We show that lowering of the gravitational cutoff relative to the Planck mass, imposed by black hole physics in theories with N species, has an independent justification from quantum information theory. First, this scale marks the limiting capacity of any information processor. Secondly, by taking into the account the limitations of the quantum information storage in any system with species, the bound on the gravity cutoff becomes equivalent to the holographic bound, and this equivalence automatically implies the equality of entanglement and Bekenstein-Hawking entropies. Next, the same bound follows from quantum cloning theorem. Finally, we point out that by identifying the UV and IR threshold scales of the black hole quasi-classicality in four-dimensional field and high-dimensional gravity theories, the bound translates as the correspondence between the two theories. In case when the high-dimensional background is AdS, this reproduces the well-known AdS/CFT relation, but also suggests a generalization of the correspondence beyond AdS spaces. In particular, it reproduces a recently suggested duality between a four-dimensional CFT and a flat five dimensional theory, in which gravity crosses over from four to five dimensional regime in far infrared.
Using the complexity equals action proposal we study holographic complexity for hyperscaling violating theories in the presence of a finite cutoff that, in turns, requires to obtain all counter terms needed to have finite boundary energy momentum tensor. These terms could give non-trivial contributions to the complexity. We observe that having a finite UV cutoff would enforce us to have a cutoff behind the horizon whose value is fixed by the UV cutoff; moreover, certain counter term should be defined on the cutoff behind the horizon too.
We study the black hole entropy as entanglement entropy and propose a resolution to the species puzzle. This resolution comes out naturally due to the fact that in the presence of $N$ species the universal gravitational cutoff is $Λ=M_{\rm Planck}/\sqrt{N}$, as opposed to $M_{\rm Planck}$. We demonstrate consistency of our solution by showing the equality of the two entropies in explicit examples in which the relation between $M_{\rm Planck}$ and $Λ$ is known from the fundamental theory.
We show that general cutoff scalar field theories in four dimensions are perturbatively renormalizable through the use of diagrammatic techniques and an adapted BPH renormalization method. Weinberg's convergence theorem is used to show that operators in the Lagrangian with dimension greater than four, which are divided by powers of the cutoff, produce perturbatively only local divergences in the two-, three-, and four-point correlation functions. We also show that the renormalized Green's functions are the same as in ordinary $Φ^4$ theory up to corrections suppressed by inverse powers of the c…
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…
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^…
We conjecture an intrinsic UV cutoff for the validity of the effective field theory with a large number of species coupled to gravity. In four dimensions such a UV cutoff takes the form $Λ=\sqrt{λ/ N}M_p$ for $N$ scalar fields with the same potential $λϕ_i^4$, $i=1,...,N$. This conjecture implies that the assisted chaotic inflation or N-flation might be in the swampland, not in the landscape. Similarly a UV cutoff $Λ=gM_p/\sqrt{N}$ is conjectured for the U(1) gauge theory with $N$ species.
We set an upper bound on the gravitational cutoff in theories with exact quantum numbers of large N periodicity, such as Z_N discrete symmetries. The bound stems from black hole physics. It is similar to the bound appearing in theories with N particle species, though a priori, a large discrete symmetry does not imply a large number of species. Thus, there emerges a potentially wide class of new theories, that address the hierarchy problem by lowering the gravitational cutoff due to existence of large Z_{10^32}-type symmetries.
The most natural expectation away from asymptotic limits in moduli space of supergravity theories is the desert scenario, where there are few states between massless fields and the quantum gravity cutoff. In this paper we initiate a systematic study of these regions deep in the moduli space, and use it to place a bound on the number of massless modes by relating it to the black hole species problem. There exists a consistent sub-Planckian UV cutoff (the species scale) which resolves the black hole species problem without bounding the number of light modes. We reevaluate this in the context of …
We generalize the $T\overline{T}$ deformation of CFT$_2$ to higher-dimensional large-$N$ CFTs, and show that in holographic theories, the resulting effective field theory matches semiclassical gravity in AdS with a finite radial cutoff. We also derive the deformation dual to arbitrary bulk matter theories. Generally, the deformations involve background fields as well as CFT operators. By keeping track of these background fields along the flow, we demonstrate how to match correlation functions on the two sides in some simple examples, as well as other observables.
