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Hamiltonian Truncation with Larger Dimensions

Hamiltonian Truncation (HT) is a numerical approach for calculating observables in a Quantum Field Theory non-perturbatively. This approach can be applied to theories constructed by deforming a conformal field theory with a relevant operator of scaling dimension $Δ$. UV divergences arise when $Δ$ is larger than half of the spacetime dimension $d$. These divergences can be regulated by HT or by using a more conventional local regulator. In this work we show that extra UV divergences appear when using HT rather than a local regulator for $Δ\geq d/2+1/4$, revealing a striking breakdown of locality. Our claim is based on the analysis of conformal perturbation theory up to fourth order. As an example we compute the Casimir energy of $d=2$ Minimal Models perturbed by operators whose dimensions take values on either side of the threshold $d/2+1/4$.