$\mathcal S$-modular transformation of the~$\mathcal N=2$ superconformal algebra characters
Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 260-284
Voir la notice de l'article provenant de la source Math-Net.Ru
The $\mathcal N=2$ superconformal algebra characters have to exhibit modular invariance in order to be appropriately applied in quantum superstring theories. The nonunitary characters are given by higher-level Appell functions and different kinds of Jacobi theta functions are involved within their algebraic structures. Evaluating their $\mathcal T$-modular invariance appears to be quite simple, but verifying their $\mathcal S$-modular invariance entails a serious mathematical physics exploration. In this regard, we use a new vocabulary for Jacobi theta functions, namely “spectral theta functions,” which allows us to come up with the $\mathcal S$-modular transformation of nonunitary (nontrivial) $\mathcal N=2$ characters for the central charge $c=3(1-2p/u)$, where $(u,p)$ is a pair of coprime positive integers.
Keywords:
$\mathcal N=2$ superconformal algebra characters,
$\mathcal S$-modular transformation, spectral theta functions,
higher-level Appell functions.
@article{TMF_2023_217_2_a1,
author = {M. R. Bahraminasab and M. Ghominejad},
title = {$\mathcal S$-modular transformation of the~$\mathcal N=2$ superconformal algebra characters},
journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
pages = {260--284},
publisher = {mathdoc},
volume = {217},
number = {2},
year = {2023},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a1/}
}
TY - JOUR AU - M. R. Bahraminasab AU - M. Ghominejad TI - $\mathcal S$-modular transformation of the~$\mathcal N=2$ superconformal algebra characters JO - Teoretičeskaâ i matematičeskaâ fizika PY - 2023 SP - 260 EP - 284 VL - 217 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a1/ LA - ru ID - TMF_2023_217_2_a1 ER -
%0 Journal Article %A M. R. Bahraminasab %A M. Ghominejad %T $\mathcal S$-modular transformation of the~$\mathcal N=2$ superconformal algebra characters %J Teoretičeskaâ i matematičeskaâ fizika %D 2023 %P 260-284 %V 217 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a1/ %G ru %F TMF_2023_217_2_a1
M. R. Bahraminasab; M. Ghominejad. $\mathcal S$-modular transformation of the~$\mathcal N=2$ superconformal algebra characters. Teoretičeskaâ i matematičeskaâ fizika, Tome 217 (2023) no. 2, pp. 260-284. http://geodesic.mathdoc.fr/item/TMF_2023_217_2_a1/