The functional renormalization group flow of a scalar field theory with quartic couplings and a sharp spatial momentum cutoff is presented in four-dimensional Minkowski space-time for the bare action by retaining the entanglement of the IR and the UV particle modes. It is argued that the open interaction channels have to be taken into account in quantum field theory defined by the help of a cutoff, and a non-perturbative UV-IR entanglement is found in closed or almost closed models.
It is shown that by imposing the relativistic symmetries on the cutoff in field theories one rules out all known non-perturbative regulators except the point splitting. The relativistic cutoff dynamics is non-local in time and thereby unstable, bringing the very existence of relativistic field theory into question. It is argued within the context of a scalar field theory model that the combination of the point splitting with a sufficiently fast suppression in the field amplitude may lead to stable semiclassical dynamics and to a new kind of realistic vacuum structure.
We investigate the realization of the emergent universe scenario in theories with natural UV cutoffs, namely a minimum length and a maximum momentum, quantified by a new deformation parameter in the generalized uncertainty principle. We extract the Einstein static universe solutions and we examine their stability through a phase-space analysis. As we show, the role of the new deformation parameter is crucial in a twofold way: Firstly, it leads to the appearance of new Einstein static universe critical points, that are absent in standard cosmology. Secondly, it provides a way for a graceful exi…
The three-point current correlation function in Euclidean spacetime for a strongly coupled system with non-Abelian global symmetry, $\langle J^a_i(x)J^b_j(y)J^c_k(z)\rangle$, is calculated from the weakly coupled AdS dual. The contribution from the first non-renormalizable bulk operator, $(F_{μν})^3$, is calculated and shown to lead to a polarization structure different from the leading contribution, which comes from the renormalizable $(F_{μν})^2$ operator. The non-renormalizable correction is suppressed by powers of the cutoff scale $Λ$. This suggests a possible experimental probe of the eff…
We investigate the perturbative renormalisation of deformed conformal field theories from the Hamiltonian perspective. We discuss the relation with conformal perturbation theory, to which we provide an explicit match up to third order in the coupling, and show how second-order anomalous dimensions in the Wilson-Fisher fixed points are straightforwardly computed in the Hamiltonian framework. The second part of the paper focuses on the cutoff employed in the truncated conformal space approach of Yurov and Zamolodchikov. We discuss the appearance of non-covariant and non-local counterterms to sec…
We consider a scalar quantum field theory, in which the interaction takes the form of a field cutoff; the energy diverges to infinity whenever the value of the field at some point falls outside a finite interval. In a simple (1+1)-dimensional version of this theory, we may calculate the results of certain scattering processes exactly. The main feature of the nontrivial solutions is the appearance of shock fronts, whose time development is irreversible. The resulting nonunitarity implies that these theories are, at a minimum, radically different from conventional quantum field theories.
Relying solely on unitarity and the consistency with large-distance black hole physics, we derive model-independent properties of the microscopic black holes and of short-distance gravity in theories with N particle species. In this class of theories black holes can be as light as M_{Planck}/\sqrt{N} and be produced in particle collisions above this energy. We show, that the micro black holes must come in the same variety as the species do, although their label is not associated with any conserved charge measurable at large distances. In contrast with big Schwarzschildian ones, the evaporation…
We consider unitary and weakly coupled theories of gravity that extend Einstein gravity and reduce to it asymptotically at large distances. Our discussion is restricted to such theories that, similarly to Einstein gravity, contain black holes as semiclassical states in a range of scales. We show that, at a given scale, the entropy of these black holes has to be larger than the number of elementary light species in the theory. Our bound follows from the observation that the black hole entropy has to be larger than the product of its mass and horizon radius (in units of Planck's constant divided…
We give a new perspective on the dynamics of conformal theories realized in the SU(N) gauge theory, when the number of flavors N_f is within the conformal window. Motivated by the RG argument on conformal theories with a finite IR cutoff Λ_{IR}, we conjecture that the propagator of a meson G_H(t) on a lattice behaves at large t as a power-law corrected Yukawa-type decaying form G_H(t) = c_H \exp{(-m_H t)}/t^{α_H} instead of the exponentially decaying form c_H\exp{(-m_H t)}, in the small quark mass region where m_H \le c Λ_{IR}: m_H is the mass of the ground state hadron in the channel H and c …
