JHEP08(2018)082
supersymmetry. See [19–25] for the explicit construction. This interface can be extended
to a nullike interface [26].
Since there are many successful applications in N = 4 SYM theory, one might also
apply Janus deformations to the ABJM theory. However, the coupling constant of the
U(N)×U(N) ABJM theory is N/k with Chern-Simons level k, which is given by a discrete
numerical value. So it is unnatural to consider spatially varying coupling constant for the
ABJM theory. For this reason, the Janus deformation of the coupling constant is not
possible in the ABJM theory. On the other hand, this difficulty can be circumvented by
introducing a parameter [27] in the Bagger-Lambert-Gustavsson theory [28, 29], which is
another effective action of M2-branes. In [27], the authors considered Janus configurations
using a spacetime dependent vacuum expectation value of a scalar field and a constant mass
parameter. Although the Janus deformation of the ABJM theory has not been constructed
yet, Janus solutions have already been studied in 11-dimensional supergravity and gauged
N = 8 supergravity in 4-dimensions [30–35]. In addition, other related Janus solutions
were introduced in [36–40].
In this work, we construct a supersymmetric Janus mABJM model, that is, a model
with a spacetime dependent mass term. The deformation preserves the half of supersym-
metry of the mABJM theory. The mass parameter in the mABJM theory is originated from
a constant 4-form flux [41, 42]. The flux term is identified with the Wess-Zumino (WZ)
type coupling. Our model admits a mass deformation after the supersymmetric completion
for the flux term. As a result, we construct a large class of N = 3 Janus mABJM models.
This paper is organized as follows. In section 2, we summarize the supersymme-
try transformation of the mABJM theory and construct the Janus mABJM models with
spacetime dependent mass parameters. In section 3, we clarify the origin of the spacetime-
dependent mass term by using the WZ-type coupling. In section 4, we conclude with a
summary and a discussion for future directions.
2 N = 3 supersymmetric Janus mABJM models
Like the Janus extension in the N = 4 super Yang-Mills theory [19–22, 25], which was con-
structed by introducing the spacetime-dependent continuous coupling constant, one can
introduce the spacetime dependence of the continuous mass parameter in the mABJM the-
ory. In this section, we consider Janus extensions of the mABJM theory and construct the
N = 3 supersymmetric Janus mABJM models with one spatial coordinate and one light-
cone coordinate dependences, respectively. After reviewing the supersymmetric structure
of the N = 6 mABJM theory with constant mass parameter, we construct the N = 3
supersymmetric Janus models in 3-dimensions.
2.1 Supersymmetry of the N = 6 mABJM theory
We briefly summarize the supersymmetric structure of the N = 6 ABJM theory with
the action,
S =
Z
d
3
x (L
0
+ L
CS
− V
ferm
− V
bos
) , (2.1)
– 2 –
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