Superconformal Chern–Simons Theories

Abstract

We explore the possibilities for constructing Lagrangian descriptions of threedimensional superconformal classical gauge theories that contain a Chern-Simons term, but no kinetic term, for the gauge fields. Classes of such theories with N = 1 and N = 2 supersymmetry are found. However, interacting theories of this type with N = 8 supersymmetry do not exist.

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

“…it exhibits N = 2 supersymmetry in the three directions (x 0 , x 1 , x 2 ) common to all the branes. 1 The low energy description of this system is in terms of a U(Nc) gauge theory that lives on the D3-branes which are suspended along the 6-direction between the n NS5-branes and the n ′ NS5 ′ -branes. The matter content of this theory comprises of: (a) an N = 2 vector multiplet V , (b) N f pairs of N = 2 chiral multiplets Q i ,Q i (i = 1, 2, · · · , N f ) in the fundamental and anti-fundamental representations of the gauge group and (c) two chiral supermultiplets X, Y in the adjoint representation.…”

“…Ref. [1] explored various Chern-Simons theories with this purpose, but did not find one with N = 8 supersymmetry. Theories with this amount of supersymmetry were constructed in [2 -6] and were related to M2-brane dynamics in [7,8].…”

Infrared stability of ABJ-like theories

“…Recently, a renew interest in three dimensional superconformal Chern-Simons (CS) theories [1] has been triggered by the formulation of the AdS4/CFT3 correspondence between CS matter theories and M/string theory. The low energy dynamics of a stack of N M2-branes in M-theory probing a C 4 /Z k singularity is given by a N = 6 supersymmetric two-level (k, −k) CS theory for gauge group U(N) × U(N) with SU(2) A × SU(2) B invariant matter in the bifundamental representation [2].…”

Observables in the Guarino-Jafferis-Varela/CS-SYM duality

“…The magnetic coupling constant m is identified with the Romans mass F 0 . In fact, this solution has fixed points that uplift to N = 2 AdS 4 × SS 5 . Since the internal space has the topology of a sphere, we expect that this solution arises as the near…”

“…The theory is still superconformal, but has less supersymmetry, has an extra parameter k that forms a 't Hooft coupling λ = N/k, and has both the SYM term interesting for particle physics and a CS term at level k that as we will see can dominate the IR and imply a certain interesting level-rank duality. The theory arises as a deformation of the maximal N = 8 SU(N ) SYM (with adjoint fields) on the worldvolume of N D2-branes (see also [4]), and the resulting SCFT has been studied in [5].…”