Self-Completeness of Einstein Gravity

We argue, that in Einsteinian gravity the Planck length is the shortest length of nature, and any attempt of resolving trans-Planckian physics bounces back to macroscopic distances due to black hole formation. In Einstein gravity trans-Planckian propagating quantum degrees of freedom cannot exist, instead they are equivalent to the classical black holes that are fully described by lighter infra-red degrees of freedom and give exponentially-soft contribution into the virtual processes. Based on this property we argue that pure-Einstein (super)gravity and its high-dimensional generalizations are self-complete in deep-UV, but not in standard Wilsonian sense. We suggest that certain strong-coupling limit of string theory is built-in in pure Einstein gravity, whereas the role of weakly-coupled string theory limit is to consistently couple gravity to other particle species, with their number being set by the inverse string coupling. We also discuss some speculative ideas generalizing the notion of non-Wilsonian self-completeness to other theories, such as the standard model without the Higgs.Comment: 40 pages, Late

Species and Strings

Based on well-known properties of semi-classical black holes, we show that weakly-coupled string theory can be viewed as a theory of N = 1/g_s^2 particle species. This statement is a string theoretic realization of the fact that the fundamental scale in any consistent D-dimensional theory of gravity is not the Planck length l_D, but rather the species scale L_N = N^1/(D-2) l_D. Using this fact, we derive the bound on semi-classical black hole entropy in any consistent theory of gravity as S > N, which when applied to string theory provides additional evidence for the former relation. This counting also shows that the Bekenstein-Hawking entropy can be viewed as the entanglement entropy, without encountering any puzzle of species. We demonstrate that the counting of species extends to the M-theory limit. The role of the species scale is now played by the eleven-dimensional Planck length, beyond which resolution of distances is gravitationally-impossible. The conclusion is, that string theory is a theory of species and gets replaced by a pure gravitational theory in the limit when species become strongly coupled and decouple.Comment: 20 page

Strong Coupling Holography

We show that whenever a 4-dimensional theory with N particle species emerges as a consistent low energy description of a 3-brane embedded in an asymptotically-flat (4+d)-dimensional space, the holographic scale of high-dimensional gravity sets the strong coupling scale of the 4D theory. This connection persists in the limit in which gravity can be consistently decoupled. We demonstrate this effect for orbifold planes, as well as for the solitonic branes and string theoretic D-branes. In all cases the emergence of a 4D strong coupling scale from bulk holography is a persistent phenomenon. The effect turns out to be insensitive even to such extreme deformations of the brane action that seemingly shield 4D theory from the bulk gravity effects. A well understood example of such deformation is given by large 4D Einstein term in the 3-brane action, which is known to suppress the strength of 5D gravity at short distances and change the 5D Newton's law into the four-dimensional one. Nevertheless, we observe that the scale at which the scalar polarization of an effective 4D-graviton becomes strongly coupled is again set by the bulk holographic scale. The effect persist in the gravity decoupling limit, when the full theory reduces to a 4D system in which the only memory about the high-dimensional holography is encoded in the strong coupling scale. The observed intrinsic connection between the high-dimensional flat space holography and 4D strong coupling suggests a possible guideline for generalization of AdS/CFT duality to other systems.Comment: 26 pages, Late

Black Hole's Quantum N-Portrait

We establish a quantum measure of classicality in the form of the occupation number, $N$, of gravitons in a gravitational field. This allows us to view classical background geometries as quantum Bose-condensates with large occupation numbers of soft gravitons. We show that among all possible sources of a given physical length, $N$ is maximized by the black hole and coincides with its entropy. The emerging quantum mechanical picture of a black hole is surprisingly simple and fully parameterized by $N$. The black hole is a leaky bound-state in form of a cold Bose-condensate of $N$ weakly-interacting soft gravitons of wave-length $\sqrt{N}$ times the Planck length and of quantum interaction strength 1/N. Such a bound-state exists for an arbitrary $N$. This picture provides a simple quantum description of the phenomena of Hawking radiation, Bekenstein entropy as well as of non-Wilsonian UV-self-completion of Einstein gravity. We show that Hawking radiation is nothing but a quantum depletion of the graviton Bose-condensate, which despite the zero temperature of the condensate produces a thermal spectrum of temperature $T \, = \, 1/\sqrt{N}$. The Bekenstein entropy originates from the exponentially growing with $N$ number of quantum states. Finally, our quantum picture allows to understand classicalization of deep-UV gravitational scattering as $2 \rightarrow N$ transition. We point out some fundamental similarities between the black holes and solitons, such as a t'Hooft-Polyakov monopole. Both objects represent Bose-condensates of $N$ soft bosons of wavelength $\sqrt{N}$ and interaction strength 1/N. In short, the semi-classical black hole physics is 1/N-coupled large-$N$ quantum physics.Comment: 37 pages, Late

