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Gauged Supergravities in Different Frames

Explore the embedding tensor formulation of D=4 gauged supergravities and the relevance of symplectic frames in unveiling new N=8 SUGRAs with local SO(8) symmetry. Understand mass deformations and scalar potential for moduli stabilization in different vacua. Learn about the role of symplectic frames in defining global symmetries and gauge connections in string/M-theory compactifications.

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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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