Solving the simplest theory of quantum gravity

Abstract

We solve what is quite likely the simplest model of quantum gravity, the worldsheet theory of an infinitely long, free bosonic string in Minkowski space. Contrary to naive expectations, this theory is non-trivial. We illustrate this by constructing its exact factorizable S-matrix. Despite its simplicity, the theory exhibits many of the salient features expected from more mature quantum gravity models, including the absence of local off-shell observables, a minimal length, a maximum achievable (Hagedorn) temperature, as well as (integrable relatives of) black holes. All these properties follow from the exact S-matrix. We show that the complete finite volume spectrum can be reconstructed analytically from this S-matrix with the help of the thermodynamic Bethe Ansatz. We argue that considered as a UV complete relativistic 2-dimensional quantum field theory the model exhibits a new type of renormalization group flow behavior, "asymptotic fragility". Asymptotically fragile flows do not originate from a UV fixed point. arXiv:1205.6805v2 [hep-th]

SO(N) gauge theories in 2 + 1 dimensions: glueball spectra and confinement

“…(4.3) encodes all the finite-l corrections that are significant, at our value of l, given our errors. As remarked earlier, this is to be expected since we know that all correction terms to σl up to O(1/l 5 ) are universal [30][31][32][33][34][37][38][39][40][41][42][43] flux tubes and these terms are precisely what one obtains when expanding the Nambu-Goto expression in powers of 1/σl 2 . Of course when the flux tube is not stable it is not clear that it should be described by an effective string action, and here our numerical tests in SO (3) and SO (5) are useful.…”

“…(4.3): one cannot get a good fit with just the leading O(1/l) Luscher correction [62,63]. In the more accurate case of SO (6) we again have a very good fit a 2 σ = 0.016014 (27) l ∈ [18,42], χ 2 /n dof = 0.89 : SO(6). (4.5)…”

“…(See also [35,36].) It has also been shown to arise as a good approximation at small l from the near-integrability of the world-sheet action [37][38][39][40][41][42][43]. Moreover it has been checked numerically with some precision in SU(N ) for flux tubes carrying both fundamental and higher representation fluxes.…”

T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ and LST

“…In this section we discuss some aspects of the recent work [4,5] (see also [6,7]) on the theory obtained by deforming the Lagrangian of a two dimensional conformal field theory JHEP07(2017)122…”

“…where 6) JHEP07 (2017)122 and v is a constant associated with the compact CFT N . Recall that x 1 is periodically identified,…”