Differences

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

--- superconformal_field_theory [2021/04/06 21:51]
Brian McPeak
+++ — (current)
@@ Line 1: / Line 1: @@
-==== Classification of superconformal algebras ====
-A classification of possible superconformal algebras was given by [[https://inspirehep.net/literature/120988|Nahm]] in 1977. The outline of the argument is as follows:
-  - Consider a superalgebra $L = g_0 \oplus g_1$, where $g_0$ and $g_1$ denote the even and odd part of the superalgebra, respectively
-  - Prove that $L$ must be simple
-  - The list of simple superalgebras is known. We select from the list the algebras satisfying (a) $g_0$ contains the conformal algebra $so(d, 2)$ and (b) $g_1$ transforms in a spinorial representation of the SC
-  - the result is the following classification: \begin{align}
-d = 3: & \qquad \mathfrak{osp}(\mathcal{N}|4) \\
-d = 4: & \qquad \mathfrak{su}(2,2| \mathcal{N})\\
-d = 5: & \qquad \\
-d = 6: & \qquad
- \end{align}
-In addition to assumptions (a) and (b), this result relies on a sort of unitarity assumption-- specifically, we must assume that there is a positive definite inner product on the algebra.

CFT Zoo