We argue that the theory of a massive higher spin field coupled to electromagnetism in flat space possesses an intrinsic, model independent, finite upper bound on its UV cutoff. By employing the Stueckelberg formalism we do a systematic study to quantify the degree of singularity of the massless limit in the cases of spin 2, 3, 3/2, and 5/2. We then generalize the results for arbitrary spin to find an expression for the maximum cutoff of the theory as a function of the particle's mass, spin, and electric charge. We also briefly explain the physical implications of the result and discuss how it could be sharpened by use of causality constraints.
The properties of strongly gravitating systems suggest that field theory overcounts the states of a system. Reducing the number of degrees of freedom, without abandoning the notion of effective field theory, may be achieved through a connection between the ultraviolet and infrared cutoffs. We provide an implementation of this idea within the Wilsonian approach to the renormalization group. We derive an exact flow equation that describes the evolution of the effective action. We discuss the implications for the existence of infrared fixed points and the running of couplings. We also give an alt…
We show that it is possible to formulate a gauge theory starting from a local action at the ultraviolet (UV) momentum cutoff which is BRS invariant. One has to require that fields in the UV action and the fields in the effective action are not the same but related by a local field transformation. The few relevant parameters involved in this transformation (six for the $SU(2)$ gauge theory), are perturbatively fixed by the gauge symmetry.
The momentum UV cutoff in Quantum Field Theory is usually treated as an auxiliary device allowing to obtain finite amplitudes satisfying all physical requirements. It is even absent (not explicit) in the most popular approach - the dimensional regularization. We point out that the momentum cutoff treated as a bona fide physical scale, presumably equal or related to the Planck scale, would lead to unacceptable predictions. One of the dangers is a non-zero mass of the photon. In the naive approach, even with the cutoff equal to the Planck scale, this mass would grossly exceed the existing experi…
We study the thermodynamics of charged rotating black hole in large extra dimensions scenario where quantum gravity effects are taken into account. We consider the effects of minimal length, minimal momentum, and maximal momentum as natural cutoffs on the thermodynamics of charged rotating TeV-scale black holes. In this framework the effect of the angular momentum and charge on the thermodynamics of the black hole are discussed. We focus also on frame dragging and Sagnac effect of the micro black holes.
We study ultraviolet cutoffs associated with the Weak Gravity Conjecture (WGC) and Sublattice Weak Gravity Conjecture (sLWGC). There is a magnetic WGC cutoff at the energy scale $e G_N^{-1/2}$ with an associated sLWGC tower of charged particles. A more fundamental cutoff is the scale at which gravity becomes strong and field theory breaks down entirely. By clarifying the nature of the sLWGC for nonabelian gauge groups we derive a parametric upper bound on this strong gravity scale for arbitrary gauge theories. Intriguingly, we show that in theories approximately saturating the sLWGC, the scale…
We compute holographic complexity of charged black brane solutions in arbitrary dimensions for the near horizon limit of near extremal case using two different methods. The corresponding complexity may be obtained either by taking the limit from the complexity of the charged black brane, or by computing the complexity for near horizon limit of near extremal solution. One observes that these results coincide if one assumes to have a cutoff behind horizon whose value is fixed by UV cutoff and also taking into account a proper counterterm evaluated on this cutoff. We also consider the situation f…
We show that the confinement-deconfinement phase transition of supersymmetric Yang-Mills theories with 16 supercharges in various dimensions can be realized through the Hawking-Page phase transition between the near horizon geometries of black Dp-branes and BPS Dp-branes by removing a small radius region in the geometry in order to realize a confinement phase, which generalizes the Herzog's discussion for the holographic hard-wall AdS/QCD model. Removing a small radius region in the gravitational dual corresponds to introducing an IR cutoff in the dual field theory. We also discuss the Hawking…
A projection method is proposed to treat the one-dimensional Schrodinger equation for a single particle when the Generalized Uncertainty Principle (GUP) generates an ultraviolet (UV) wavevector cutoff. The existence of a unique coordinate representation called the naive one is derived from the one-parameter family of discrete coordinate representations. In this bandlimited Quantum Mechanics a continuous potential is reconstructed from discrete sampled values observed by means of a particle in maximally localized states. It is shown that bandlimitation modifies the speed of the center and the s…
Quantum gravity arguments and the entropy bound for effective field theories proposed in PRL 82, 4971 (1999) lead to consider two correlated scales which parametrize departures from relativistic quantum field theory at low and high energies. A simple estimate of their possible phenomenological implications leads to identify a scale of around 100 TeV as an upper limit on the domain of validity of a quantum field theory description of Nature. This fact agrees with recent theoretical developments in large extra dimensions. Phenomenological consequences in the beta-decay spectrum and cosmic ray ph…
We clarify a point concerning the ultraviolet behaviour of the Quantum Field Theory of gravity, under the assumption of the existence of an ultraviolet Fixed Point. We explain why Newton's constant should to scale like the inverse of the square of the cutoff, even though it is technically inessential. As a consequence of this behaviour, the existence of an UV Fixed Point would seem to imply that gravity has a built-in UV cutoff when described in Planck units, but not necessarily in other units.
