N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals (0806.1218v4)

Abstract: We construct three dimensional Chern-Simons-matter theories with gauge groups U(N)xU(N) and SU(N)xSU(N) which have explicit N=6 superconformal symmetry. Using brane constructions we argue that the U(N)xU(N) theory at level k describes the low energy limit of N M2-branes probing a C^4/Z_k singularity. At large N the theory is then dual to M theory on AdS_4xS^7/Z_k. The theory also has a 't Hooft limit (of large N with a fixed ratio N/k) which is dual to type IIA string theory on AdS_4xCP^3. For k=1 the theory is conjectured to describe N M2-branes in flat space, although our construction realizes explicitly only six of the eight supersymmetries. We give some evidence for this conjecture, which is similar to the evidence for mirror symmetry in d=3 gauge theories. When the gauge group is SU(2)xSU(2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.

• The paper formulates N=6 Chern-Simons-matter theories using U(N)×U(N) and SU(N)×SU(N) gauge groups to model M2-brane dynamics.
• It employs brane construction techniques to reveal enhanced supersymmetry and establish dualities with AdS₄ geometries in M-theory and type IIA string theory.
• Key insights on moduli spaces corroborate the duality conjectures, linking gauge theory dynamics with the geometry of M2-branes probing C⁴/Z_k singularities.

An Analysis of N = 6 Superconformal Chern-Simons-Matter Theories

The paper focuses on the construction and paper of three-dimensional Chern-Simons-matter theories exhibiting N = 6 superconformal symmetry. These theories are expressed through gauge groups U(N) × U(N) and SU(N) × SU(N), which are intrinsically related to M2-branes in the field of M-theory and exhibit intriguing properties when analyzed in the AdS/CFT correspondence framework.

The core aspect of these theories is their role in modeling the low-energy dynamics of M2-branes that probe transverse spaces featuring C^4/Z_k singularities. In particular, the gauge theory variant at level k is conjectured to describe M2-branes in flat spaces when k = 1. The duality aspect of these theories is explored through the perspective of their M-theory and type IIA string theory counterparts. Specifically, in the large-N limit, the Chern-Simons theory is dual to M-theory on AdS_4×S^7/Z_k, while the ’t Hooft limit reflects a duality with type IIA string theory on AdS_4×CP^3.

Key advancements in the paper stem from the brane constructions, which provide insight into the connections between these three-dimensional Chern-Simons-matter theories and their higher-dimensional counterparts in M-theory. By applying the brane construction techniques to type IIB string theory, the authors demonstrate that the resultant IR conformal theory possesses enhanced N = 6 supersymmetry, presenting compelling evidence aligning with the proposed duality conjectures.

An interesting aspect of the theory under consideration is the case involving SU(2) × SU(2) gauge groups, where an enhancement to N = 8 superconformal symmetry emerges due to additional symmetries bestowed upon the theory. This situation mirrors the Bagger-Lambert theory, thereby providing a notable instance where the structure of supersymmetries and underlying symmetries aligns with existing precedent in the domain.

Moreover, the evaluation of the moduli space offers vital insights into the relationship between the superconformal theories and M2-branes. Specifically, these theories are shown to have moduli spaces that are consistent with M2-branes probing the defined singularities, corroborating the conjectures regarding duality and underlying geometric structures.

The paper not only explores the conceptual and mathematical underpinnings of these theories but also introduces potential implications, such as the applicability of these models to condensed matter systems where Chern-Simons terms often manifest. Beyond the theoretical implications, the research may offer avenues for extending the understanding of diverse systems in the context of the AdS/CFT correspondence, encompassing a variety of compactification geometries in the string theory landscape.

The meticulous analysis in this paper provides substantive contributions to the understanding of highly supersymmetric gauge theories, highlighting potential avenues for further exploration in theoretical physics. Future research may expand upon these findings, incorporating additional elements or dimensional transitions that could yield even deeper insights into M-theory and beyond.