CFT Zoo

Differences

This shows you the differences between two versions of the page.

Link to this comparison view

Both sides previous revision Previous revision
Next revision 		Previous revision
tag:superconformal [2021/04/06 22:55]
Brian McPeak 		tag:superconformal [2021/04/10 06:23] (current)
Scott Lawrence [Superconformal field theories]
Line 1: Line 1:
 ====== 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 $d > 6$.
Line 20: Line 20:
 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 \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  \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   \,     \\
 % %
 d = 6: & \qquad \mathfrak{osp}(6,2| \mathcal{N}) \ \supset \      \mathfrak{so}(6,2) \times  \mathfrak{su}(2 \mathcal{N})_R      d = 6: & \qquad \mathfrak{osp}(6,2| \mathcal{N}) \ \supset \      \mathfrak{so}(6,2) \times  \mathfrak{su}(2 \mathcal{N})_R     
Last modified: 2021/04/06 22:55
CC Attribution-Noncommercial-Share Alike 4.0 International Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Noncommercial-Share Alike 4.0 International