%0 Journal Article %T Minimal lectures on two-dimensional conformal field theory %+ Institut de Physique Théorique - UMR CNRS 3681 (IPHT) %A Ribault, Sylvain %Z 20 pages, lectures given at the September 2016 Carg\`ese school %< avec comité de lecture %Z t16/187 %@ 2542-4653 %J SciPost Physics %I SciPost Foundation %V 1 %8 2018-06-10 %D 2018 %Z 1609.09523 %R 10.21468/SciPostPhysLectNotes.1 %Z Physics [physics]/Mathematical Physics [math-ph]Journal articles %X We provide a brief but self-contained review of conformal field theory on the Riemann sphere. We first introduce general axioms such as local conformal invariance, and derive Ward identities and BPZ equations. We then define Liouville theory and minimal models by specific axioms on their spectrums and degenerate fields. We solve these theories by computing three- and four-point functions, and discuss their existence and uniqueness. %G English %2 https://cea.hal.science/cea-01469008/document %2 https://cea.hal.science/cea-01469008/file/1609.09523.pdf %L cea-01469008 %U https://cea.hal.science/cea-01469008 %~ CEA %~ CNRS %~ DSM-IPHT %~ CEA-UPSAY %~ TDS-MACS %~ UNIV-PARIS-SACLAY %~ CEA-UPSAY-SACLAY %~ CEA-DRF %~ TEST-HALCNRS %~ GS-MATHEMATIQUES %~ GS-PHYSIQUE