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Towards a Quintic Ginzburg-Landau Description of the (2,7) Minimal Model

Andrei Katsevich ¹, Igor Klebanov ^1,2, Zimo Sun ^1,3, and Grigory Tarnopolsky ⁴

¹Joseph Henry Laboratories, Princeton University, Princeton, New Jersey 08544, USA
²Princeton Center for Theoretical Science, Princeton University, Princeton, New Jersey 08544, USA
³Institute for Advanced Study, Princeton, New Jersey 08540, USA
⁴Department of Physics, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA

Phys. Rev. Lett. 136, 111602 – Published 19 March, 2026

DOI: https://doi.org/10.1103/9zz4-pvp7

Abstract

We discuss dimensional continuation of the massless scalar field theory with the $i ϕ^{5}$ interaction term. It preserves the so-called $P T$ symmetry, which acts by $ϕ \to - ϕ$ accompanied by $i \to - i$ . 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 nonunitary 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 $i ϕ^{3}$ with a quasiprimary 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 conformal field theory (CFT). Finally, we conjecture that the minimal models $M (2, 2 n + 1)$ are described by the massless scalar field theories with the $i ϕ^{2 n - 1}$ interaction terms.

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References (63)

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https://github.com/Andrew-Kot/TCSAM2q.

Phys. Rev. Lett. 136, 111602– Published 19 March, 2026

Vol. 136, Iss. 11 — 20 March 2026

Received 20 November 2025
Revised 17 January 2026
Accepted 11 February 2026

DOI: https://doi.org/10.1103/9zz4-pvp7

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Towards a Quintic Ginzburg-Landau Description of the (2,7) Minimal Model

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