# Reflections on Conformal Spectra

- Institution: CERN
- Department: TH Journal Club on String Theory
- Speaker: Petr Kravchuk
- Year: 2015
- Language: English
- Source: [CERN](https://videos.cern.ch/record/3002682)
- Licence: [CERN](http://copyright.web.cern.ch)
- Who can watch: Teens profiles and older (sources give no ratings; placed by Invisible Network from the source's own words)

We use modular invariance and crossing symmetry of conformal field theory to reveal approximate reflection symmetries in the spectral decompositions of the partition function in two dimensions in the limit of large central charge and of the four-point function in any dimension in the limit of large scaling dimensions Δ0 of external operators. We use these symmetries to motivate universal upper bounds on the spectrum and the operator product expansion coefficients, which we then derive by independent techniques. Some of the bounds for four-point functions are valid for finite Δ0 as well as for large Δ0. We discuss a similar symmetry in a large spacetime dimension limit. Finally, we comment on the analogue of the Cardy formula and sparse light spectrum condition for the four-point function. (based on 1510.08772 with Kim & Ooguri). This seminar will be given via videolink .

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## Lectures

1. [Reflections on Conformal Spectra](https://invisiblenetwork.ai/learn/cern/3002682/de5ed0863aa4), 1 h (CERN's player)