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

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OutlineThe Klebanov-Polyakov-Sezgin-Sundell conjectures:HS gravity in AdS 4 ↔ 3d vector modelsVasiliev’s higher spin gauge theory in 4dthe “Type A” and “Type B” modelsParity violating modelsChern-Simons theory with vector fermion matterExact planar thermal free energy on R 2Higher spin symmetry at large N and conjectural AdS dualSummary and conclusionsBased on work with S. Minwalla, S. Prakash, S. Trivedi, S. Wadia, X. YinSimone Giombi (PI) Chern-Simons and higher spins Lebedev Inst., Jun 1 2012 2 / 24
Klebanov-Polyakov-Sezgin-Sundell (’02) conjecture:Vasiliev’s minimal bosonic HS gravity in AdS 4 is dual tofree or critical 3d O(N) vector model, in the O(N) singlet sector.S = 1 2∫d 3 x∂ µ φ i ∂ µ φ i ↔ “type A” HS gravity∫S =(∆, S) = (1, 0) + + ∑ s even(s + 1, s)d 3 xψ i γ µ ∂ µ ψ i ↔ “type B” HS gravity(∆, S) = (2, 0) − + ∑ s even(s + 1, s)Critical theories: interacting fixed points reached after perturbing these freetheories by quartic interaction. Correspond to change of boundary conditionon the bulk scalar field in the HS gravity side.Non-minimal versions (all integer spins): vector models with complex fieldsin U(N) singlet sector.Simone Giombi (PI) Chern-Simons and higher spins Lebedev Inst., Jun 1 2012 3 / 24
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Page 5 and 6: Klebanov-Polyakov-Sezgin-Sundell (
Page 7 and 8: The Vasiliev’s equationsdA + A
Page 9 and 10: Chern-Simons vector modelSG, S. Min
Page 11 and 12: Chern-Simons vector modelI will dis
Page 13 and 14: Exact fermion propagatorThe basic i
Page 15 and 16: Exact fermion propagatorEmploying t
Page 17 and 18: FNV 2 T 30.250.200.150.100.050.2 0.
Page 19 and 20: Higher spin symmetry at large NBut
Page 21 and 22: Comments on the holographic dualAt
Page 23 and 24: Comments on the holographic dualFro

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