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 ?