Discrete symmetries, dynamical tadpoles, and the swampland

The thesis has the purpose to describe the role that discrete symmetries and dynamical tapdoles have in the Swampland program. The first part of the talk will describe how to uncover the discrete global symmetries arising on D3-branes probing general orbifold singularities of general toric Calabi-Yau 3-folds. We will, then, look at the discrete gauge symmetries that are the gravity dual realizations of such discrete symmetries. They are used as a support for the first precise formulation of two Swampland conjectures for EFT coupled to gravity in the presence of discrete symmetries. The first conjecture relates the gauge coupling of a continuous abelian gauge symmetry with the order of the gauge symmetry. The second conjecture is a refinement of the Strong AdS Distance conjecture in the presence of discrete symmetries associated to 3-forms. It can be used to justify the presence of separation of scale in DGKT-like vacua of massive type IIA compactifications. In the second part of the talk we will focus on tadpoles associated to dynamical fields, i.e. dynamical tadpoles, arising from supersymmetry breaking. In particular, we will consider type IIB toroidal orbifold compactification with orientifolds, fluxes and mobile D7-branes. We focus on the backreaction on the action of ED3-brane instantons coming from D7-branes slightly moved from their stable position. If the generated dynamical tadpole is ignored, such the axion WGC for such BPS ED3-branes can be violated, signaling an incompatibility with Quantum Gravity.