Energy-momentum tensor in the 2D Ising CFT in full modular space
Abstract
A set of lattice operators for the energy-momentum (EM) tensor in the Ising CFT is derived in the spin variables. Our expression works under arbitrary affine transformation both on triangular and hexagonal lattices (where the former includes the rectangular lattices). The correctness of the operators is numerically confirmed in Monte Carlo calculations by comparing the results with the conformal Ward identity, including the operator normalization. In the derivation of the EM tensor, a staggered structure of the affine-transformed hexagonal lattice is analyzed, which shows a peculiar shift from the circumcenter dual lattice and appears as a mixing angle between the holomorphic part and the antiholomorphic part . The details of this contribution will appear in a subsequent paper.
Keywords
Cite
@article{arxiv.2502.00512,
title = {Energy-momentum tensor in the 2D Ising CFT in full modular space},
author = {Richard C. Brower and George T. Fleming and Nobuyuki Matsumoto and Rohan Misra},
journal= {arXiv preprint arXiv:2502.00512},
year = {2025}
}
Comments
9 pages, 4 figures, talk presented at the 41st International Symposium on Lattice Field Theory (Lattice2024), July 28th - August 3rd, 2024, Liverpool, UK