It has been pointed out that the perturbation spectrum predicted by inflation may be sensitive to a natural ultraviolet cutoff, thus potentially providing an experimentally accessible window to aspects of Planck scale physics. A priori, a natural ultraviolet cutoff could take any form, but a fairly general classification of possible Planck scale cutoffs has been given. One of those categorized cutoffs, also appearing in various studies of quantum gravity and string theory, has recently been implemented into the standard inflationary scenario. Here, we continue this approach by investigating it…
This article is an addendum to [1]. We extend our computation of the on-shell scattering amplitudes in an arbitrary inflaton background $\barϕ_1$. Although the effective Einstein frame cutoff for $\barϕ_1>>M_P/\sqrtξ$ turns out to be $\barϕ_1$ or $ξ\barϕ_1$ for the $U(1)$ model, this is not the case for the realistic doublet Higgs model where the effective Einstein frame cutoff turns out to be the standard $M_P/\sqrtξ$ for both the Palatini and metric formulations. Then, as it has been pointed out in [1] the background $\barϕ_1$ is the effective Jordan frame cutoff for both the Palatini and me…
We calculate the impact of quantum gravity-motivated ultraviolet cutoffs on inflationary predictions for the cosmic microwave background spectrum. We model the ultraviolet cutoffs fully covariantly to avoid possible artifacts of covariance breaking. Imposing these covariant cutoffs results in the production of small, characteristically $k-$dependent oscillations in the spectrum. The size of the effect scales linearly with the ratio of the Planck to Hubble lengths during inflation. Consequently, the relative size of the effect could be as large as one part in $10^5$; i.e., eventual observabilit…
The holographic charged fluid with anomalous current in Einstein-Maxwell gravity has been generalized from the infinite boundary to the finite cutoff surface by using the gravity/fluid correspondence. After perturbing the boosted Reissner-Nordstrom (RN)-AdS black brane solution of the Einstein-Maxwell gravity with the Chern-Simons term, we obtain the first order perturbative gravitational and Maxwell solutions, and calculate the stress tensor and charged current of the dual fluid at finite cutoff surfaces which contains undetermined parameters after demanding regularity condition at the future…
The existence of a natural ultraviolet cutoff at the Planck scale is widely expected. In a previous Letter, it has been proposed to model this cutoff as an information density bound by utilizing suitably generalized methods from the mathematical theory of communication. Here, we prove the mathematical conjectures that were made in this Letter.
We investigate the noncommutative analogue of the spontaneously broken linear sigma model at the one-loop quantum level. In the commutative case, renormalization of a theory with a spontaneously broken continuous global symmetry depends on cancellations that enable the limited set of counterterms consistent with that symmetry to remove the divergences even after its spontaneous breaking, while preserving the masslessness of the associated Goldstone modes. In the noncommutative case, we find that these cancellations are violated, and the renormalized one-loop correction to the inverse pion prop…
Following earlier work on the same topic, we consider once more scalar field theories on the world sheet parametrized by the light cone coordinates. For most of the way, we use the same approach as in the previous work, but there is an important new development. To avoid the light cone singularity at p^{+}=0, one world sheet coordinate had to be discretized, introducing a cutoff into the model.In the earlier work, this cutoff could not be removed, making the model unreliable. In the present article, we show that, by a careful choice of the mass counter term, both the infrared singularity at p^…
Based on the previous paper arXiv:1207.5309, we investigate the possibility to find out the bulk viscosity of dual fluid at the finite cutoff surface via gravity/fluid correspondence in Einstein-Maxwell gravity. We find that if we adopt new conditions to fix the undetermined parameters contained in the stress tensor and charged current of the dual fluid, two new terms appear in the stress tensor of the dual fluid. One new term is related to the bulk viscosity term, while the other can be related to the perturbation of energy density. In addition, since the parameters contained in the charged c…
The need for a cutoff in the Lamb shift calculation suggests that high-energy virtual photons do not interact with real particles. In this paper, we assume that the creation of high-energy virtual particles is suppressed by a Boltzmann factor. As a result, the Coulomb potential is modified, and the zero-point energy density and one-particle-irreducible self-energy of the scalar field are finite.
