Remark About Scaling Limit of ABJ Theory

TL;DR

This paper explores the scaling limit of ABJ superconformal Chern-Simons-matter theories, demonstrating how they can lead to L-BLG theories and additional Chern-Simons theories, extending previous work on ABJM models.

Contribution

It generalizes the scaling limit from ABJM to ABJ theories, establishing a consistent method to derive L-BLG and additional Chern-Simons theories from ABJ models.

Findings

Derived a new scaling limit for ABJ theories.

Connected ABJ theories to L-BLG and U(M-N) Chern-Simons theories.

Extended previous ABJM-based results to more general models.

Abstract

We generalize the suggestion presented in arXiv:0806.3498 that the 3d N=8 superconformal SU(N) Chern-Simons-matter theory of Lorentzian Bagger-Lambert-Gustavson type (L-BLG) can be obtained through the scaling limit from N=6 superconformal U(N)xU(N) Chern-Simons-matter theory of Aharony, Bergman, Jafferis and Maldacena (ABJM) to the case when we study the scaling limit of N=6 superconformal U(M)xU(N) Chern-Simons-matter theory of Aharony, Bergman and Jafferis (ABJ). We show that if we extend the ABJ theory in the same way as in arXiv:0811.1540 we can define a consistent limit that leads to SU(N) L-BLG theory together with U(M-N) Chern-Simons theory of level k.