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From spinning conformal blocks to matrix Calogero-Sutherland models
DESY Hamburg, Theory Grp, Notkestr 85, D-22607 Hamburg, Germany..
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
2018 (English)In: Journal of High Energy Physics (JHEP), ISSN 1126-6708, E-ISSN 1029-8479, no 4, article id 052Article in journal (Refereed) Published
Abstract [en]

In this paper we develop further the relation between conformal four-point blocks involving external spinning fields and Calogero-Sutherland quantum mechanics with matrix-valued potentials. To this end, the analysis of [1] is extended to arbitrary dimensions and to the case of boundary two-point functions. In particular, we construct the potential for any set of external tensor fields. Some of the resulting Schrodinger equations are mapped explicitly to the known Casimir equations for 4-dimensional seed conformal blocks. Our approach furnishes solutions of Casimir equations for external fields of arbitrary spin and dimension in terms of functions on the conformal group. This allows us to reinterpret standard operations on conformal blocks in terms of group-theoretic objects. In particular, we shall discuss the relation between the construction of spinning blocks in any dimension through differential operators acting on seed blocks and the action of left/right invariant vector fields on the conformal group.

Place, publisher, year, edition, pages
SPRINGER , 2018. no 4, article id 052
Keywords [en]
Conformal and W Symmetry, Conformal Field Theory, Differential and Algebraic Geometry, Field Theories in Higher Dimensions
National Category
Mathematical Analysis
Identifiers
URN: urn:nbn:se:kth:diva-227224DOI: 10.1007/JHEP04(2018)052ISI: 000430128700001Scopus ID: 2-s2.0-85045376686OAI: oai:DiVA.org:kth-227224DiVA, id: diva2:1208996
Note

QC 20180521

Available from: 2018-05-21 Created: 2018-05-21 Last updated: 2018-05-21Bibliographically approved

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