Classification of modular symmetries in non-supersymmetric heterotic string theories

A bstract We study modular symmetries in non-supersymmetric heterotic string theories on toroidal backgrounds with Wilson line modulus, constructed by stringy Scherk-Schwartz compactification. In particular, we focus on a subgroup of the T-duality group 𝒪( D +16 , D, ℤ) with D = 2 given by an outer automorphism of the Narain lattice, which can be mapped to the Siegel modular group Sp(4 , ℤ). We classify the modular symmetries and a 𝒞 P -like symmetry on T 2 and its orbifolds with symmetric and asymmetric orbifold twists. It turns out that the non-supersymmetric heterotic string theories only enjoy a part of modular symmetries in contrast to supersymmetric ones. Furthermore, the gauge symmetry is maximally enhanced at fixed points of modular symmetries on T 2 on which we analyze the vacuum structure of eight-dimensional tachyon-free vacua.