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Gauged Supergravities in Different Frames

Gauged Supergravities in Different Frames. Dr. Mario Trigiante (Politecnico di Torino). F.Cordaro, P.Frè, L.Gualtieri, P.Termonia, M.T. 9804056 Wit, Samtleben, M.T. 0311224 ; Dall’Agata, Inverso, M.T. 1209.0760. Plan of the Talk.

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Gauged Supergravities in Different Frames

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  1. Gauged Supergravities in Different Frames Dr. Mario Trigiante (Politecnico di Torino) F.Cordaro, P.Frè, L.Gualtieri, P.Termonia, M.T. 9804056 Wit, Samtleben, M.T. 0311224; Dall’Agata, Inverso, M.T. 1209.0760

  2. Plan of the Talk • Overview and Motivations: Gauged Supergravity and string/M-theory compactifications. • Embedding tensor formulation of D=4 gauged SUGRAs and duality • Relevance of symplectic frames: New N=8 SUGRAs with SO(8) local symmetry • Conclusions

  3. D=4 ungauged Supergravity M1,3 x MRicci flat Flux = 0 Global symmetries Dualities Superstring M-theory • Minimal coupl. • mass. def. • V(f) D=4 gauged Supergravity M1,3 x M Flux ¹ 0 Embedding tensor • Mass deformations: spontaneous SUSY breaking • Scalar potential: moduli stabilization in Minkoswki, dS or AdS vacua Introduction • D=4 Supergravity from Superstring/M-theory:

  4. Scalar fields (described by a non-lin. Sigma-model) are non-minimally coupled to the vector ones Linear action g¢ A B g = 2 G C D s E/M duality promotes G to global sym. of f.eqs. E B. ids. Fmn Fmn Gmn Gmn • Smaller symmetry of the action: Ungauged (extended) Supergravities • Electric-magnetic duality symmetry of Maxwell equations now must also involve the scalar fields (Gaillard-Zumino) Non-linear action onf G = Isom(Mscal) Sp(2 nv, R)

  5. Coupling of scalar fields to vectors is fixed up to a symplectic transfomation on F and G (Symplectic Frame) The Issue of Symplectic Frames • Different symplectic frames (SF) may yield inequivalent actions with different global symmetry groups Ge but same physics • In the SUGRA description of string/M-theory compactifications, SF fixed by the resulting scalar-vector couplings

  6. Split total scalars so that: isometry • is an invariance of the theory • is realized on the vector fields and their magnetic duals by an anti-symplectic duality transformation Parity as an anti-Symplectic Duality • Distinction between the scalar/pseudo-scalar fields depends • on the choice of the symplectic frame

  7. Local invariance w.r.t. G • Description of gauging which is independent of the SF: E symplectic 2nv x 2nv matrix • All information about • the gauging encoded • in a G-tensor: • the embedding tensor [Cordaro, Frè, Gualtieri, Termonia, M.T. 9804056; Nicolai, Samtleben 0010076; de Wit, Samtleben, M.T. 0311224 ] Gauging • Gauging consists in promoting a group G ½ Ge½G from global tolocal • symmetry of the action. Different SF ) different choices for G.

  8. Restore SUSY of the action: Fermion shifts: Mass terms: Scalar potential: Linear: Closure: Locality • String/M-theory • origin: [D’Auria, Gargiulo, Ferrara, M.T., Vaulà 0303049; Angelantonj, Ferrara, M.T. 0306185; de Wit, Samtleben, M.T. 0311224…] • Emb. tensor from E11 and tensor hiearachies [de Wit, Samtleben 0501243; Riccioni, West 0705.0752; de Wit, Nicolai, Samtleben, 0801.1294] • Manifestly G-covariant formulation de Wit, Samtleben, M.T. 0507289

  9. (1) g (8) A  (28) AAB (56) ABC (70)ABCD gravitational Mscal = = N=8, D=4 SUGRA 32 supercharges A,B28 of SU(8)R • Scalar fields in non-linear -model with target space

  10. Gaugings defined by Linear constraints Quad. constraints • First gauging: [de Wit, Nicolai ’82] • Looking for SO(8): Original dWN gauging Hull’s CSO(p,q,r)-gaugings Same groups gauged by the magnetic vectors

  11. Take generic • Quadratic constraints • Gauge connection: • Features of E: it centralizes so(8) in Sp(56)and is NOT in E7(7) for • generic angle: but not in SU(28) for generic w Choice corresponds to an SO(8)-gauging in a different SF in which A’IJ are electric

  12. Scalar potential: where and de Wit, Samtleben, M.T. 0705.2101 • Studied vacua with a G2 residual symmetry: suffices to restrict to • G2singlets • w analogue of de Roo-Wagemann’s angle in N=4, N=2: parametrizes • inequivalent theories. • Vacua of original dWN theory (w=0) studied by Warner and recently by • Fischbacher (found several critical points, not complete yet)

  13. Dall’Agata, Inverso, M.T. 1209.0760 Borghese, Guarino, Roest, 1209.3003

  14. Discrete symmetries of Veff: originate from non trivial symmetries of the whole theory (Parity) (SO(8) Triality) • Inequivalent theories only for • Possible relation to compactifiation of D=11 SUGRA on • with torsion (w) (ABJ) [Aharony, Bergman, Jafferis, 0807.4924] • w does not affect action terms up to second order in the fluctuations about • the N=8 vacuum (mass spectrum).

  15. Conclusions • Showed in a given example how initial choice of SF determines, after gauging, physical properties of the model • Study vacua of the new family of SO(8)-gauged maximal SUGRAS • RG flow from new N=0 G2 vacuum to N=8 SO(8) one (both stable AdS4)

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