Towards a Quintic Ginzburg-Landau Description of the $(2,7)$ Minimal Model
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| Format: | Preprint |
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2025
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| _version_ | 1866911226020233216 |
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| author | Katsevich, Andrei Klebanov, Igor R. Sun, Zimo Tarnopolsky, Grigory |
| author_facet | Katsevich, Andrei Klebanov, Igor R. Sun, Zimo Tarnopolsky, Grigory |
| contents | We discuss dimensional continuation of the massless scalar field theory with the $iϕ^5$ interaction term. It preserves the so-called $\mathcal{PT}$ symmetry, which acts by $ϕ\rightarrow -ϕ$ accompanied by $i\rightarrow -i$. Below its upper critical dimension $10/3$, this theory has interacting infrared fixed points. We argue that the fixed point in $d=2$ describes the non-unitary minimal conformal model $M(2,7)$. We identify the operators $ϕ$ and $ϕ^2$ with the Virasoro primaries $ϕ_{1,2}$ and $ϕ_{1,3}$, respectively, and $iϕ^3$ with a quasi-primary operator, which is a Virasoro descendant of $ϕ_{1,3}$. Our identifications appear to be consistent with the operator product expansions and with considerations based on integrability. Using constrained Padé extrapolations, we provide estimates of the critical exponents in $d=3$. We also comment on possible lattice descriptions of $M(2,7)$ and discuss RG flows to and from this CFT. Finally, we conjecture that the minimal models $M(2, 2n+1)$ are described by the massless scalar field theories with the $iϕ^{2n-1}$ interaction terms. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_19085 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Towards a Quintic Ginzburg-Landau Description of the $(2,7)$ Minimal Model Katsevich, Andrei Klebanov, Igor R. Sun, Zimo Tarnopolsky, Grigory High Energy Physics - Theory Statistical Mechanics We discuss dimensional continuation of the massless scalar field theory with the $iϕ^5$ interaction term. It preserves the so-called $\mathcal{PT}$ symmetry, which acts by $ϕ\rightarrow -ϕ$ accompanied by $i\rightarrow -i$. Below its upper critical dimension $10/3$, this theory has interacting infrared fixed points. We argue that the fixed point in $d=2$ describes the non-unitary minimal conformal model $M(2,7)$. We identify the operators $ϕ$ and $ϕ^2$ with the Virasoro primaries $ϕ_{1,2}$ and $ϕ_{1,3}$, respectively, and $iϕ^3$ with a quasi-primary operator, which is a Virasoro descendant of $ϕ_{1,3}$. Our identifications appear to be consistent with the operator product expansions and with considerations based on integrability. Using constrained Padé extrapolations, we provide estimates of the critical exponents in $d=3$. We also comment on possible lattice descriptions of $M(2,7)$ and discuss RG flows to and from this CFT. Finally, we conjecture that the minimal models $M(2, 2n+1)$ are described by the massless scalar field theories with the $iϕ^{2n-1}$ interaction terms. |
| title | Towards a Quintic Ginzburg-Landau Description of the $(2,7)$ Minimal Model |
| topic | High Energy Physics - Theory Statistical Mechanics |
| url | https://arxiv.org/abs/2510.19085 |