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Abstract

The incorporation of Wilson lines leads to an extension of the modular
symmetries of string compactification beyond SL(2, Z). In the simplest
case with one Wilson line Z, Kahler modulus T and complex structure
modulus U, we are led to the Siegel modular group Sp(4, 7L). It includes
SL(2, Z)(T) x SL(2, Z)(U) as well as Z(2) mirror symmetry, which
interchanges T and U. Possible applications to flavor physics of the
Standard Model require the study of orbifolds of Sp(4, 7L) to obtain
chiral fermions. We identify the 13 possible orbifolds and determine
their modular flavor symmetries as subgroups of Sp(4, 7L). Some cases
correspond to symmetric orbifolds that extend previously discussed cases
of SL(2, Z). Others are based on asymmetric orbifold twists (including
mirror symmetry) that do no longer allow for a simple intuitive
geometrical interpretation and require further study. Sometimes they can
be mapped back to symmetric orbifolds with quantized Wilson lines. The
symmetries of Sp(4, 7L) reveal exciting new aspects of modular
symmetries with promising applications to flavor model building. (C)
2021 The Authors. Published by Elsevier B.V.