In the tunneling framework of Hawking radiation, charged massive particle's tunneling in charged non-rotating TeV-Scale black hole is investigated. To this end, we consider natural cutoffs as a minimal length, a minimal momentum, and a maximal momentum through a generalized uncertainty principle. We focus on the role played by these natural cutoffs on the luminosity of charged non-rotating micro black hole by taking into account the full implications of energy and charge conservation as well as the back- scattered radiation.
Based on reasonable assumptions, we propose a new expression for Lloyd's bound, which confines the complexity growth of charged black holes. We then revisit holographic complexity for charged black branes in the presence of a finite cutoff. Using the proposed Lloyd's bound we find a relation between the UV and the behind the horizon cutoff. This is found to be consistent with the factorization of the partition function at leading order in large N. We argue that the result may be thought of as a holographic realization of strong cosmic censorship.
With the help of a Stueckelberg field we construct a regularized U(1) gauge invariant action through the introduction of cutoff functions. This action has the property that it converges formally to the unregularized action of QED when the ultraviolet cutoff goes to infinity. Integrating out exactly the Stueckelberg field we obtain a simple effective regularized action, which is fully gauge invariant and gives rise to the same prediction as QED at the tree level and to the one loop order.
To achieve a maximal locality in a trivial field theory, we maximize the ultraviolet cutoff of the theory by fine tuning the infrared values of the parameters. This optimization procedure is applied to the scalar theory in $D+1$ dimensions ($D \geq 4$) with one extra dimension compactified on a circle with radius $R$. The optimized, infrared values of the parameters are then compared with the corresponding ones of the uncompactified theory in $D$ dimensions, which is assumed to be the low-energy effective theory. We find that these values approximately agree with each other, as long as $R^{-1}…
The idea of relating the infrared and ultraviolet cutoffs is applied to Brans-Dicke theory of gravitation. We find that extended holographic dark energy from the Hubble scale or the particle horizon as the infrared cutoff will not give accelerating expansion. The dynamical cosmological constant with the event horizon as the infrared cutoff is a viable dark energy model.
We clarify the notion of Wilsonian renormalization group (RG) invariance in supersymmetric gauge theories, which states that the low-energy physics can be kept fixed when one changes the ultraviolet cutoff, provided appropriate changes are made to the bare coupling constants in the Lagrangian. We first pose a puzzle on how a quantum modified constraint (such as Pf(Q^i Q^j) = Λ^{2(N+1)} in SP(N) theories with N+1 flavors) can be RG invariant, since the bare fields Q^i receive wave function renormalization when one changes the ultraviolet cutoff, while we naively regard the scale Λas RG invarian…
The quantum structure of Spacetime at the Planck scale suggests the use, in defining interactions between fields, of the Quantum Wick product. The resulting theory is ultraviolet finite, but subject to an adiabatic cutoff in time which seems difficult to remove. We solve this problem here by another strategy: the fields at a point in the interaction Lagrangian are replaced by the fields at a quantum point, described by an optimally localized state on QST; the resulting Lagrangian density agrees with the previous one after spacetime integration, but gives rise to a different interaction hamilto…
At present no theory of a massive graviton is known that is consistent with experiments at both long and short distances. The problem is that consistency with long distance experiments requires the graviton mass to be very small. Such a small graviton mass however implies an ultraviolet cutoff for the theory at length scales far larger than the millimeter scale at which gravity has already been measured. In this paper we attempt to construct a model which avoids this problem. We consider a brane world setup in warped AdS spacetime and we investigate the consequences of writing a mass term for …
We consider one loop graviton corrections to scalar field Green's functions in the de Sitter phase of an inflationary space-time, a topic relevant to the computation of cosmological observables beyond linear order. By embedding de-Sitter space into an ultraviolet complete theory such as M-theory we argue that the ultraviolet (UV) cutoff of the effective field theory should be taken to be fixed in physical coordinates, whereas the infrared (IR) cutoff is expanding as space expands. In this context, we demonstrate how to implement three different regularization schemes -- the brute force cutoff …
The Wilsonian renormalization group implies that an arbitrary four dimensional field theory with an ultraviolet cutoff is equivalent to a theory which is renormalizable by power counting at energy scales much below the cutoff. This applies to any theory including those with non-renormalizable interactions as long as we fine-tune the mass parameters. We analyze two simple models with current-current interactions but without elementary gauge fields from this viewpoint. We show how to tune the parameters of the models so that they become equivalent to QED at energies much below the cutoff.
