Black Hole Formation and Classicalization in Ultra-Planckian 2 -> N Scattering

We establish a connection between the ultra-Planckian scattering amplitudes in field and string theory and unitarization by black hole formation in these scattering processes. Using as a guideline an explicit microscopic theory in which the black hole represents a bound-state of many soft gravitons at the quantum critical point, we were able to identify and compute a set of perturbative amplitudes relevant for black hole formation. These are the tree-level N-graviton scattering S-matrix elements in a kinematical regime (called classicalization limit) where the two incoming ultra-Planckian gravitons produce a large number N of soft gravitons. We compute these amplitudes by using the Kawai-Lewellen-Tye relations, as well as scattering equations and string theory techniques. We discover that this limit reveals the key features of the microscopic corpuscular black hole N-portrait. In particular, the perturbative suppression factor of a N-graviton final state, derived from the amplitude, matches the non-perturbative black hole entropy when N reaches the quantum criticality value, whereas final states with different value of N are either suppressed or excluded by non-perturbative corpuscular physics. Thus we identify the microscopic reason behind the black hole dominance over other final states including non-black hole classical object. In the parameterization of the classicalization limit the scattering equations can be solved exactly allowing us to obtain closed expressions for the high-energy limit of the open and closed superstring tree-level scattering amplitudes for a generic number N of external legs. We demonstrate matching and complementarity between the string theory and field theory in different large-s and large-N regimes.Comment: 55 pages, 7 figures, LaTeX; v2: typos removed; final version to appear in Nucl. Phys.

Suppressing Quantum Fluctuations in Classicalization

We study vacuum quantum fluctuations of simple Nambu-Goldstone bosons - derivatively coupled single scalar-field theories possessing shift-symmetry in field space. We argue that quantum fluctuations of the interacting field can be drastically suppressed with respect to the free-field case. Moreover, the power-spectrum of these fluctuations can soften to become red for sufficiently small scales. In quasiclassical approximation, we demonstrate that this suppression can only occur for those theories that admit such classical static backgrounds around which small perturbations propagate faster than light. Thus, a quasiclassical softening of quantum fluctuations is only possible for theories which classicalize instead of having a usual Lorentz invariant and local Wilsonian UV- completion. We illustrate our analysis by estimating the quantum fluctuations for the DBI-like theories.Comment: 6 pages, no figures, published version, more general discussion of uncertainty relation in QFT, improved and more general derivation of the main resul

UV-Completion by Classicalization

We suggest a novel approach to UV-completion of a class of non-renormalizable theories, according to which the high-energy scattering amplitudes get unitarized by production of extended classical objects (classicalons), playing a role analogous to black holes, in the case of non-gravitational theories. The key property of classicalization is the existence of a classicalizer field that couples to energy-momentum sources. Such localized sources are excited in high-energy scattering processes and lead to the formation of classicalons. Two kinds of natural classicalizers are Nambu-Goldstone bosons (or, equivalently, longitudinal polarizations of massive gauge fields) and scalars coupled to energy-momentum type sources. Classicalization has interesting phenomenological applications for the UV-completion of the Standard Model both with or without the Higgs. In the Higgless Standard Model the high-energy scattering amplitudes of longitudinal $W$-bosons self-unitarize via classicalization, without the help of any new weakly-coupled physics. Alternatively, in the presence of a Higgs boson, classicalization could explain the stabilization of the hierarchy. In both scenarios the high-energy scatterings are dominated by the formation of classicalons, which subsequently decay into many particle states. The experimental signatures at the LHC are quite distinctive, with sharp differences in the two cases.Comment: 37 page

Probing Quantum Geometry at LHC

We present an evidence, that the volumes of compactified spaces as well as the areas of black hole horizons must be quantized in Planck units. This quantization has phenomenological consequences, most dramatic being for micro black holes in the theories with TeV scale gravity that can be produced at LHC. We predict that black holes come in form of a discrete tower with well defined spacing. Instead of thermal evaporation, they decay through the sequence of spontaneous particle emissions, with each transition reducing the horizon area by strictly integer number of Planck units. Quantization of the horizons can be a crucial missing link by which the notion of the minimal length in gravity eliminates physical singularities. In case when the remnants of the black holes with the minimal possible area and mass of order few TeV are stable, they might be good candidates for the cold dark matter in the Universe.Comment: 14 pages, Late

