Gauging Supergravity in Three Dimensions
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Transcript of Gauging Supergravity in Three Dimensions
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
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.
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
Gauged Supergravity in Three Dimensions
Nicolai, Samtleben (2001); de Wit, Herger, Samtleben (2003)
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)
Non-Abelian Duality Nicolai, Samtleben; de Wit, Herger, Samtleben
Constraints
The embedding tensor satisfies linear and quadratic
constraints due to supersymmetry and gauge invariance
Linear Constraints
The Global Limit
Three types of Gaugings
Conformal Gaugings
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
Superconformal Gaugings
BLG
ABJM
Hohm, Roest, Samtleben, Sezgin + E.B.
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)
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
Non-central Charges
Non-central Charges
Supermultiplets
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.
Summary
non-trivial worldvolume/target space when
gauging isometries of hypercomplex/hyper-Kähler manifoldCecotti, Samtleben, Sezgin + E.B., in preparation
Only massive deformations,
no interacting gauge theories
new superconformal CS gaugings
Open Questions
Are there more general gaugings in BLG model ?
What about massive sugra ?
What about multiple M5-branes ?