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…
The dual fluid description for a general cutoff surface at radius r=r_c outside the horizon in the charged AdS black brane bulk space-time is investigated, first in the Einstein-Maxwell theory. Under the non-relativistic long-wavelength expansion with parameter ε, the coupled Einstein-Maxwell equations are solved up to O(ε^2). The incompressible Navier-Stokes equation with external force density is obtained as the constraint equation at the cutoff surface. For non-extremal black brane, the viscosity of the dual fluid is determined by the regularity of the metric fluctuation at the horizon, who…
In theories with many copies of the Standard Model virtual black hole exchange may produce effective higher dimensional operators that can be treated below the cutoff scale as fundamental vertices of interspecies non-gravitational interaction. We consider the vertex that couples fermions of one species through magnetic moment to photons of other species, and study the quantum corrections it generates. In particular, we find kinetic mixing between photons of different species produced via fermion loops. Diagonalization of gauge kinetic terms then renders the fermions millicharged under other sp…
A recent proposal relates two dimensional holographic conformal field theories deformed by the integrable $T\bar{T}$ flow to AdS$_3$ with a finite radial cutoff. We investigate this proposal by studying perturbative correlation functions on the two sides. For low point correlators of the stress tensor, we successfully match the deformed CFT results at large central charge to bulk results obtained in classical pure gravity. The deformed CFT also provides definite predictions for loop corrections in the bulk. We then include matter fields in the bulk. To reproduce the classical bulk two-point fu…
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…
Fermionic terms in a class of locally supersymmetric theories called "liberated supergravity" are nonrenormalizable interactions proportional to inverse powers of the supersymmetry breaking scale and Planck mass. This property defines an intrinsic cutoff for liberated supergravities, which are therefore effective theories valid only below energies that never exceed the cutoff. Requiring that the cutoff exceeds current theoretical and observational bounds shows that the new scalar potential terms allowed by liberated supergravity can neither change the cosmological constant predicted by supergr…
Many examples of gravitational duals exist of theories that are highly supersymmetric and conformal in the UV yet have the same massless states as {\cal N}=2,1,0 QCD. We discuss such theories with an explicit UV cutoff and propose that, by tuning higher dimension operators at the cutoff by hand, the effects of the extra matter states in the UV may be removed from the IR physics. We explicitly work in the AdS-Schwartzschild description of QCD_4 and tune the operator TrF^4 by relaxing the near horizon limit to reproduce the lattice 0^{++} glueball mass results. We find that to reproduce the latt…
We study the sparticle spectroscopy and electroweak breaking of theories where supersymmetry is broken by compactification (Scherk-Schwarz mechanism) at a TeV. The evolution of the soft terms above the compactification scale and the resulting sparticle spectrum are very different from those of the usual MSSM and gauge mediated theories. This is traced to the softness of the Scherk-Schwarz mechanism which leads to scalar sparticle masses that are only logarithmically sensitive to the cutoff starting at two loops. As a result, squarks and sleptons are naturally an order of magnitude lighter than…
Affine Toda theory is a relativistic integrable theory in two dimensions possessing solutions describing a number of different species of solitons when the coupling is chosen to be imaginary. These nevertheless carry real energy and momentum. To each species of soliton there has to correspond an antisoliton species. There are two different ways of realising the antisoliton whose equivalence is shown to follow from a surprising identity satisfied within the underlying affine Kac-Moody group. This is the classical analogue of the crossing property of analytic S-matrix theory. Since a complex par…
Quantum field theories require a cutoff to regulate divergences that result from local interactions, and yet physical results can not depend on the value of this cutoff. The renormalization group employs a transformation that changes the cutoff to isolate hamiltonians that produce cutoff-independent eigenvalues. The similarity renormalization group is based on similarity transformations that regulate off-diagonal matrix elements, forcing the hamiltonian towards a band-diagonal form as the cutoff is lowered. This avoids pathologies that plagued tradition transformations acting on hamiltonians, …
We show how the $T^2$ deformation of large $N$, holographic conformal field theories arise from coupling them to the quadratic mass term of ghost-free massive gravity. We then show that in a certain approximation, the equations arising from the variation of the background frame field are those of the Randall--Sundrum II scenario.
