On the spectrum of the N=2SU(3)⊗SU(2)⊗U(1) gauge theory from D=11 supergravity

Abstract

The authors determine the spectrum of the representations contributing to the zero, one, two, three-forms on Mpqr spaces: then, they calculate the eigenvalues of the Laplacian on zero-forms and of the *d operator on three-forms. These latter can be given only implicitly since they are the roots of a 15th-order secular equation. In the sector of the two-forms there is a zero-mode corresponding to the fact that the second Betti number B2 is equal to one. Hence there is an extra U1 vector multiplet and the effective theory in four-dimensions is N=2 supergravity coupled to the N=2 gauge multiplet of SU(3)(X)SU(2)(X)U(1). There are also scalar zero-modes in the (10,3) and (10,3) of SU(3)(X)SU(2). They show that they are not elements of a N=2 hypermultiplet but rather of a bigger multiplet containing also vectors and other spins. Hypermultiplets whose states are all massive are not excluded and using the results of the spectrum can now be systematically searched.