Moduli stars in the non relativistic limit

We study the possibility of formation of moduli oscillons analitically in the non relativistic regime. We start by introducing moduli as the scalar fields that arise in string theory and see how they can be stabilized in the KKLT scenario. We then consider the possibility of moduli coming together to form compact objects known as moduli stars and place them in the broader landscape of boson stars, taking into consideration also their formation mechanisms and possible experimental signals. The first step to do so is the construction of the non relativistic effective field theory, which we perform through the means of a non local operator that enables us to compute non relativistic corrections in a systematic way. This result is not present in the literature, so we check it by computing the NREFT via the traditional method of diagram matching: the two results turn out to be related by a field redefinition and are therefore equivalent low energy descriptions. Next, we turn to the corresponding effective Hamiltonian, looking for minima and maxima that would represent stable and unstable configurations. By studying it in different regimes we conclude that, in the absence of gravity, the only extremal point is a maximum non compatible with a bound state.