Modular differential equations with movable poles and admissible RCFT characters

Abstract

Studies of modular linear differential equations (MLDE) for the classification of rational CFT characters have been limited to the case where the coefficient functions (in monic form) have no poles, or poles at special points of moduli space. Here we initiate an exploration of the vast territory of MLDEs with two characters and any number of poles at arbitrary points of moduli space. We show how to parametrise the most general equation precisely and count its parameters. Eliminating logarithmic singularities at all the poles provides constraint equations for the accessory parameters. By taking suitable limits, we find recursion relations between solutions for different numbers of poles. The cases of one and two movable poles are examined in detail and compared with predictions based on quasi-characters to find complete agreement. We also comment on the limit of coincident poles. Finally we show that there exist genuine CFT corresponding to many of the newly-studied cases. We emphasise that the modular data is an output, rather than an input, of our approach.

Duality defects in Dn-type Niemeier lattice CFTs

“…Two dimensional conformal field theory(CFT) [1] has seen renewed interests in recent times. These developments have happened in the classification problem through the modular bootstrap program [2][3][4][5][6][7][8][9][10][11][12] as well as through the 4D-2D correspondence [13]. The program of classification of conformal field theories was initiated in the late 1980s [14][15][16] with the hope of classifying rational CFT(RCFT) [17] with a fixed number of characters.…”