Solitonic D-branes and brane annihilation

We point out some intriguing analogies between field theoretic solitons (topological defects) and D-branes. Annihilating soliton-antisoliton pairs can produce stable solitons of lower dimensionality. Solitons that localize massless gauge fields in their world volume automatically imply the existence of open flux tubes ending on them and closed flux tubes propagating in the bulk. We discuss some aspects of this localization on explicit examples of unstable wall-anti-wall systems. The annihilation of these walls can be described in terms of tachyon condensation which renders the world-volume gauge field non-dynamical. During this condensation the world volume gauge fields (open string states) are resonantly excited. These can later decay into closed strings, or get squeezed into a network flux tubes similar to a network of cosmic strings formed at a cosmological phase transition. Although, as in the $D$-brane case, perturbatively one can find exact time-dependent solutions, when the energy of the system stays localized in the plane of the original soliton, such solutions are unstable with respect to decay into open and closed string states. Thus, when a pair of such walls annihilates, the energy is carried away (at least) by closed string excitations (``glueballs''), which are the lowest energy excitations about the bulk vacuum. Suggested analogies can be useful for the understanding of the complicated D-brane dynamics and of the production of topological defects and reheating during brane collision in the early universe.Comment: a typo correcte

Classicalization of Gravitons and Goldstones

We establish a close parallel between classicalization of gravitons and derivatively-coupled Nambu-Goldstone-type scalars. We show, that black hole formation in high energy scattering process represents classicalization with the classicalization radius given by Schwarzschild radius of center of mass energy, and with the precursor of black hole entropy being given by number of soft quanta composing this classical configuration. Such an entropy-equivalent is defined for scalar classicalons also and is responsible for exponential suppression of their decay into small number of final particles. This parallel works in both ways. For optimists that are willing to hypothesize that gravity may indeed self-unitarize at high energies via black hole formation, it illustrates that the Goldstones may not be much different in this respect, and they classicalize essentially by similar dynamics as gravitons. In the other direction, it may serve as an useful de-mystifier of via-black-hole-unitarization process and of the role of entropy in it, as it illustrates, that much more prosaic scalar theories essentially do the same. Finally, it illustrates that in both cases classicalization is the defining property for unitarization, and that it sets-in before one can talk about accompanying properties, such as entropy and thermality of static classicalons (black holes). These properties are by-products of classicalization, and their equivalents can be defined for non-gravitational cases of classicalization.Comment: 23 page

Primordial black holes from cosmic necklaces

Cosmic necklaces are hybrid topological defects consisting of monopoles and strings. We argue that primordial black holes(PBHs) may have formed from loops of the necklaces, if there exist stable winding states, such as coils and cycloops. Unlike the standard scenario of PBH formation from string loops, in which the kinetic energy plays important role when strings collapse into black holes, the PBH formation may occur in our scenario after necklaces have dissipated their kinetic energy. Then, the significant difference appears in the production ratio. In the standard scenario, the production ratio $f$ becomes a tiny fraction $f\sim 10^{-20}$, however it becomes $f \sim 1$ in our case. On the other hand, the typical mass of the PBHs is much smaller than the standard scenario, if they are produced in the same epoch. As the two mechanisms may work at the same time, the necklaces may have more than one channel of the gravitational collapse. Although the result obtained in this paper depends on the evolution of the dimensionless parameter $r$, the existence of the winding state could be a serious problem in some cases. Since the existence of the winding state in brane models is due to the existence of a non-tivial circle in the compactified space, the PBH formation can be used to probe the structure of the compactified space. Black holes produced by this mechanism may have peculiar properties.Comment: 22pages, 3 figures, added many comments, +1 figure, accepted for publication in JHE

Multiple Inflation, Cosmic String Networks and the String Landscape

Motivated by the string landscape we examine scenarios for which inflation is a two-step process, with a comparatively short inflationary epoch near the string scale and a longer period at a much lower energy (like the TeV scale). We quantify the number of $e$-foldings of inflation which are required to yield successful inflation within this picture. The constraints are very sensitive to the equation of state during the epoch between the two inflationary periods, as the extra-horizon modes can come back inside the horizon and become reprocessed. We find that the number of $e$-foldings during the first inflationary epoch can be as small as 12, but only if the inter-inflationary period is dominated by a network of cosmic strings (such as might be produced if the initial inflationary period is due to the brane-antibrane mechanism). In this case a further 20 $e$-foldings of inflation would be required at lower energies to solve the late universe's flatness and horizon problems.Comment: 27 pages, 6 figures; v2: refences adde

On Brane Inflation With Volume Stabilization

The distance between BPS branes in string theory corresponds to a flat direction in the effective potential. Small deviations from supersymmetry may lead to a small uplifting of this flat direction and to brane inflation. However, this scenario can work only if the BPS properties of the branes and the corresponding flatness of the inflaton potential are preserved in the theories with the stable volume compactification. We present an ``inflaton trench'' mechanism that keeps the inflaton potential flat due to shift symmetry, which is related to near BPS symmetry in our model.Comment: 12 pages, 2 figure

Formation of monopoles and domain walls after brane inflation

We study cosmological defect formation after brane inflation. The cosmological defects are corresponding to the branes that have less than three spacial dimensions in the uncompactified spacetime. Contrary to the previous arguments, production of monopoles and domain walls are not always negligible. Monopoles and domain walls are formed by the branes extended between mother branes.Comment: 27pages, 7 figures, many comments, footnotes and reviews are added, to appear in JHE