TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.3.074
TI  - The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories
PY  - 2025/09/25
UR  - https://www.scipost.org/SciPostPhys.19.3.074
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 3
SP  - 074
A1  - Woolley, Mitchell
AB  - 6d (2,0) SCFTs of type $\mathfrak{g}$ have protected subsectors that were conjectured in [C. Beem et al., J. High Energy Phys. 05, 017 (2015)] to be captured by $\mathcal{W}_\mathfrak{g}$ algebras. We write down the crossing equations for mixed four-point functions $\langle S_{k_1} S_{k_2}S_{k_3}S_{k_4}\rangle$ of 1/2-BPS operators $S_{k_i}$ in 6d (2,0) theories and detail how a certain twist reduces this system to a 2d meromorphic CFT multi-correlator bootstrap problem. We identify the relevant 6d (2,0) $\mathcal{W}$-algebras of type $\mathfrak{g} = \{A_{N-1},D_N\}$ as truncations of $\mathcal{W}_{1+∞}$ and solve OPE associativity conditions for their structure constants, both using OPEdefs and the holomorphic bootstrap of [M. Headrick et al., J. High Energy Phys. 07, 059 (2015)]. With this, we solve the multi-correlator bootstrap for twisted 6d four-point correlators $\mathcal{F}_{k_1k_2k_3k_4}$ involving all $S_{k_i}$ up to $\{k_i\}=4$ and extract closed-form expressions for 6d OPE coefficients. We describe the implications of our CFT data on conformal Regge trajectories of the (2,0) theories and finally, demonstrate the consistency of our results with protected higher-derivative corrections to graviton scattering in M-theory on $AdS_7× S^4/\mathbb{Z}_\mathfrak{o}$.
ER  -

@Article{10.21468/SciPostPhys.19.3.074,
	title={{The $\mathcal{W}$-algebra bootstrap of 6d $\mathcal{N}=(2,0)$ theories}},
	author={Mitchell Woolley},
	journal={SciPost Phys.},
	volume={19},
	pages={074},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.3.074},
	url={https://scipost.org/10.21468/SciPostPhys.19.3.074},
}