13 Unbroken Supersymmetry

Chapter 13
Unbroken Supersymmetry

Page 389, fourth line: the sign of the coefficients A_ij should be minus

The metric is that of a Cahen-Wallach symmetric space, whose coset construction is reviewed in Section ..., with A_ij = -λ²δ_ij.
Addendum: The algebra takes the form

$1 2 1 2 [Pi,Mj ] = 4λ δijPv , [Pu, Pi] = Mi , [Pu,Mi ] = - 4λ Pi .$
Page 389, Eqs. (13.96): a factor of λ is missing in the first equation

$Γ s(Pa) = - i4λσ2 γuγ1γa Γ s(Mi ) = - 18 λ2γuγi, Γ s(V ) = 0. (13.96)$
Addendum: The spinorial representation of P_v is trivial: Γ_s(P_v) = 0.
Page 393, Eq. (13.111): The sign of the vector field should be changed to minus and the parameter λ₆ in the 1-form ω should be divided by the square root of 2:

$2 2 2 √ -- λ6 1 2 3 4 dˆs = (dt + ω) - d⃗x(4), ˆV = - 3ω , ω = √--(x dx - x dx ). (13.111 ) 2$