Center Symmetry Breaking in Calabi--Yau Compactifications

It is widely believed that global symmetries must be broken in Quantum Gravity. This includes higher-form symmetries, which are commonplace in supergravity coupled to vector multiplets. Recently, a quantitative criterion for the breaking of (higher-form) symmetries in effective field theories of gravity has been proposed. We studied this criterion in the context of center one-form symmetries broken by BPS states in Calabi–Yau compactifications of type IIA string theory and M-theory. In a simple toy model, we evaluated the parameters quantifying the extent of symmetry breaking for large and small values of the moduli, comparing the scales of significant breaking with other relevant physical scales.