Strictly speaking, the SU(5) GUT breaks into the unbroken Standard Model, and its multiplets have weak-isospin and weak-hypercharge degrees of freedom. Standard-Model breaking then makes electric charge out of them.
Q = I3 + Y
(electric charge) = (projected weak isospin) + (weak hypercharge)
Here are the Standard Model's unbroken elementary-fermion multiplets with (QCD, weak isospin, weak hypercharge) values. A c means charge conjugate:
- L (left-handed electron, neutrino): (1, 2, -1/2) -- Lc: (1, 2, 1/2)
- E (right-handed electron): (1,1,-1) -- Ec: (1,1,1)
- N (right-handed neutrino): (1,1,0) -- Nc: (1,1,0)
- Q (left-handed up, down quarks): (3,2,1/6) -- Qc: (3*,2,-1/6)
- U (right-handed up quark): (3,1,2/3) -- Uc: (3*,1,-2/3)
- D (right-handed down quark: (3,1,-1/3) -- Dc: (3*,1,1/3)
Here is where they are in the Georgi-Glashow SU(5) model (multiplet number, chirality, indices in asymmetric tensor,):
- 1L (0): Nc
- 5R (1): D + Lc
- 10L (2): Q + Uc + Ec
- 10R (3): Qc + U + E
- 5L (4): Dc + L
- 1R (5): N
In all of these multiplets, the weak-hypercharge values add up to 0. That's because the weak hypercharge is derived from a SU(5) operator, and SU(N) operators are traceless (diagonal components adding to 0). One can show that these are the only WHC values that are consistent with SU(5), to within a multiplicative factor.
This is what makes the up quark charged +2/3, the down quark charged -1/3, the neutrino charged 0, and the electron charge -1. Since quarks are confined as multiples of 3, antiquarks being negative quarks, that means that hadrons all have integer charges, just like the electron.