Charged structure constants from modularity

Das, Diptarka; Datta, Shouvik; Pal, Sridip

doi:10.1007/jhep11(2017)183

Cited by 45 publications

(72 citation statements)

References 57 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…First, there are error terms from approximating the discrete spectrum by a continuous density of states. This error for the density of states ρ(∆) that is insensitive to the spin has recently been quantified in [19,20] (see also Appendix C of [21]). Second, there are contributions to the density of states from the lowest twist, non-vacuum primary operators, corresponding to the last term in (2.13).…”

Section: Extended Cardy Formulamentioning

confidence: 94%

“…Among other things, there are error terms from approximating the discrete spectrum by a continuous density of states as mentioned in Section 3. It would be interesting to extend the analysis in [19][20][21] to control the error in a rigorous way. For a CFT with a finite twist gap (and hence necessarily irrational), there is generally no huge degeneracy at a given energy level, so we expect the error due to granularity to be much smaller than that of a rational CFT.…”

Section: Twist Gap Revisitedmentioning

confidence: 99%

See 1 more Smart Citation

Light-cone modular bootstrap and pure gravity

et al. 2019

View full text Add to dashboard Cite

We explore the large spin spectrum in two-dimensional conformal field theories with a finite twist gap, using the modular bootstrap in the lightcone limit. By recursively solving the modular crossing equations associated to different P SL(2, Z) elements, we identify the universal contribution to the density of large spin states from the vacuum in the dual channel. Our result takes the form of a sum over P SL(2, Z) elements, 1 A priori, there could be theories without conserved currents, but with an accumulation of operators towards vanishing twist, and therefore have zero twist gap.2 These are the P SL(2, Z) images of the cusp at τ = i∞. 3 More precisely, this is a sum over the coset P SL(2, Z)/Γ ∞ where Γ ∞ is the subgroup generated by T : τ → τ + 1 that stabilizes the cusp at τ = i∞.4 In [1] this argument was credited to Tom Hartman.

show abstract

Section: Extended Cardy Formulamentioning

confidence: 94%

Section: Twist Gap Revisitedmentioning

confidence: 99%

Light-cone modular bootstrap and pure gravity

et al. 2019

View full text Add to dashboard Cite

show abstract

“…Another obvious extension of this work is to consider extended Virasoro algebra and putting the results 16 The author thanks Ken Intriligator for discussion on this point. of [4] on rigorous footing. It would also be interesting to investigate the torus two point function [29][30][31] using similar methods.…”

Section: Discussion and Outlookmentioning

confidence: 98%

Bound on asymptotics of magnitude of three point coefficients in 2D CFT

Pal

2020

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

We use methods inspired from complex Tauberian theorems to make progress in understanding the asymptotic behavior of the magnitude of heavy-lightheavy three point coefficients rigorously. The conditions and the precise sense of averaging, which can lead to exponential suppression of such coefficients are investigated. We derive various bounds for the typical average value of the magnitude of heavy-light-heavy three point coefficients and verify them numerically. arXiv:1906.11223v2 [hep-th] 1 Jul 2019 -2 -

show abstract

“…We remark that if one assumes that g > c 12 , then it is possible to achieve the regime of validity of the Cardy fromula for * > 1 24 . This does not follow automatically from the above eq.…”

Section: Analysis At Large Central Chargementioning

confidence: 93%

Tauberian-Cardy formula with spin

Pal

Sun

2020

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Charged structure constants from modularity

Cited by 45 publications

References 57 publications

Light-cone modular bootstrap and pure gravity

Light-cone modular bootstrap and pure gravity

Bound on asymptotics of magnitude of three point coefficients in 2D CFT

Tauberian-Cardy formula with spin

Contact Info

Product

Resources

About