Status  Confirmed 
Seminar Series  SEMLPTHE 
Subjects  condmat.statmech,hepth,mathph 
Date  Friday 9 November 2018 
Time  11:00 
Institute  LPTHE 
Seminar Room  Bibliothèque 
Speaker's Last Name  Shimada 
Speaker's First Name  Hirohiko 
Speaker's Email Address  
Speaker's Institution  OIST Okinawa 
Title  The hierarchy of the OPE coefficients and the lowlying operators in CFT 
Abstract  The continuous families of CFT with varying central charge has gained importance after the revival of the conformal bootstrap in d>2. Unlike the 2d rational CFTs, the 4point function of the fundamental fields has infinitely many intermediate channels, which shows a treelike pattern of the unitarity violation. The O(n) model for n<2 offers one nice example, where such properties are studied in detail. We discuss the basic examples in arXiv:1803.06938, where the analytic properties and exponential decays of the OPE coefficients are related to the symmetry of the hyperbolic geometry. We also use a special polynomial of n arising from the multiplicities in the torus partition function and see how the lowlying dimensions are constrained from the modular invariance. 
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