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

Abstract

We construct three dimensional Chern-Simons-matter theories with gauge groups U (N ) ×U (N ) and SU (N ) ×SU (N ) which have explicit N = 6 superconformal symmetry. Using brane constructions we argue that the U (N ) × U (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 4 × S 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 4 × CP 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) × SU (2) our theory has extra symmetries and becomes identical to the Bagger-Lambert theory.

Transport properties of spacetime-filling branes

“…In this case L 3 2κ 2 ∼ N 2 . Another example is that of ABJM theory when d = 3 [18]. There is an AdS 4 solution of radius L and trivial dilaton for V = − 6 L 2 , originating from a reduction of M-theory on the orbifold S 7 /Z k .…”

“…Adding up these two contributions the total free energy in the canonical ensemble is 18) and the negativity shows that for any value of the temperature these solutions are preferred over the corresponding thermal solutions. The speed of sound for z = 1 cannot be calculated.…”

“…After the JHEP04 (2014)042 integration is performed the pole in the imaginary part of the optical conductivity is obtained from the asymptotic constant to which σ −1 flows at large radius. With the solution to (4.17a) at hand, the ω → 0 limit of the real part of the optical conductivity is obtained integrating (4.17b) 18) with k 0 an integration constant. To fix its value plug this solution into (4.17c).…”

Seiberg duality in Chern-Simons theories with fundamental and adjoint matter

“…Theories with this amount of supersymmetry were constructed in [2 -6] and were related to M2-brane dynamics in [7,8]. Theories with N = 6 and N = 5 supersymmetry were recently discussed in [9,10]. A non-supersymmetric variant was considered in [11].…”

Spiky strings inAdS4×CP3with Neveu-Schwarz flux

“…Recently Aharony, Bergman, Jafferis and Maldacena (ABJM) [1] proposed a new class of gauge theory-string theory duality between N = 6 Chern-Simons (CS) theory and type IIA string theory on AdS 4 × CP 3 . Based on this Aharony, Bergman, and Jafferis (ABJ) [2] identified further a class of AdS 4 /CF T 3 duality with extended supersymmetry namely, a three dimensional N = 6 superconformal Chen-Simons theory with a gauge group U (M ) k × U (N ) −k , with k being the level of the CS theory, is dual to type IIA string theory on AdS 4 × CP 3 with B N S holonomy turned on over CP 1 ⊂ CP 3 .…”