TY  - JOUR
AU  - Ghosh, Kausik
AU  - Kaviraj, Apratim
AU  - Paulos, Miguel F.
TI  - Polyakov blocks for the 1D conformal field theory mixed-correlator bootstrap
JO  - Physical review / D
VL  - 109
IS  - 6
SN  - 2470-0010
CY  - Ridge, NY
PB  - American Physical Society
M1  - PUBDB-2024-04945
M1  - arXiv:2307.01257
SP  - L061703
PY  - 2024
N1  - Phys.Rev.D 109 (2024) 6, L061703. 6+7 pages, 4 figures, Fig. 1 modified for clarity, minor corrections, further explanations, and references added
AB  - We introduce manifestly crossing-symmetric expansions for arbitrary systems of 1D CFT correlators. These expansions are given in terms of certain Polyakov blocks which we define and show how to compute efficiently. Equality of operator product expansion and Polyakov block expansions leads to sets of sum rules that any mixed correlator system must satisfy. The sum rules are diagonalized by correlators in tensor product theories of generalized free fields. We show that it is possible to do a change of a basis that diagonalizes instead mixed correlator systems involving elementary and composite operators in a single field theory. As an application, we find the first nontrivial examples of optimal bounds, saturated by the mixed correlator system ϕ,ϕ2 in the theory of a single generalized free field.
KW  - field theory: conformal (INSPIRE)
KW  - operator: composite (INSPIRE)
KW  - correlation function (INSPIRE)
KW  - sum rule (INSPIRE)
KW  - bootstrap (INSPIRE)
KW  - operator product expansion (INSPIRE)
KW  - dimension: 1 (INSPIRE)
LB  - PUB:(DE-HGF)16
UR  - <Go to ISI:>//WOS:001195573300004
DO  - DOI:10.1103/PhysRevD.109.L061703
UR  - https://bib-pubdb1.desy.de/record/611508
ER  -