Mathematical and Theoretical Physics Seminar: "Conformal field theories and three point functions"
(sign-up)Subham Dutta Chowdhury, Indian Institute of Science, Bangalore
Physics and Mathematics
Conformal invariance allows additional unique parity-odd tensor-structures for three-point functions involving the stress tensor, T, and a conserved U(1) current, j, in 2+1 dimensional conformal field theories that violate parity, apart from the usual parity even structures. Following the conformal collider physics setup of Hofman and Maldacena, we put constraints on the parity violating as well as parity preserving parameters of a general CFT in d=3. We find that large N Chern-Simons theories coupled to a fundamental fermion/boson saturate the bounds that we have derived. An application of the conformal collider bounds is observed in the form of sum rules which puts constraints on spectral densities of any CFT at finite temperature. We derive spectral sum rules in the shear channel for conformal field theories at finite temperature in general $d\geq 3$ dimensions. We show that the sum rule can be written in terms the parity even Hofman-Maldacena variables $t_2$, $t_4$ which determine the three point function of the stress tensor. We then use collider constraints and obtain bounds on the sum rule which are valid in any CFT.
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