TY - JOUR

T1 - On string functions of the generalized parafermionic theories, mock theta functions, and false theta functions

AU - Борозенец, Николай Евгеньевич

AU - Мортенсон, Эрик Тодд

PY - 2026/1

Y1 - 2026/1

N2 - Kac and Wakimoto introduced the admissible highest weight representations as a conjectural classification of all modular-invariant representations of the affine Kac–Moody algebras. For the affine Kac–Moody algebra A1(1) their conjectural construction has been proved. Using Kac and Wakimoto's result, Ahn, Chung, and Tye introduced the generalized Fateev–Zamolodchikov parafermionic theories, whose chiral current algebras were recently studied as extensions of the parafermionic vertex operator algebra at admissible level. The characters of the parafermionic vertex operator algebra are string functions of A1(1) up to a simple appropriate factor. For the 1/2-level string functions, we present their mixed mock modular properties as well as elegant mock theta conjecture-like identities involving second-order mock theta functions from Ramanujan's Lost Notebook. In addition, we give an elementary proof that the negative level string functions can be evaluated in terms of false theta functions.

AB - Kac and Wakimoto introduced the admissible highest weight representations as a conjectural classification of all modular-invariant representations of the affine Kac–Moody algebras. For the affine Kac–Moody algebra A1(1) their conjectural construction has been proved. Using Kac and Wakimoto's result, Ahn, Chung, and Tye introduced the generalized Fateev–Zamolodchikov parafermionic theories, whose chiral current algebras were recently studied as extensions of the parafermionic vertex operator algebra at admissible level. The characters of the parafermionic vertex operator algebra are string functions of A1(1) up to a simple appropriate factor. For the 1/2-level string functions, we present their mixed mock modular properties as well as elegant mock theta conjecture-like identities involving second-order mock theta functions from Ramanujan's Lost Notebook. In addition, we give an elementary proof that the negative level string functions can be evaluated in terms of false theta functions.

KW - Admissible highest weight representations

KW - False theta functions

KW - Hecke-type double-sums

KW - Mock theta functions

KW - Parafermionic characters

KW - Parafermionic vertex operator algebras

KW - String functions

UR - https://www.mendeley.com/catalogue/3b4a356e-bf43-31f6-9666-5f27cb1fd2ef/

U2 - 10.1016/j.aim.2025.110684

DO - 10.1016/j.aim.2025.110684

M3 - Article

VL - 484

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

M1 - 110684

ER -