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arXiv · 2602.19880

Effective Hamiltonians and Wilson--Polchinski renormalisation

Ricky Li·Benoit Vicedo
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Abstract

We develop a novel approach to the Wilsonian renormalisation of Hamiltonians for 2-dimensional quantum field theories on the cylinder described in the UV by marginally relevant deformations of conformal field theories. To introduce a Wilsonian short-distance cutoff we make essential use of free field realisations of the full vertex operator algebra in the UV. Our method is intrinsically non-perturbative; we derive a Hamiltonian analogue of Polchinski's equation describing the flows of all couplings. As a primary example of our general method, we apply it to the marginal anisotropic deformation of the $\mathfrak{su}_2$ Wess--Zumino--Witten model at level 1, which is equivalent to the sine-Gordon model on the cylinder. In particular, we reproduce the standard renormalisation group flow of the sine-Gordon model near the Kosterlitz--Thouless point to second order in the couplings, a result usually derived using Lagrangian/path-integral methods.

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Ricky Li, Benoit Vicedo. 2026-02-23. Effective Hamiltonians and Wilson--Polchinski renormalisation. https://arxiv.org/abs/2602.19880

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