On non-linear action for gauged M2-brane

Abstract

We propose a non-linear extension of U (1) × U (1) (abelian) ABJM model including T M 2 (higher derivative) corrections. The action proposed here is expected to describe a single M2-brane proving C 4 /Z k target space. The model includes couplings with the 3-form background in the eleven-dimensional supergravity which is consistent with the orbifold projection. We show that the novel higgs mechanism proposed by Mukhi and Papageorgakis does work even in the presence of higher derivative corrections and couplings with the background field, giving the correct structure of the Dirac-Born-Infeld action with Wess-Zumino term for a D2-brane. We also find half BPS solutions in the full nonlinear theory which is interpreted as an another M2-brane intersecting with the original M2-brane. A possible generalization to U (N ) × U (N ) gauge group is briefly discussed. a shin-s(at)th.phys.titech.ac.jp Recently, the low-energy description of multiple M2-branes has been intensively studied. Bagger, Lambert and Gustavsson proposed a three dimensional N = 8 supersymmetric model with SO(8) R R-symmetry (BLG model) as an effective theory of multiple M2-branes which is based on the three-algebra structure [1,2]. On the other hand, Aharony-Bergman-Jafferis-Maldacena recently proposed a three dimensional N = 6 superconformal Chern-Simons-matter theory as an alternative model of N coincident M2-branes probing C 4 /Z k orbifold (ABJM model) [3]. The gauge group is U(N) × U(N) and four complex scalar fields are introduced as the (anti) bi-fundamental representation of the gauge group. Two gauge fields A m and m corresponding to each U(N)s have levels k and −k respectively and the Lagrangian of the ABJM model exhibits an SU(4) R R-symmetry. For SU(2) × SU(2) gauge group, the N = 6 supersymmetry is enhanced to N = 8 and the ABJM model coincides with the BLG model [4]. It is also argued in [3] that the model is dual to M-theory on AdS 4 × S 7 /Z k at large-N.A lot of works on the classical solutions of this model have been achieved. In [5], a BPS fuzzy funnel configuration that represents an M5-brane intersecting with multiple M2-branes was found 1 . A domain wall solution that interpolates between a fuzzy sphere and trivial vacua was found in the mass deformed ABJM model [8]. There is a detail discussion on the dimensionality of the fuzzy sphere [7]. Other BPS objects such as vortices, Q-balls and so on were studied in [9,10,11,12].It is known that M2-branes in eleven dimensions are reduced to D2-branes in ten dimensions by compactifing one of the transverse direction to the M2-branes. This procedure is performed by the novel higgs mechanism proposed in [13]. It has been shown that the U(N)×U(N) ABJM theory is reduced to U(N) super Yang-Mills theory describing N coincident D2-branes. Since the super Yang-Mills action is the leading order approximation in α ′ (string scale) expansion of the non-abelian Dirac-Born-Infeld (DBI) action, it is natural to expect that the ABJM action is modified by the higher derivative membrane corrections that ...

Higher derivative BLG: Lagrangian and supersymmetry transformations

“…This theory has manifest N = 6 supersymmetry 5 together with an SU (4) R-symmetry and can be formulated using complex 3-algebras [38]. With the exception of the abelian U (1) × U (1) theory [39], the order 1/T M2 higher derivative extension of the ABJM model has not been examined.…”

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.…”

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

“…In the effective field theory of multiple Dp-branes, the WZ-type action includes the couplings to higher rank RR form fields, which are usually referred to as the Myers couplings [3]. Like the WZ-type couplings of D-branes in string theory, WZ-type couplings of multiple M2-branes can be constructed [4][5][6][7][8][9][10] in the context of the effective field theories, for instance, the Bagger-Lambert-Gustavsson theory [11] and the Aharony-Bergman-Jafferis-Maldacena(ABJM) theory [12]. These WZ-type couplings describe the couplings between M2-branes and 3-and 6-form gauge fields in 11-dimensional supergravity.…”