CFT Zoo

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minimal_models [2021/09/17 20:39]
Brian McPeak [Example: Critical Ising Model] 		minimal_models [2021/09/17 21:26] (current)
Brian McPeak [Example: Critical Ising Model]
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 Let's determine the level-two descendent which vanishes. This is the same as the primary of the  subrepresentation we mod out by, defined by Let's determine the level-two descendent which vanishes. This is the same as the primary of the  subrepresentation we mod out by, defined by
  
-$$ | \chi_{2,1} \rangle =  (a L_{-1}^2 + L_{-2} ) | \Delta_{2,1} \rangle \, .$$+$$ | \chi_{2,1} \rangle =  L_{2,1} | \Delta_{2,1} \rangle = (a L_{-1}^2 + L_{-2} ) | \Delta_{2,1} \rangle \, .$$
  
 This will be a primary if $L_1  | \chi_{2,1} \rangle = 0$ and if $L_2  | \chi_{2,1} \rangle = 0$.  Using the $c = 1/2$ Virasoro algebra, and solving these constraints, we find This will be a primary if $L_1  | \chi_{2,1} \rangle = 0$ and if $L_2  | \chi_{2,1} \rangle = 0$.  Using the $c = 1/2$ Virasoro algebra, and solving these constraints, we find
  
-$$ | \chi_{2,1} \rangle =  (-\frac{4}{3} L_{-1}^2 + L_{-2} ) | \Delta_{2,1} \rangle \, .$$+$$ L_{2,1} =  -\frac{4}{3} L_{-1}^2 + L_{-2}  \, .$$ 
 + 
 +Therefore the degenerate field $\sigma$ must satisfy 
 + 
 +$$ L_{2,1} \sigma(z) = 0 \, .$$ 
 + 
 +This equation will allow us to compute the four-point function 
 + 
 +(To Be Finished Later) 
 + 
 ====More Examples==== ====More Examples====
  
Last modified: 2021/09/17 20:39
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