Black Hole Macro-Quantumness

It is a common wisdom that properties of macroscopic bodies are well described by (semi)classical physics. As we have suggested this wisdom is not applicable to black holes. Despite being macroscopic, black holes are quantum objects. They represent Bose-Einstein condensates of N-soft gravitons at the quantum critical point, where N Bogoliubov modes become gapless. As a result, physics governing arbitrarily-large black holes (e.g., of galactic size) is a quantum physics of the collective Bogoiliubov modes. This fact introduces a new intrinsically-quantum corrections in form of 1/N, as opposed to exp(-N). These corrections are unaccounted by the usual semiclassical expansion in h and cannot be recast in form of a quantum back-reaction to classical metric. Instead the metric itself becomes an approximate entity. These 1/N corrections abolish the presumed properties of black holes, such as non existence of hair, and are the key to nullifying the so-called information paradox.Comment: 14 page

Black Hole Masses are Quantized

We give a simple argument showing that in any sensible quantum field theory the masses of black holes cannot assume continuous values and must be quantized. Our proof solely relies on Poincare-invariance of the asymptotic background, and is insensitive to geometric characteristics of black holes or other peculiarities of the short distance physics. Therefore, our results are equally-applicable to any other localized objects on asymptotically Poincare-invariant space, such as classicalons. By adding a requirement that in large mass limit the quantization must approximately account for classical results, we derive an universal quantization rule applicable to all classicalons (including black holes) in arbitrary number of dimensions. In particular, this implies, that black holes cannot emit/absorb arbitrarily soft quanta. The effect has phenomenological model-independent implications for black holes and other classicalons that may be created at LHC. We predict, that contrary to naive intuition, the black holes and/or classicalons, will be produced in form of fully-fledged quantum resonances of discrete masses, with the level-spacing controlled by the inverse square-root of cross-section.Comment: 23 pages, Late

Black Hole Quantum Mechanics in the Presence of Species

Recently within the context of a microscopic quantum theory, the Black Hole's Quantum N-Portrait, it was shown that continuous global symmetries are compatible with quantum black hole physics. In the present paper we revise within the same framework the semi-classical black hole bound on the number of particle species N_{species}. We show that unlike the bound on global charge, the bound on species survives in the quantum picture and gives rise to a new fundamental length-scale, L_{species} = sqrt{N_{species}} L_P$, beyond which the resolution of species identities is impossible. This finding nullifies the so-called species problem. This scale sets the size of the lightest quantum black hole in the theory, Planckion. A crucial difference between the gravitational and non-gravitational species emerges. For gravitational species, the lightest black holes are exactly at the scale of perturbative unitarity violation, which is a strong indication for self-UV-completion of gravity. However, non-gravitational species create a gap between the perturbative unitarity scale and the lightest black holes, which must be filled by some unitarity-restoring physics. Thus, self-UV-completion of gravity implies that the number of non-gravitational species must not exceed the gravitational ones.Comment: 14 pages, 7 figure

Classical Limit of Black Hole Quantum N-Portrait and BMS Symmetry

Black hole entropy, denoted by N, in (semi)classical limit is infinite. This scaling reveals a very important information about the qubit degrees of freedom that carry black hole entropy. Namely, the multiplicity of qubits scales as N, whereas their energy gap and their coupling as 1/N. Such a behavior is indeed exhibited by Bogoliubov-Goldstone degrees of freedom of a quantum-critical state of N soft gravitons (a condensate or a coherent state) describing the black hole quantum portrait. They can be viewed as the Goldstone modes of a broken symmetry acting on the graviton condensate. In this picture Minkowski space naturally emerges as a coherent state of infinite-N gravitons of infinite wavelength and it carries an infinite entropy. In this paper we ask what is the geometric meaning (if any) of the classical limit of this symmetry. We argue that the infinite-N limit of Bogoliubov-Goldstone modes of critical graviton condensate is described by recently-discussed classical BMS super-translations broken by the black hole geometry. However, the full black hole information can only be recovered for finite N, since the recovery time becomes infinite in classical limit in which N is infinite.Comment: 15 pages, Late