Chern-Simons vector models and higher spins - Ginzburg ...

The Vasiliev’s equationsMaster fields:1. W (x|y, ȳ, z, ¯z) = W µ dx µ 1-form in space-time2. S(x|y, ȳ, z, ¯z) = S α dz α + S ˙α d¯z ˙α 1-form in (z, ¯z)-space3. B(x|y, ȳ, z, ¯z) scalarx µ : spacetime, y α , ȳ ˙α , z α , ¯z ˙α : twistor variables.Collecting W and S into the 1-form A = W µ dx µ + S α dz α + S ˙α d¯z ˙α ,Vasiliev’s equation can be written asdA + A ∗ A = V(B ∗ κ)dz 2 + ¯V(B ∗ ¯κ)d¯z 2dB + A ∗ B − B ∗ π(A) = 0Simone Giombi (PI) Chern-Simons and higher spins Lebedev Inst., Jun 1 2012 6 / 24