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| Format: | Preprint |
| Veröffentlicht: |
2026
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| Online-Zugang: | https://arxiv.org/abs/2602.19880 |
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| _version_ | 1866915812251533312 |
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| author | Li, Ricky Vicedo, Benoit |
| author_facet | Li, Ricky Vicedo, Benoit |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19880 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Effective Hamiltonians and Wilson--Polchinski renormalisation Li, Ricky Vicedo, Benoit High Energy Physics - Theory Mathematical Physics 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. |
| title | Effective Hamiltonians and Wilson--Polchinski renormalisation |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2602.19880 |