Light-cone modular bootstrap and pure gravity

We prove a 2 dimensional Tauberian theorem in context of 2 dimensional conformal field theory. The asymptotic density of states with conformal weight (h,h) → (∞, ∞) for any arbitrary spin is derived using the theorem. We further rigorously show that the error term is controlled by the twist parameter and insensitive to spin. The sensitivity of the leading piece towards spin is discussed. We identify a universal piece in microcanonical entropy when the averaging window is large. An asymptotic spectral gap on (h,h) plane, hence the asymptotic twist gap is derived. We prove an universal inequality stating that in a compact unitary 2D CFT without any conserved current Ag ≤ π(c−1)r 2 24 is satisfied, where g is the twist gap over vacuum and A is the minimal "areal gap", generalizing the minimal gap in dimension to (h ,h ) plane and r = 4 √ 3 π 2.21. We investigate density of states in the regime where spin is parametrically larger than twist with both going to infinity. Moreover, the large central charge regime is studied. We also probe finite twist, large spin behavior of density of states.

Section: Finite Twist-large Spinsupporting

confidence: 86%

“…) is a very small number compared to 1 c−1 , this matches with the leading result appeared in the lightcone bootstrap program [4][5][6][7][8] i.e.…”

Section: Analysis For All the Operatorssupporting

confidence: 86%

“…For c > 1, the argument can be made specific for primaries, hence the asymptotic gap. This in some sense complements the bound on primary twist gap over the vacuum 4 [8,20].…”

Section: Probing Spectral Gap Via Circle Of Order One Areasupporting

confidence: 68%

Section: Contentsmentioning

confidence: 74%

Section: Large Spin Finite Twist Sectormentioning

confidence: 95%

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