Discrete stress-energy tensor in the loop O(n) model

We study the loop O (n) model on the honeycomb lattice. By means of local non-planar deformations of the lattice, we construct a discrete stress-energy tensor. For n 0, 2, it gives a new observable satisfying a part of Cauchy-Riemann equations. We conjecture that it is approximately discrete-holomorphic and converges to the stress-energy tensor in the continuum, which is known to be a holomorphic function with the Schwarzian conformal covariance. In support of this conjecture, we prove it for the case of n=1 which corresponds to the Ising model. Moreover, in this case, we show that the correlations of the discrete stress-energy tensor with primary fields converge to their continuous counterparts, which satisfy the OPEs given by the CFT with central charge c=1/2. Proving the conjecture for other values of n remains a challenge. In particular, this would open a road to establishing the convergence of the interface to the corresponding SLE_κ in the scaling limit.