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

TY - JOUR

T1 - Towards a Quintic Ginzburg-Landau Description of the (2,7) Minimal Model

AU - Katsevich, Andrei

AU - Klebanov, Igor

AU - Sun, Zimo

AU - Tarnopolsky, Grigory

N1 - Publisher Copyright: © 2026 authors. Published by the American Physical Society.

PY - 2026/3/20

Y1 - 2026/3/20

N2 - We discuss dimensional continuation of the massless scalar field theory with the iϕ5 interaction term. It preserves the so-called PT symmetry, which acts by ϕ→-ϕ accompanied by i→-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 ϕ2 with the Virasoro primaries ϕ1,2 and ϕ1,3, respectively, and iϕ3 with a quasiprimary operator, which is a Virasoro descendant of ϕ1,3. 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(2,2n+1) are described by the massless scalar field theories with the iϕ2n-1 interaction terms.

AB - We discuss dimensional continuation of the massless scalar field theory with the iϕ5 interaction term. It preserves the so-called PT symmetry, which acts by ϕ→-ϕ accompanied by i→-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 ϕ2 with the Virasoro primaries ϕ1,2 and ϕ1,3, respectively, and iϕ3 with a quasiprimary operator, which is a Virasoro descendant of ϕ1,3. 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(2,2n+1) are described by the massless scalar field theories with the iϕ2n-1 interaction terms.

UR - https://www.scopus.com/pages/publications/105033341362

UR - https://www.scopus.com/pages/publications/105033341362#tab=citedBy

U2 - 10.1103/9zz4-pvp7

DO - 10.1103/9zz4-pvp7

M3 - Article

C2 - 41931815

SN - 0031-9007

VL - 136

JO - Physical review letters

JF - Physical review letters

IS - 11

M1 - 111602

ER -