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Gauging Supergravity in Three Dimensions

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

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Gauging Supergravity in Three Dimensions

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

  2. From SUGRA to (conformal) SUSY de Roo, Hohm, Roest + E.B. Why CFT in Three Dimensions? 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)

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

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

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

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

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

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

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

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

  16. Non-central Charges

  17. Non-central Charges

  18. Supermultiplets

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

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

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

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