We show that the well-known Čerenkov Effect contains new phenomena arising from the quantum nature of charged particles. The Čerenkov transition amplitudes allow coupling between the charged particle and the emitted photon through their orbital angular momentum (OAM) and spin, by scattering into preferred angles and polarizations. Importantly, the spectral response reveals a discontinuity immediately below a frequency cutoff that can occur in the optical region. Specifically, with proper shaping of electron beams (ebeams), we predict that the traditional Čerenkov radiation angle splits into tw…
The Hamiltonian approach to the quantum field theory is considered. Since there are additional difficulties such as the Haag theorem and Stueckelberg divergences, renormalization of the time-dependent dynamical quantum field theory is much more complicated than renormalization of the S-matrix. It is necessary to consider the regularized theory with ultraviolet and infrared cutoffs and impose the conditions not only on the dependence of the Hamiltonian on the cutoffs (as usual) but also on the dependence of the initial states. It happens that one should consider the initial states to be singula…
We study the dual fluid on a finite cutoff surface outside the black brane horizon in the third order Lovelock gravity. Using nonrelativistic long-wavelength expansion, we obtain the incompressible Navier-Stokes equations of dual fluid with external force density on the finite cutoff surface. The viscosity to entropy density ratio $η/s$ is independent of cutoff surface and does not get modification from the third order Lovelock gravity influence. The obtained ratio agrees with the results obtained by using other methods, such as the Kubo formula at the AdS boundary and the membrane paradigm at…
We consider the decay of a false vacuum in circumstances where the methods suggested by Coleman run into difficulties. We find that in these cases quantum fluctuations play a crucial role. Namely, they naturally induce both an ultraviolet and infrared cutoff scales, determined by the parameters of the classical solution, beyond which this solution cannot be trusted anymore. This leads to the appearance of a broad class of new $O(4)$ invariant instantons, which would have been singular in the absence of an ultraviolet cutoff. We apply our results to a case where the potential is unbounded from …
We consider a model for a Planck scale ultraviolet cutoff which is based on Shannon sampling. Shannon sampling originated in information theory, where it expresses the equivalence of continuous and discrete representations of information. When applied to quantum field theory, Shannon sampling expresses a hard ultraviolet cutoff in the form of a bandlimitation. This introduces nonlocality at the cutoff scale in a way that is more subtle than a simple discretization of space: quantum fields can then be represented as either living on continuous space or, entirely equivalently, as living on any o…
The construction of quantum field theory (QFT) of a free massive scalar field with respect to a general congruence of observers is considered, the splitting into positive- and negative-frequency modes being defined by diagonalization of the instantaneous Hamiltonian. The explicit expression for the ultraviolet asymptotics of the average number of particles created from the vacuum is found. It is shown that, for a general congruence of observers in the $D$-dimensional spacetime with $D\geqslant3$, the total number of created particles diverges in the ultraviolet domain in the regularization rem…
We present the first numerical study of the ultraviolet dynamics of non-asymptotically free gauge-fermion theories at large number of matter fields. As testbed theories we consider non-abelian SU(2) gauge theories with 24 and 48 Dirac fermions on the lattice. For these number of flavors asymptotic freedom is lost and the theories are governed by a gaussian fixed point at low energies. In the ultraviolet they can develop a physical cutoff and therefore be trivial, or achieve an interacting safe fixed point and therefore be fundamental at all energy scales. We demonstrate that the gradient flow …
