Problems of 4D GUTs

Abstract

There are two aesthetic (perhaps more fundamental) problems concerning 4D GUTs. They have to do with the complicated sectors necessary for GUT symmetry breaking and Higgs doublet-triplet splitting. These sectors are sufficiently complicated that it is difficult to imagine that they may be derived from a more fundamental theory, such as string theory. In fact, in the heterotic string it is well-known that the largest chiral matter representation in either SU(5) or SO(10), which is massless in 4D, is the adjoint representation. Moreover for SO(10) there are no examples of semi-realistic models with a massless adjoint. Why should you care about string theory? Because it is the only known possible extension of the Standard Model which includes quantum gravity. In order to resolve these difficulties, it becomes natural to discuss grand unified theories in higher spatial dimensions. These are the so-called orbifold GUT theories discussed in the next section. They have their own problems, i.e. they are non-renormalizable theories requiring an infinite number of higher dimensional counter terms. In later chapters we shall discuss ways of embedding orbifold GUTs into the Heterotic string.