Partially Supersymmetric ABJM Theory with Flux

Abstract

Starting with generic Wess-Zumino type coupling to constant four-form and the dual seven-form field strengths in the ABJM theory, we obtain mass-deformed theories with N = 2, 4 supersymmetries. These theories contain massless scalar fields and allow the implementation of the Mukhi-Papageorgakis Higgsing procedure. Using this procedure, we connect the Higgsed theories to three-dimensional mass-deformed SYM theories. These are also connected by the four-dimensional N = 1 * , 2 * mass-deformed SYM theories through dimensional reduction. We classify the three-dimensional mass-deformed SYM theories of N = 1, 2, 4 supersymmetry, of which a few cases of N = 1, 2 are connected neither by MP Higgsing procedure nor dimensional reduction.

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.…”

“…The deformation preserves the half of supersymmetry of the mABJM theory. The mass parameter in the mABJM theory is originated from a constant 4-form flux [30,31]. The flux term is identified with the Wess-Zumino (WZ) type coupling.…”

Aspects of massive ABJM models with inhomogeneous mass parameters

“…The N = 3 ImABJM model is derived from the N = 6 mABJM theory in the previous subsection. Naturally enough, we begin with the N = 4 supersymmetric constant mass deformation of the ABJM theory [5] and construct the N = 2 Inhomogeneous deformation in this subsection. With specific mass matrices,…”

“…Above all we recall the N = 2 mass-deformed ABJM theory with a constant mass parameter [5]. When the following mass matrices,…”

“…Due to the non-dynamical nature of the Chern-Simons gauge fields, an interesting extension is realized by use of a supersymmetry-preserving mass deformation, which gives rise to the mass-deformed ABJM (mABJM) theory [2,3]. The mass parameter is originated from the self-dual constant 4-form field strength accompanied by the Wess-Zumino type coupling with M2 branes [4,5] in the 11-dimensional supergravity. Gravity dual of the mABJM theory is identified as the LLM geometry [6] with Z k orbifold.…”