Non-Supersymmetric CS-Matter Theories with Known AdS Duals

Table 3

Bosonic KK spectrum of the SW theory at level 𝑚=2𝑛, with 𝑛≥1. The states with negative Dynkin labels should be excluded. In the case 𝑛=1 some of the fields are absent, reflecting the fact that the original 𝑆⁷ multiplet is shorter.

Spin	𝑆𝑈(4)	Δ
2^+	[𝑛−1,0,𝑛−1]	𝑛+2
1^−(1)	[𝑛−1,0,𝑛−1]+[𝑛,0,𝑛]+[𝑛,1,𝑛−2]+[𝑛−2,1,𝑛]	𝑛+1
1^+	[𝑛−1,0,𝑛−1]+[𝑛−1,0,𝑛−1]+[𝑛+1,0,𝑛−3]+[𝑛−3,0,𝑛+1]+[𝑛,1,𝑛−2]+[𝑛−2,1,𝑛]+[𝑛−1,1,𝑛−3]+[𝑛−3,1,𝑛−1]+[𝑛−2,2,𝑛−2]	𝑛+2
1^−(2)	[𝑛−1,0,𝑛−1]+[𝑛−2,0,𝑛−2]+[𝑛−1,1,𝑛−3]+[𝑛−3,1,𝑛−1]	𝑛+3
0^+(1)	[𝑛,0,𝑛]	𝑛
0^−(1)	[𝑛−1,0,𝑛−1]+[𝑛+1,0,𝑛−3]+[𝑛−3,0,𝑛+1]+[𝑛,1,𝑛−2]+[𝑛−2,1,𝑛]+[𝑛−1,2,𝑛−1]	𝑛+1
0^+(2)	[𝑛−1,0,𝑛−1]+[𝑛,0,𝑛]+[𝑛−2,0,𝑛−2]+[𝑛,1,𝑛−2]+[𝑛−2,1,𝑛]+[𝑛−1,1,𝑛−3]+[𝑛−3,1,𝑛−1]+[𝑛−2,2,𝑛−2]+[𝑛,2,𝑛−4]+[𝑛−4,2,𝑛]	𝑛+2
0^−(2)	[𝑛−1,0,𝑛−1]+[𝑛+1,0,𝑛−3]+[𝑛−3,0,𝑛+1]+[𝑛−1,1,𝑛−3]+[𝑛−3,1,𝑛−1]+[𝑛−3,2,𝑛−3]	𝑛+3
0^+(3)	[𝑛−2,0,𝑛−2]	𝑛+4