Constraints on higher spin CFT2

Any unitary compact two-dimensional CFT with c > 1 and no symmetries beyond Virasoro has a parametrically large density of primary states at large spin forh >h extr ∼ c−1 24 , of a universal form determined by modular invariance. By including the contribution of light primary operators and multi-twist composites constructed from them in the modular bootstrap, we find thath extr receives corrections in a large spin expansion, which we compute at finite c. The analysis uses a formulation of the modular S-transform as a Fourier transform acting on the density of primary states. For theories with gravitational duals,h extr is interpreted as the extremality bound of rotating BTZ black holes, receiving quantum corrections which we compute at one loop by prohibiting naked singularities in the quantum-corrected geometry. This gravity result is reproduced by modular bootstrap in a semiclassical c → ∞ limit.

Section: Universal Results For Unitary Compact Cftsmentioning

confidence: 76%

Quantum corrections to the BTZ black hole extremality bound from the conformal bootstrap

Maxfield

2019

“…We find that the numerical upper bounds depend on the choice of W(g)-algebra when the central charge is small, namely c rank(g). For the case of W(A 2 )-algebra, this problem has been recently discussed in [23,24].…”

Section: Jhep12(2017)045mentioning

confidence: 99%

“…The two-dimensional CFTs with W(A 2 ) = W(2, 3) symmetry have been studied recently in [23,24]. To investigate the universal constraints on the spectrum of higher-spin "irrational" CFTs, i.e., c > 2, the authors of [23,24] apply the modular bootstrap method to the torus two-point function…”

Section: Bootstrapping With W-algebramentioning

confidence: 99%

“…To investigate the universal constraints on the spectrum of higher-spin "irrational" CFTs, i.e., c > 2, the authors of [23,24] apply the modular bootstrap method to the torus two-point function…”

Section: Bootstrapping With W-algebramentioning

confidence: 99%

“…We also observe that the location at which the degeneracy diverge is independent of the presence of holomorphic/anti-holomorphic currents other than Wsymmetry. The divergence can be explained from the fact that infinitely many primaries get accumulated at h = c−r 24 [14,23]. For the self-containment, we briefly present the derivation of [14,23] below.…”

Section: Accumulation Of the Spectrummentioning

confidence: 99%

See 2 more Smart Citations

Modular constraints on conformal field theories with currents

Bae

Lee

Song

2017

We study constraints coming from the modular invariance of the partition function of two-dimensional conformal field theories. We constrain the spectrum of CFTs in the presence of holomorphic and anti-holomorphic currents using the semi-definite programming. In particular, we find the bounds on the twist gap for the non-current primaries depend dramatically on the presence of holomorphic currents, showing numerous kinks and peaks. Various rational CFTs are realized at the numerical boundary of the twist gap, saturating the upper limits on the degeneracies. Such theories include Wess-Zumino-Witten models for the Deligne's exceptional series, the Monster CFT and the Baby Monster CFT. We also study modular constraints imposed by W-algebras of various type and observe that the bounds on the gap depend on the choice of W-algebra in the small central charge region.

Modular constraints on superconformal field theories

Bae

Lee

Song

2019

We constrain the spectrum of N = (1, 1) and N = (2, 2) superconformal field theories in two-dimensions by requiring the NS-NS sector partition function to be invariant under the Γ θ congruence subgroup of the full modular group SL(2, Z). We employ semi-definite programming to find constraints on the allowed spectrum of operators with or without U (1) charges. Especially, the upper bounds on the twist gap for the non-current primaries exhibit interesting peaks, kinks, and plateau. We identify a number of candidate rational (S)CFTs realized at the numerical boundaries and find that they are realized as the solutions to modular differential equations associated to Γ θ . Some of the candidate theories have been discussed by Höhn in the context of self-dual extremal vertex operator (super)algebra. We also obtain bounds for the charged operators and study their implications to the weak gravity conjecture in AdS 3 . #1 Throughout this paper, we only consider parity invariant CFTs so that left-moving and rightmoving fermions have the same boundary condition.