A non-linear representation of the d=2 so (4)-extended superconformal algebra

Abstract

We present a non-linear representation of the so(4)-extended d=2 superconformal algebra in terms of one boson and four Majorana fermions. The matter fields and the currents can be grouped into a single N= 4 superfield. Breaking the supersymmetry to N= 3 or N= 2 leads to new representations of the N= 3,2 superconformal algebras.

$$ \mathcal{N}=\left(3,3\right) $$ holography on AdS3 × (S3 × S3 × S1)/ℤ2

“…Thus, we expect the theory to be 18 One can again show this directly by using a character argument as we did above for the untwisted sector.…”

“…The generators of the large N = 4 algebra can be realised in terms of the free fields 3 as presented in appendix A (see also [4,18]). …”

“…Thus, we also manifestly see that all massless states are in fact orbifold-invariant. 18 Now let us now determine the multiplicity of the twisted sector state. It turns out to be 2, as we now explain.…”

The operator product expansion between the 16 lowest higher spin currents in the $$\mathcal{N}=4$$ N = 4 superspace

“…, this central charge is a positive multiple of 3 and can be realized by one real scalar and four Majorana fermions [21]. Note that there is no twisted anomaly, where the spin-0 current (w) transforms as a primary field under the stress energy tensor L(z).…”

“…21 The fusion rule between the N = 2 higher spin-1 current and the N = 2 higher spin-2 current is given by 11) where the last term, which resides in the next 16 higher spin currents, has its component expressions in the first four equations of (4.2) with s = 2. Recall that the next higher N = 4 multiplet has four N = 2 higher spin currents denoted by T (2) …”