Discrete Symmetries and their Stringy Origin

Abstract

Discrete symmetries have proven to be very useful in controlling the phenomenology of theories beyond the standard model. In this work we explore how these symmetries emerge from string compactifications. Our approach is twofold: On the one hand, we consider the heterotic string on orbifold backgrounds. In this case the discrete symmetries can be derived from the orbifold conformal field theory, and it can be shown that they are in close relation with the orbifold geometry. We devote special attention to <em>R</em>-symmetries, which arise from discrete remnants of the Lorentz group in compact space. Further we discuss the physical implications of these symmetries both in the heterotic mini-landscape and in newly constructed models based on the <em>Z</em>₂x<em>Z</em>₄ orbifold. In both cases we observe that the discrete symmetries favor particular locations in the orbifold where the particles of standard model should live. On the other hand we consider a class of F-theory models exhibiting an SU(5) gauge group, times additional U(1) symmetries. In this case, the smooth compactification background does not permit us to track the discrete symmetries as transparently as in orbifold models. Hence, we follow a different approach and search for discrete subgroups emerging after the U(1)s are broken. We observe that in this approach it is possible to obtain the standard <em>Z</em>₂ matter parity of the MSSM.