Modular linear differential equations for four-point sphere conformal blocks

Journal of High Energy Physics

Regular Article - Theoretical Physics

Ratul Mahanta¹  Tanmoy Sengupta² 

[1] INFN, Sezione di Bologna, viale Berti Pichat 6/2, 40127, Bologna, Italy;The Institute of Mathematical Sciences, IV Cross Road, C.I.T. Campus, Taramani, 600113, Chennai, India;Homi Bhabha National Institute, Training School Complex, Anushaktinagar, 400094, Mumbai, India;

关键词: Conformal and W Symmetry;    Field Theories in Lower Dimensions;    Integrable Field Theories;    Scale and Conformal Symmetries;   

DOI  :  10.1007/JHEP02(2023)158

 received in 2022-12-07, accepted in 2023-02-01,  发布年份 2023

来源: Springer

【 摘 要 】

We construct modular linear differential equations (MLDEs) w.r.t. subgroups of the modular group whose solutions are Virasoro conformal blocks appearing in the expansion of a crossing symmetric 4-point correlator on the sphere. This uses a connection between crossing transformations and modular transformations. We focus specifically on second order MLDEs with the cases of all identical and pairwise identical operators in the correlator. The central charge, the dimensions of the above operators and those of the intermediate ones are expressed in terms of parameters that occur in such MLDEs. In doing so, the q-expansions of the solutions to the MLDEs are compared with those of Virasoro blocks; hence, Zamolodchikov’s elliptic recursion formula provides an important input. Using the actions of respective subgroups, bootstrap equations involving the associated 3-point coefficients have been set up and solved as well in terms of the MLDE parameters. We present explicit examples of MLDEs corresponding to BPZ and novel non-BPZ equations, as well as unitary and non-unitary CFTs.

【 授权许可】

Unknown   
© The Author(s) 2023