Coset construction of Tricritical Ising CFT

Question

In http://iopscience.iop.org/1742-5468/2008/03/P03010 the authors state that the Tricritical Ising Model (TIM) CFT can be obtained from a Wess Zumino Witten construction based in the coset $\frac{(E_7)_1\otimes(E_7)_1}{(E_7)_2}$, where $(E_7)_k$ is the exceptional Lie algebra $E_7$ at level $k$.

My question is: Is there another coset construction of TIM CFT that does not use an exceptional Lie algebra?

This post imported from StackExchange Physics at 2015-03-25 13:19 (UTC), posted by SE-user Raul Santos

Answer 1

Tricritical Ising model belongs to the family of minimal models ($M(5,4)$). There are several different coset constructions that represent them, one of them is the following:

$M(m+1,m)=SU(2)_{m-2} \times SU(2)_1/SU(2)_{m-1}$

This post imported from StackExchange Physics at 2015-03-25 13:19 (UTC), posted by SE-user Meng Cheng

Comments

Thanks a lot, that is very helpful!

This post imported from StackExchange Physics at 2015-03-25 13:19 (UTC), posted by SE-user Raul Santos