Modular Symmetry and the Strong CP Problem

I will discuss a recently proposed solution to the strong CP problem based on modular symmetry. The latter is inherent to toroidal compactifications in string theory. I will show that modular symmetry allows for simple effective theories of flavour and CP where (i) the QCD angle vanishes, (ii) the CKM phase is large, (iii) quark and lepton masses and mixings can be reproduced up to order one coefficients. This solution is further extended to incorporate features that appear in string compactifications: quarks with mostly positive modular weights and non-trivial gauge kinetic functions. This requires assuming that singularities and zeroes appear only at special points in the moduli space, such as decompactification limits.

Based on 2305.08908, 2406.01689 and 2505.20395.