## Theta problem and asymptotic Hodge theory

##### Summary

In this thesis we study the recently proposed conjecture by Cumrum Vafa and Sergio Cecotti, about a possible solution of the theta problem in QCD as a result of Quantum Gravitational consistency of the theory in the UV. The authors claim that one might be able to argue that the value of the theta angle can be fixed for theories corresponding to the Landscape of String theory. They support their claim by testing the theta angle corresponding to the graviphoton of N=2 Supergravity obtained by type IIB compactification on rigid Calabi-Yau manifolds. They find that indeed for most cases θ=0(only around 50 such manifolds are known). We test the conjecture in a more general context. More precisely, we investigate the behaviour of the corresponding theta angles for the 4D low energy theory of type IIB strings compactified on Calabi-Yau threefolds with arbitrary hodge numbers near the boundaries of the complex structure moduli space. For this task, we employ several tools from degenerating variations of Hodge structures. Based on the data coming from the Sl(2) orbit theorem we manage to find an electric-magnetic basis for the real threeforms which gives a vanishing theta angle in the strong coupling limit for every type of one modulus denegeration and enhancement between these. Moreover we investigate the weak coupling regime where we reproduce the known behaviour for the large volume-large complex structure point but also find similar expressions for any type of singular loci. This universal behaviour in each regime provides evidence for the restriction of the theta angle values due to Quantum Gravitational consistency for the first time since the original proposal.