CFT Zoo

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tag:superconformal [2021/04/06 22:56]
Brian McPeak 		tag:superconformal [2021/04/10 06:23] (current)
Scott Lawrence [Superconformal field theories]
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 ====== Superconformal field theories ====== ====== Superconformal field theories ======
  
-Superconformal field theories, or SCFTs, are theories whose spacetime symmetries include both the [[Conformal Group|conformal group]] and some amount of [[Supersymmetry|supersymmetry]].+Superconformal field theories, or SCFTs, are theories whose spacetime symmetries include both the [[:conformal invariance|conformal group]] and some amount of [[:Supersymmetry|supersymmetry]].
  
 It follows from the classification given below that there are no SCFTs in dimension $d > 6$. It follows from the classification given below that there are no SCFTs in dimension $d > 6$.
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 d = 3: & \qquad \mathfrak{osp}(\mathcal{N}|4) \ \supset \  \mathfrak{so}(3,2) \times  \mathfrak{so}(\mathcal{N})_R \, ,       \\ d = 3: & \qquad \mathfrak{osp}(\mathcal{N}|4) \ \supset \  \mathfrak{so}(3,2) \times  \mathfrak{so}(\mathcal{N})_R \, ,       \\
 % %
-d = 4: & \qquad \mathfrak{su}(2,2| \mathcal{N}) \ \supset \ \mathfrak{so}(4,2) \times  \mathfrak{su}(\mathcal{N})_R \times \mathfrak{u}(1)_R \, ,   \qquad \qquad    \mathcal{N} \neq 4  \\        & \qquad \mathfrak{psu}(2,2| 4) \ \supset \ \mathfrak{so}(4,2) \times  \mathfrak{su}(4)_R \, ,   \qquad \qquad \qquad  \qquad  \mathcal{N}  = 4\\+d = 4: & \qquad \mathfrak{su}(2,2| \mathcal{N}) \ \supset \ \mathfrak{so}(4,2) \times  \mathfrak{su}(\mathcal{N})_R \times \mathfrak{u}(1)_R \, ,  \  \, \qquad \qquad    \mathcal{N} \neq 4  \\  
 +& \qquad \mathfrak{psu}(2,2| 4) \ \supset \ \mathfrak{so}(4,2) \times  \mathfrak{su}(4)_R \, ,  \  \, \qquad \qquad \qquad  \qquad  \mathcal{N}  = 4\\
 % %
 d = 5: & \qquad \mathfrak{f}(4) \ \supset \   \mathfrak{so}(5,2) \times  \mathfrak{su}(2)_R \qquad \qquad \qquad  \qquad  \qquad \qquad \mathcal{N} = 1   \,     \\ d = 5: & \qquad \mathfrak{f}(4) \ \supset \   \mathfrak{so}(5,2) \times  \mathfrak{su}(2)_R \qquad \qquad \qquad  \qquad  \qquad \qquad \mathcal{N} = 1   \,     \\
Last modified: 2021/04/06 22:56
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