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Discrete stress-energy tensor in the loop O(n) model | | Dmitry Chelkak
; Alexander Glazman
; Stanislav Smirnov
; | | Date: |
21 Apr 2016 | | 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 $nin [-2,2]$, 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. | | Source: | arXiv, 1604.6339 | | Services: | Forum | Review | PDF | Favorites | |
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