Workshop "Gauge theories and spin systems: Yang-Mills theory, continuous symmetry, and disorder"

On the logarithmic CFT structure of 2D critical percolation

Jul 30, 2025, 11:00 AM

1h

Poppelsdorfer Allee 45, 1. EG, Lecture room (HIM)

Scheduled Talks

Speaker

Prof. Federico Camia (New York University Abu Dhabi)

Description

The large-scale behavior of two-dimensional critical percolation is expected to be described by a conformal field theory (CFT). Moreover, the latter is believed to be a log CFT, exhibiting logarithmic singularities together with the usual power-law divergences of CFT correlations functions. After a general introduction, I will discuss various (log) CFT features of the scaling limit of two- dimensional critical percolation, such as:
- the recent proof of the conformal covariance of connection probabilities,
- its implications for the proof of the Delfino-Viti conjecture,
- asymptotic expansions that can be interpreted as operator product expansions (OPEs),
- the first rigorous proof of the emergence of logarithmic singularities,
- the percolation “energy” field and its logarithmic partner.