The $$ \mathcal{N} $$ = 4 higher spin algebra for generic ? parameter

Higher Spin Symmetry and N = 4 SYM

We assemble the spectrum of single-trace operators in free N = 4 SU (N) SYM theory into irreducible representations of the Higher Spin symmetry algebra hs(2, 2|4). Higher Spin representations or YT-pletons are associated to Young tableaux (YT) corresponding to representations of the symmetric group compatible with the cyclicity of color traces. After turning on interactions g YM = 0, YT-pletons...

Exercises for Higher Algebra

(1) Let R be a division ring. Prove that every module over R is free. You will need to use Zorn’s lemma: Recall that a partially order set (=poset) S is a set with a relation x ≤ y defined between some pairs of elements x, y ∈ S, such that: (i) x ≤ x ; (ii) x ≤ y and y ≤ x implies x = y ; (iii) x ≤ y , y ≤ z ⇒ x ≤ z . A chain in S is a subset T ⊂ S such that for all t, t ′ in T , either t ≤ t ′...

The Dirac Algebra for Any Spin∗

Superspace Formulation of 4 D Higher Spin Gauge Theory

Interacting AdS4 higher spin gauge theories with N ≥ 1 supersymmetry so far have been formulated as constrained systems of differential forms living in a twistor extension of 4D spacetime. Here we formulate the minimal N = 1 theory in superspace, leaving the internal twistor space intact. Remarkably, the superspace constraints have the same form as those defining the theory in ordinary spacetim...

An Exact Solution of 4 D Higher - Spin Gauge Theory

We give a one-parameter family of exact solutions to four-dimensional higher-spin gauge theory invariant under a deformed higher-spin extension of SO(3, 1) and parameterized by a zeroform invariant. All higher-spin gauge fields vanish, while the metric interpolates between two asymptotically AdS4 regions via a dS3-foliated domainwall and two Robertson-Walker-like H3foliated spacetimes – one in ...