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Massimo Taronna

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Albert Einstein Institute (Berlin-Potsdam-Golm)

On HS symmetries, cubic interactions, AdS & CFT

based on arXiv:1311.0242 w. E.Joung and arXiv:1305.5180 w. N.Boulanger, D.Ponomarev, E.Skvortsov

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Desired Goals!

• Uncover the symmetries behind String Theory

• Shed light on holography and Quantum Gravity

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...topology matters!!

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History teaches us: Symmetry has always paid off!

HS Gravity!

Symmetry

What is the “maximal” symmetry of Quantum Gravity?

Fradkin & Vasiliev (‘80s): Higher-Spin Symmetry!

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too big symmetry => too simple theory...

Cons:

Pros: • Deformation (gauging) of symmetries (Algebroid, field

dependent structure constants)

• Almost all checks of AdS/CFT driven by symmetry (maximal symmetry => proof of Holography?)

To do List

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• HS systematics

• HS holography

• HS on non-trivial backgrounds (black-holes!)

• …

Some of this today

E.Joung and M.T. ‘13 6

Cubic Couplings Classification

Fradkin, Vasiliev ‘86; Konstein, Vasiliev ‘90; Maldacena, Zhiboedov 2011

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Coleman-Mandula in AdS/CFT!

AdS3/CFT2

Algebra: UIR

AdS4/CFT3 Moyal (unique)

Scalar & Spinor Singletons

AdS5/CFT4 One parameter family

(doubletons) Gunaydin et all; Boulanger, Skvortsov; Manvelyan, Mkrtcyan, Mkrtcyan, Theisen

AdS6+n/CFT5+n Scalar singleton

Boulanger, Ponomarev, Skvortsov, M.T. ‘13

Assumptions: symmetric tensors + one HS generator + no colour (+ Gravity)!

(Virasoro!!)

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Outlook • Admissibility will put further constraints

• Deformation (Lie Algebroids!)

• More general backgrounds (Black-Holes!)

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