Abelian gauge invariance of the WZ-type coupling in ABJM theory

Abstract

We construct the interaction terms between the worldvolume fields of multiple M2-branes and 3-form gauge field of 11-dimensional supergravity, in the context of ABJM theory. The obtained Wess-Zumino-type coupling is simultaneously invariant under the U L (N )×U R (N ) non-Abelian gauge transformation of the ABJM theory and the Abelian gauge transformation of the 3-form field in 11-dimensional supergravity.

Janus ABJM models with mass deformation

“…In order to introduce such WZ-type couplings as interaction terms in the M2-brane theory, the non-Abelian U(N) × U(N) gauge symmetry of the ABJM theory should be preserved by the interaction terms. In relation with this issue, there were several works in the literature [30,31,[33][34][35][36][37][38][39]. Specially in [31,35,[37][38][39], the gauge invariant WZ-type couplings were constructed under the assumption that the 3-form and 6-form gauge fields depend on scalar fields Y A , Y † A as well as worldvolume coordinates (t, w 1 , w 2 ) of the M2-branes.…”

“…In relation with this issue, there were several works in the literature [30,31,[33][34][35][36][37][38][39]. Specially in [31,35,[37][38][39], the gauge invariant WZ-type couplings were constructed under the assumption that the 3-form and 6-form gauge fields depend on scalar fields Y A , Y † A as well as worldvolume coordinates (t, w 1 , w 2 ) of the M2-branes. The deformed quartic potential termV flux in (2.16) in the mABJM theory can be identified with the WZ-type coupling for the 6-form gauge field in the presence of the constant self-dual 4-form field strength [30,31,37].…”

“…In the construction of the WZ-type coupling, the dependence of form fields on the transverse scalars seems natural[31,35,[37][38][39]. Therefore, the field strengths also depend on the transverse scalars.…”