The super W∞ algebra

Abstract

We construct a higher-spin N = 2 superalgebra whose bosonic sector is W~o0)Wl+~. It can be realised in terms of bilinear currents involving free complex bosonic and fermionic fields. We also discuss the spectral flow, and various truncations.

Higher spins and Yangian symmetries

“…, N . The bilinear U(N ) singlets (where we take the ψ i to transform in the fundamental representation of U(N ), and theψ i in the anti-fundamental) generate the linear W 1+∞ algebra [30][31][32], see also [26]. Thus the Yangian generators should also be expressed in terms of such bilinears, and one finds that One can also check that the above generators give rise to the correct W -generators using our general identification between the W ∞ generators and the affine Yangian generators.…”

Partition functions of higher spin black holes and their CFT duals

“…A theory of D free complex fermions furnishes W 1+∞ symmetry with central charge c = D [39]. The W 1+∞ algebra has spins s = 1, 2, 3, .…”

“…According to [39] the relevant spin-3 current is, up to a normalization constant b that we will fix in a moment,…”

“…At λ = 0 the W ∞ [λ] algebra is related to the algebra W 1+∞ [38] by a constraint that removes the spin-1 current. Since the W 1+∞ algebra can be represented by free fermions [39], we can compute its partition function with the spin-1 constraint imposed. We then find precise agreement with (1.1) at λ = 0.…”

The higher spin rectangle

“…This is actually a result of bosonization of the freefermion representation of W 1+∞ [11,17,[30][31][32]. Similar to the previous case, the rest of the operators in eq.…”