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arXiv · 1604.06339

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

Dmitry Chelkak·Alexander Glazman·Stanislav Smirnov
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Abstract

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 $n\in [0,2]$, 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 $\mathrm{SLE}_\kappa$ in the scaling limit.

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Dmitry Chelkak, Alexander Glazman, Stanislav Smirnov. 2016-04-21. Discrete stress-energy tensor in the loop O(n) model. https://arxiv.org/abs/1604.06339

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