Unrenormalizable theories contain infinitely many free parameters. Considering these theories in terms of the Wilsonian renormalization group (RG), we suggest a method for removing this large ambiguity. Our basic assumption is the existence of the maximal ultraviolet cutoff in a cutoff theory, and we require that the theory be so fine-tuned as to reach the maximal cutoff. The theory so obtained behaves as a local continuum theory to the shortest distance. In concrete examples of the scalar theory we find that at least in a certain approximation to the Wilsonian RG, this requirement enable us t…
In the `condensed phase' of effective quantum field theories one expects deviations from exact Lorentz invariance at ultralow momenta | k| < delta where the shell 'delta' should only vanish in the strict local limit of the theory when the ultraviolet cutoff 'Lambda' tends to infinity. I explore this idea for the Higgs condensate suggesting that, in this case, the resulting relation connecting 'delta', 'Lambda' and the Fermi scale might provide a simple physical solution of the `hierarchy problem'. In this picture, the Planck scale is not a purely ultraviolet quantity but embodies in its numeri…
We show how quantum fields can be used to measure the curvature of spacetime. In particular, we find that knowledge of the imprint that spacetime curvature leaves in the correlators of quantum fields suffices, in principle, to reconstruct the metric. We then consider the possibility that the quantum fields obey a natural ultraviolet cutoff, for example, at the Planck scale. We investigate how such a cutoff limits the spatial resolution with which curvature can be deduced from the properties of quantum fields. We find that the metric deduced from the quantum correlator exhibits a peculiar scali…
Group field theory is a generalization of matrix models, with triangulated pseudomanifolds as Feynman diagrams and state sum invariants as Feynman amplitudes. In this paper, we consider Boulatov's three-dimensional model and its Freidel-Louapre positive regularization (hereafter the BFL model) with a ?ultraviolet' cutoff, and study rigorously their scaling behavior in the large cutoff limit. We prove an optimal bound on large order Feynman amplitudes, which shows that the BFL model is perturbatively more divergent than the former. We then upgrade this result to the constructive level, using, i…
Quantum fields in vacuum states carry an infinite amount of quantum entanglement, and its entanglement entropy has the ultraviolet divergence. Harvesting protocols of the vacuum entanglement had been investigated, but its efficiency is very low to date. The main reason of the low efficiency originates from the fact that the extracted entanglement is embedded in a mixed state of two external devices. We propose a general protocol with high efficiency by extracting pure state entanglement from the field. We only use bi-linear interactions between the fields and external devices. Even though the …
It is suggested that the Minkowski vacuum of quantum field theories of a large number of fields N would be gravitationally unstable due to strong vacuum energy fluctuations unless an N dependent sub-Planckian ultraviolet momentum cutoff is introduced. We estimate this implied cutoff using an effective quantum theory of massless fields that couple to semi-classical gravity and find it (assuming that the cosmological constant vanishes) to be bounded by $M_Planck/N^1/4$. Our bound can be made consistent with entropy bounds and holography, but does not seem to be equivalent to either, and it relax…
The present paper is devoted to the detailed study of quantization and evolution of the point limit of the Pauli-Fierz model for a charged oscillator interacting with the electromagnetic field in dipole approximation. In particular, a well defined dynamics is constructed for the classical model, which is subsequently quantized according to the Segal scheme. To this end, the classical model in the point limit is reformulated as a second order abstract wave equation, and a consistent quantum evolution is given. This allows a study of the behaviour of the survival and transition amplitudes for th…
It has been suggested that a scalar field with negative kinetic energy, or ``ghost,'' could be the source of the observed late-time cosmological acceleration. Naively, such theories should be ruled out by the catastrophic quantum instability of the vacuum. We derive phenomenological bounds on the Lorentz-violating ultraviolet cutoff Lambda which must apply to low-energy effective theories of ghosts, in order to keep the instability at unobservable levels. Assuming only that ghosts interact at least gravitationally, we show that Lambda < 3 MeV for consistency with the cosmic gamma ray backgroun…
