Conformal loop ensembles and the stress-energy tensor

Understand

We give a construction of the stress-energy tensor of conformal field theory (CFT) as a local &#34;object&#34; in conformal loop ensembles CLE_\kappa, for all values of \kappa in the dilute regime 8/3 < \kappa <= 4 (corresponding to the central charges 0 < c <= 1, and including all CFT minimal models).

• We provide a quick introduction to CLE, a mathematical theory for random loops in simply connected domains with properties of conformal invariance, developed by Sheffield and Werner (2006).
• We consider its extension to more general regions of definition, and make various hypotheses that are needed for our construction and expected to hold for CLE in the dilute regime.
• Using this, we identify the stress-energy tensor in the context of CLE.