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

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

The Confining String from the Soft Dilaton Theorem

A candidate for the confining string of gauge theories is constructed via a representation of the ultraviolet divergences of quantum field theory by a closed string dilaton insertion, computed through the soft dilaton theorem. The resulting (critical) confining string is conformally invariant, singles out naturally $d=4$ dimensions, and can not be used to represent theories with Landau poles.Comment: 13 pages, two figures Clarifying remark added. Typos correcte