We investigate the holographic entanglement entropy of deformed conformal field theories which are dual to a cutoff AdS space. The holographic entanglement entropy evaluated on a three-dimensional Poincare AdS space with a finite cutoff can be reinterpreted as that of the dual field theory deformed by either a boost or $T \bar{T}$ deformation. For the boost case, we show that, although it trivially acts on the underlying theory, it nontrivially affects the entanglement entropy due to the length contraction. For a three-dimensional AdS, we show that the effect of the boost transformation can be…
In information theory, the link between continuous information and discrete information is established through well-known sampling theorems. Sampling theory explains, for example, how frequency-filtered music signals are reconstructible perfectly from discrete samples. In this Letter, sampling theory is generalized to pseudo-Riemannian manifolds. This provides a new set of mathematical tools for the study of space-time at the Planck scale: theories formulated on a differentiable space-time manifold can be completely equivalent to lattice theories. There is a close connection to generalized unc…
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}…
Flow equations describe the evolution of the effective action $Γ_k$ in the process of varying an infrared cutoff $k$. The presence of the infrared cutoff explicitly breaks gauge and hence BRS invariance. We derive modified Slavnov-Taylor identities, which are valid for nonvanishing $k$. They guarantee the BRS invariance of $Γ_k$ for $k\to0$, and hence allow the study of non-abelian gauge theories by integrating the flow equations. Within a perturbative expansion of $Γ_k$, we derive an equation for a $k$ dependent mass term for the gauge fields implied by the modified Slavnov-Taylor identities.
The species scale $Λ_s\leq M_{pl}$ serves as a UV cutoff in the gravitational sector of an EFT and can depend on the moduli of the theory as the spectrum of the theory varies. We argue that the dependence of the species scale $Λ_s (ϕ)$ on massless (or light) modes $ϕ^i$ satisfies $M_{pl}^{d-2} |Λ_s'/Λ_s|^2< \mathcal{O}(1)$. This bound is true at all points in moduli space including also its interior. The argument is based on the idea that the short distance contribution of massless modes to gravitational terms in the EFT cannot dramatically affect the black hole entropy. Based on string theory…
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…
The problem of computing the effective nonrelativistic potential $U_{D}$ for the interaction of charged scalar bosons within the context of D-dimensional electromagnetism with a cutoff, is reduced to quadratures. It is shown that $U_3$ cannot bind a pair of identical charged scalar bosons; nevertheless, numerical calculations indicate that boson-boson bound states do exist in the framework of three-dimensional higher-derivative electromagnetism augmented by a topological Chern-Simons term.
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…
Generalizing the kink operator of the Heisenberg spin 1/2 model, we construct a set of Klein factors explicitly such that $(1+1)$ dimensional fermion theories with arbitrary number of species are mapped onto the corresponding boson theories with the same number of species and vice versa. The actions for the resultant theories do not possess any nontrivial Klein factor. With this set of Klein factors, we are also able to map the simple boundary states such as the Neumann and the Dirichlet boundary states, of the fermion (boson) theory onto those of the boson (fermion) theory. Applications of th…
Projecting a quantum theory onto the Hilbert subspace of states with energies below a cutoff $\overline{E}$ may lead to an effective theory with modified observables, including a noncommutative space(time). Adding a confining potential well $V$ with a very sharp minimum on a submanifold $N$ of the original space(time) $M$ may induce a dimensional reduction to a noncommutative quantum theory on $N$. Here in particular we briefly report on our application of this procedure to spheres $S^d\subset\mathbb{R}^D$ of radius $r=1$ ($D=d\!+\!1>1$): making $\overline{E}$ and the depth of the well depend …
In this paper we generalize the idea of species holography to the case of Cascading DGP theories. Essence of the phenomenon is that a 4D field theory with N particle species coupled to a high-dimensional bulk gravity propagating solely a graviton becomes strongly coupled at the scale that would be the quantum gravity scale of the bulk theory if all the species were propagating in the bulk. We will see that both, crossover scales and Vainshtein scales, can be understood as holographic scales in the above sense. We confirm our results by an explicit effective field theoretic derivation of these …
Quantum gravity is analyzed from the viewpoint of the renormalization group. The analysis is based on methods introduced by J. Polchinski concerning the perturbative renormalization with flow equations. In the first part of this work, the program of renormalization with flow equations is reviewed and then extended to effective field theories that have a finite UV cutoff. This is done for a scalar field theory by imposing additional renormalization conditions for some of the nonrenormalizable couplings. It turns out that one so obtains a statement on the predictivity of the effective theory at …
