1. Gauging Supergravity in Three Dimensions Eric Bergshoeff based on collaborations with M. de Roo, O. Hohm, D. Roest, H. Samtleben and E. Sezgin Vienna, April 16 2009 University of Groningen

2. From SUGRA to (conformal) SUSY Brane physics: supersymmetry in p+1 dimensions Multiple D2-branes: supersymmetric Yang-Mills Multiple M2 branes : conformal SUSY in D=3 dimensions Bagger, Lambert; Gustavsson (2008) Why CFT in Three Dimensions? de Roo, Hohm, Roest + E.B.

3. What is known about ? New superconformal gaugings (BLG) and (ABJM) Massive deformations Gomis, Salim, Passerini; Hosomichi, Lee, Lee Non-conformal gaugings (or Lorentzian 3-algebras) Gomis, Milanesi, Russo;Benvenuti, Rodriguez-Gomez, Tonni, Verlinde; Ho, Imamura, Matsuo; Bandres, Lipstein, Schwarz; Cecotti, Sen

4. Gauged Supergravity in Three Dimensions Nicolai, Samtleben (2001); de Wit, Herger, Samtleben (2003)

5. The Embedding Tensor The embedding tensor determines which subgroup is gauged and which gauge vectors are used Nicolai, Samtleben (2001), Schwarz (2004) Puzzle: no vectors left for (conformal) gauging! Resolution: add YM CS action duality relations Nicolai, Samtleben (2001)

6. Non-Abelian Duality Nicolai, Samtleben; de Wit, Herger, Samtleben

7. Constraints The embedding tensor satisfies linear and quadratic constraints due to supersymmetry and gauge invariance

8. Linear Constraints

9. The Global Limit

10. Three types of Gaugings

11. Conformal Gaugings

12. Solving the Constraints via SUSY In this way the D=3 superconformal gaugings can be classified The linear constraints can be solved by mapping the problem to the classification of Lie superalgebras Gaiotto, Witten; Hosomichi, Lee, Park The quadratic constraints are solved by using invariant tensors

13. Superconformal Gaugings BLG ABJM Hohm, Roest, Samtleben, Sezgin + E.B.

14. Non-conformal Gaugings Gomis, Milanesi, Russo;Benvenuti, Rodriguez-Gomez, Tonni, Verlinde; Ho, Imamura, Matsuo; Bandres, Lipstein, Schwarz; Cecotti, Sen Equivalent to wrong-sign kinetic terms (Lorentzian 3-algebras)

15. Massive Deformations SUSY algebra can have non-central terms (in D=3 only) Nahm (1978) Puzzle: D=3 scalar multiplet with half-maximal supersymmetry? Gomis, Salim, Passerini; Hosomichi, Lee, Lee

16. Non-central Charges

18. Supermultiplets

19. A Realization As mass spectrum of bosonic and fermionic fluctuations around Minkowski vacuum of maximal gauged supergravity with gauge group Fischbacher, Nicolai, Samtleben (2002) Hohm, E.B.

20. Summary non-trivial worldvolume/target space when gauging isometries of hypercomplex/hyper-K ähler manifold Cecotti, Samtleben, Sezgin + E.B., in preparation Only massive deformations, no interacting gauge theories new superconformal CS gaugings

21. Open Questions Are there more general gaugings in BLG model ? What about massive sugra ? What about multiple M5-branes ?