Siegel modular flavor group and CP from string theory

Abstract

We derive the potential modular symmetries of heterotic string theory. For a toroidal compactification with Wilson line modulus, we obtain the Siegel modular group $\mathrm{Sp}(4,\mathbb{Z})$ that includes the modular symmetries $\mathrm{SL}(2,\mathbb{Z}{)}_T$ and $\mathrm{SL}(2,\mathbb{Z}{)}_U$ (of the "geometric" moduli $T$ and $U$) as well as mirror symmetry. In addition, string theory provides a candidate for a CP-like symmetry that enhances the Siegel modular group to $\mathrm{GSp}(4,\mathbb{Z})$.

18 pages, 1 figure, 1 table; v2: some statements in the conclusions clarified, matches version published in PLB

References in corpus (2)

• Unification of Flavor, CP, and Modular Symmetries
• K3 surfaces, modular forms, and non-geometric heterotic compactifications

Cited by in corpus (2)

• Electron EDM arising from modulus $\tau$ in the supersymmetric modular invariant flavor models
• Orbifolds from $\mathrm{Sp}(4,\mathbb{Z})$ and their modular symmetries