On currents in the $O(n)$ loop model
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917647823667200 |
|---|---|
| author | Jacobsen, Jesper Lykke Nivesvivat, Rongvoram Saleur, Hubert |
| author_facet | Jacobsen, Jesper Lykke Nivesvivat, Rongvoram Saleur, Hubert |
| contents | Using methods from the conformal bootstrap, we study the properties of Noether currents in the critical $O(n)$ loop model. We confirm that they do not give rise to a Kac-Moody algebra (for $n\neq 2$), a result expected from the underlying lack of unitarity. By studying four-point functions in detail, we fully determine the current-current OPEs, and thus obtain several structure constants with physical meaning. We find in particular that the terms $:\!J\bar{J}\!:$ in the identity and adjoint channels vanish exactly, invalidating the argument made in \cite{car93-1} that adding orientation-dependent interactions to the model should lead to continuously varying exponents in self-avoiding walks. We also determine the residue of the identity channel in the $JJ$ two-point function, finding that it coincides both with the result of a transfer-matrix computation for an orientation-dependent correlation function in the lattice model, and with an earlier Coulomb gas computation of Cardy \cite{car93}. This is, to our knowledge, one of the first instances where the Coulomb gas formalism and the bootstrap can be successfully compared. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_11064 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On currents in the $O(n)$ loop model Jacobsen, Jesper Lykke Nivesvivat, Rongvoram Saleur, Hubert High Energy Physics - Theory Mathematical Physics Using methods from the conformal bootstrap, we study the properties of Noether currents in the critical $O(n)$ loop model. We confirm that they do not give rise to a Kac-Moody algebra (for $n\neq 2$), a result expected from the underlying lack of unitarity. By studying four-point functions in detail, we fully determine the current-current OPEs, and thus obtain several structure constants with physical meaning. We find in particular that the terms $:\!J\bar{J}\!:$ in the identity and adjoint channels vanish exactly, invalidating the argument made in \cite{car93-1} that adding orientation-dependent interactions to the model should lead to continuously varying exponents in self-avoiding walks. We also determine the residue of the identity channel in the $JJ$ two-point function, finding that it coincides both with the result of a transfer-matrix computation for an orientation-dependent correlation function in the lattice model, and with an earlier Coulomb gas computation of Cardy \cite{car93}. This is, to our knowledge, one of the first instances where the Coulomb gas formalism and the bootstrap can be successfully compared. |
| title | On currents in the $O(n)$ loop model |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2310.11064 |