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How can a renormalization group fixed point be scale invariant without beingconformal? Polchinski (1988) showed that this may happen if the theory containsa virial current -- a non-conserved vector operator of dimension exactly$(d-1)$, whose divergence expresses the trace of the stress tensor. We pointout that this scenario can be probed via lattice Monte Carlo simulations, usingthe critical 3d Ising model as an example. Our results put a lower bound$\Delta_V>5.0$ on the scaling dimension of the lowest virial current candidate$V$, well above 2 expected for the true virial current. This implies that thecritical 3d Ising model has no virial current, providing a structuralexplanation for the conformal invariance of the model.

A structural test for the conformal invariance of the critical 3d Ising model