Quantum Gravity in Species Regime

Abstract

A large number of particle species allows to formulate quantum gravity in a special double-scaling limit, the species limit. In this regime, quantum gravitational amplitudes simplify substantially. An infinite set of perturbative corrections, that usually blur the picture, vanishes, whereas the collective and non-perturbative effects can be cleanly extracted. Such are the effects that control physics of black holes and of de Sitter and their entanglement curves. In string theory example, we show that the entropy of open strings matches the Gibbons-Hawking entropy of a would-be de Sitter state at the point of saturation of the species bound. This shows, from yet another angle, why quantum gravity/string theory cannot tolerate a de Sitter vacuum. Finally, we discuss various observational implications.

De Sitter space as BRST invariant coherent state of gravitons

“…It has been shown in [19] that by taking a so-called "species limit", one can ensure that the linear gravity represents an exact description of full quantum theory, while simultaneously maintaining the collective phenomena, such as particle creation in de Sitter. This setup is ready-made for our purposes.…”

“…This setup is ready-made for our purposes. Therefore, below, we shall follow the construction of [19] and shall implement our de Sitter coherent state (69) within this framework. This shall allow us to extract the Gibbons-Hawking particle creation process in a BRST-invariant coherent state description of de Sitter.…”

“…This is due to the fact that in the limit (86) the mean number density of the constituents is infinite and their frequencies (∼ H) are zero. This results in infinite quantum break-time, since in species regime the latter scales as [1,19],…”

“…Next, we shall introduce the N species of the scalar matter. It has been shown [19] that this theory allows for a special double-scaling limit with N → ∞, so-called "species limit", in which the quantum gravitational processes simplify significantly. All graviton non-linearities as well as their loop contributions vanish as 1/N .…”

Neutrino Physics in TeV Scale Gravity Theories

“…Remarkably, more recently it was shown [5,6] (for various aspects, see, [7][8][9][10][11]) that the effect of lowering the cutoff M * relative to Planck mass M P is an universal property of any theory with large number of particle species. Correspondingly, a general solution to the hierarchy problem based on this mechanism was proposed in [5] and further studied is subsequent papers.…”