A note on the Virasoro blocks at order 1 /  c

Bombini, Alessandro (Aff1, 0000 0004 1757 3470, Dipartimento di Fisica ed Astronomia “Galileo Galilei”, Università di Padova, Via Marzolo 8, 35131, Padua, Italy) (Aff2, I.N.F.N. Sezione di Padova, Via Marzolo 8, 35131, Padua, Italy) ; Giusto, Stefano (Aff1, 0000 0004 1757 3470, Dipartimento di Fisica ed Astronomia “Galileo Galilei”, Università di Padova, Via Marzolo 8, 35131, Padua, Italy) (Aff2, I.N.F.N. Sezione di Padova, Via Marzolo 8, 35131, Padua, Italy) ; Russo, Rodolfo (Aff3, 0000 0001 2171 1133, Centre for Research in String Theory, School of Physics and Astronomy Queen Mary University of London, Mile End Road, E1 4NS, London, United Kingdom)

03 January 2019

Abstract: We derive an explicit expression for the 1 /  c contribution to the Virasoro blocks in 2D CFT in the limit of large c with fixed values of the operators’ dimensions. We follow the direct approach of orthonormalising, at order 1 /  c , the space of the Virasoro descendants to obtain the blocks as a series expansion around z=0 . For generic conformal weights this expansion can be summed in terms of hypergeometric functions and their first derivatives with respect to one parameter. For integer conformal weights we provide an equivalent expression written in terms of a finite sum of undifferentiated hypergeometric functions. These results make the monodromies of the blocks around z=1 manifest.


Published in: EPJC 79 (2019) 3
Published by: Springer/Società Italiana di Fisica
DOI: 10.1140/epjc/s10052-018-6522-5
License: CC-BY-3.0



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