Summary: Conformal field theories play a central role in modern theoretical physics with many applications to the understanding of phase transitions, gauge theories and even the quantum physics of gravity, through Maldacena’s celebrated holographic duality. The key analytic tool in the field is the so-called conformal partial wave expansion, i.e. a Fourier-like decomposition of physical quantities into a basis of partial waves for the conformal group \(\mathrm{SO}(1,d+1)\). While the general theory of these partial waves remains largely unexplored, the very simplest specimens are known to be (close relatives of) multivariate \(BC_2\)-symmetric Heckman-Opdam hypergeometric functions. Further advances in the theory of conformal partial waves are expected to exploit a deep relation with (super-)integrability and in particular with certain limits of Gaudin integrable models.
For the entire collection see [Zbl 1496.17001].