1)$, and $g_{μν}(t,x)$ tends to $η_{μν}$ at the spatial and temporal infinities. It is shown that, apart from the Coleman-Weinberg potential, this expansion contains the terms both analytic and non-analytic in $m^{-2}$, where $m$ is the mass of a scalar field. A general unambiguous expression for the one-loop correction to the effective action on non-stationary backgrounds is derived.