Causality constrains the gravitational interactions of massive higher spin particles in both AdS and flat spacetime. We explore the extent to which these constraints apply to composite particles, explaining why they do not rule out macroscopic objects or hydrogen atoms. However, we find that they do apply to glueballs and mesons in confining large $N$ gauge theories. Assuming such theories contain massive bound states of general spin, we find parametric bounds in $(3+1)$ spacetime dimensions of the form $N\lesssim \frac{M_{Pl}}{Λ_{\text{QCD}}}$ relating $N$, the QCD scale, and the Planck scale…
In continuum field theory, it has been discussed that chiral gauge theories with Weyl fermions in anomalous gauge representations (anomalous gauge theories) can consistently be quantized, provided that some of gauge bosons are permitted to acquire mass. Such theories in four dimensions are inevitablly non-renormalizable and must be regarded as a low-energy effective theory with a finite ultraviolet (UV) cutoff. In this paper, we present a lattice framework which enables one to study such theories in a non-perturbative level. By introducing bare mass terms of gauge bosons that impose ``smoothne…
Low-energy effective theories have been used very successfully to study the low-energy limit of QCD, providing us with results for a plethora of phenomena, ranging from bound-state formation to phase transitions in QCD. These theories are consistent quantum field theories by themselves and can be embedded in QCD, but typically have a physical ultraviolet cutoff that restricts their range of validity. Here, we provide a discussion of the concept of renormalization group consistency, aiming at an analysis of cutoff effects and regularization-scheme dependences in general studies of low-energy ef…
Effective field theories that manifest UV/IR mode mixing in such a way as to be valid for arbitrarily large volumes, can be used for gravitational, non-black hole events to be accounted for. In formulating such theories with a large number of particle species $N$, we employ constraints from the muon $g-2$, higher-dimensional operator corrections due to the required UV and IR cutoffs as well as the RG evolution in a conventional field-theoretical model in curved space. While in general our bounds on $N$ do reflect $N \simeq 10^{32}$, a bound motivated by the solution to the hierarchy problem in…
We construct a set of quasi-local measurement operators in 2D CFT, and then use them to proceed the quantum energy teleportation (QET) protocol and show it is viable. These measurement operators are constructed out of the projectors constructed from shadow operators, but further acting on the product of two spatially separated primary fields. They are equivalently the OPE blocks in the large central charge limit up to some UV-cutoff dependent normalization but the associated probabilities of outcomes are UV-cutoff independent. We then adopt these quantum measurement operators to show that the …
The consistency of the EFT of two interacting spin-2 fields is checked by applying forward limit positivity bounds on the scattering amplitudes to exclude the region of parameter space devoid of a standard UV completion. We focus on two classes of theories that have the highest possible EFT cutoff, namely those theories modelled on ghost-free interacting theories of a single massive spin-2 field. We find that the very existence of interactions between the spin-2 fields implies more stringent bounds on all the parameters of the EFT, even on the spin-2 self-interactions. This arises for two reas…
Recently there has been interest in extending ghost-free massive gravity, bi-gravity, and multi-gravity by including non-standard kinetic terms and matter couplings. We first review recent proposals for this class of extensions, emphasizing how modifications of the kinetic and potential structure of the graviton and modifications of the coupling to matter are related. We then generalize existing no-go arguments in the metric language to the vielbein language in second-order form. We give an ADM argument to show that the most promising extensions to the kinetic term and matter coupling contain …
Large field inflation can be sensitive to perturbative and nonperturbative quantum corrections that spoil slow roll. A large number $N$ of light species in the theory, which occur in many string constructions, can amplify these problems. One might even worry that in a de Sitter background, light species will lead to a violation of the covariant entropy bound at large $N$. If so, requiring the validity of the covariant entropy bound could limit the number of light species and their couplings, which in turn could severely constrain axion-driven inflation. Here we show that there is no such probl…
In theories with a large number N of particle species, black hole physics imposes an upper bound on the mass of the species equal to M_{Planck}/\sqrt{N}. This bound suggests a novel solution to the hierarchy problem in which there are N \approx 10^{32} gravitationally coupled species, for example 10^{32} copies of the Standard Model. The black hole bound forces them to be at the weak scale, hence providing a stable hierarchy. We present various arguments, that in such theories the effective gravitational cutoff is reduced to Λ_G \approx M_{Planck}/\sqrt{N} and a new description is needed aroun…
Investigations of Quantum Einstein Gravity (QEG) based upon the effective average action employ a flow equation which does not contain any ultraviolet (UV) regulator. Its renormalization group trajectories emanating from a non-Gaussian fixed point define asymptotically safe quantum field theories. A priori these theories are, somewhat unusually, given in terms of their effective rather than bare action. In this paper we construct a functional integral representation of these theories. We fix a regularized measure and show that every trajectory of effective average actions, depending on an IR c…
