Running of gauge couplings in string theory

In this paper we conduct a general, model-independent analysis of the running gauge couplings within closed string theories. Unlike previous discussions in literature, our calculations fully respect underlying modular invariance and include contributions from infinite towers states which are ultimately responsible for many properties theory is famous, including an enhanced degree finiteness $\mathrm{UV}/\mathrm{IR}$ mixing. order to perform calculations, adopt formalism that was recently developed Higgs mass such theories, demonstrate can also be applied couplings. gives rise ``on-shell'' effective field (EFT) description final results expressed terms supertraces over physical states, these quantities exhibit EFT-like ``running'' as function spacetime scale. We find, however, calculation differs one deep way mass: while latter depend on purely on-shell supertraces, former have different structure causes them off-shell well. some regions parameter space, how certain expected field-theoretic behaviors emerge highly $\mathrm{UV}/\mathrm{IR}$-mixed environment. other situations, by contrast, give number intrinsically stringy transcend what might approach.