TY  - JOUR
AU  - Buric, Ilija
AU  - Lacroix, Sylvain
AU  - Mann, Jeremy A.
AU  - Quintavalle, Lorenzo
AU  - Schomerus, Volker
TI  - Gaudin models and multipoint conformal blocks III: comb channel coordinates and OPE factorisation
JO  - Journal of high energy physics
VL  - 06
IS  - 6
SN  - 1029-8479
CY  - [Trieste]
PB  - SISSA
M1  - PUBDB-2022-06290
M1  - arXiv:2112.10827
SP  - 144
PY  - 2022
N1  - 41 pages, 7 figures
AB  - We continue the exploration of multipoint scalar comb channel blocks for conformal field theories in 3D and 4D. The central goal here is to construct novel comb channel cross ratios that are well adapted to perform projections onto all intermediate primary fields. More concretely, our new set of cross ratios includes three for each intermediate mixed symmetry tensor exchange. These variables are designed such that the associated power series expansion coincides with the sum over descendants. The leading term of this expansion is argued to factorise into a product of lower point blocks. We establish this remarkable factorisation property by studying the limiting behaviour of the Gaudin Hamiltonians that are used to characterise multipoint conformal blocks. For six points we can map the eigenvalue equations for the limiting Gaudin differential operators to Casimir equations of spinning four-point blocks.
KW  - operator: differential (INSPIRE)
KW  - field theory: conformal (INSPIRE)
KW  - conformal block (INSPIRE)
KW  - factorization (INSPIRE)
KW  - operator product expansion (INSPIRE)
KW  - Hamiltonian (INSPIRE)
KW  - Gaudin model (INSPIRE)
KW  - Casimir (INSPIRE)
KW  - Scale and Conformal Symmetries (autogen)
KW  - Differential and Algebraic Geometry (autogen)
KW  - Integrable Hierarchies (autogen)
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:000815491000002
DO  - DOI:10.1007/JHEP06(2022)144
UR  - https://bib-pubdb1.desy.de/record/484477
ER  -