Gauged Supergravities in Different Frames Dr Mario Trigiante

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 • 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

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

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

The Issue of Symplectic Frames • Coupling of scalar fields to vectors is fixed up to a symplectic transfomation on F and G (Symplectic Frame) Frame • 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

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

Gauging • Gauging consists in promoting a group G ½ Ge ½ G from global to local symmetry of the action. Different SF ) different choices for G. • Local invariance w. r. t. G • Description of gauging which is independent of the SF: E symplectic 2 nv x 2 nv 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 ]

• Restore SUSY of the action: Fermion shifts: Mass terms: Scalar potential: Linear : Closure: Locality • Manifestly G-covariant formulation de Wit, Samtleben, M. T. 0507289 • 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 E 11 and tensor hiearachies [de Wit, Samtleben 0501243; Riccioni, West 0705. 0752; de Wit, Nicolai, Samtleben, 0801. 1294]

N=8, D=4 SUGRA (1) g 32 supercharges (8) A (28) AAB A, B 2 (56) ABC (70) ABCD gravitational • Scalar fields in non-linear -model with target space Mscal = = 8 of SU(8)R

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

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

• w analogue of de Roo-Wagemann’s angle in N=4, N=2: parametrizes inequivalent theories. • Scalar potential: where and de Wit, Samtleben, M. T. 0705. 2101 • Vacua of original d. WN theory (w=0) studied by Warner and recently by Fischbacher (found several critical points, not complete yet) • Studied vacua with a G 2 residual symmetry: suffices to restrict to G 2 singlets

Dall’Agata, Inverso, M. T. 1209. 0760 Borghese, Guarino, Roest, 1209. 3003

• Discrete symmetries of Veff: originate from non trivial symmetries of the whole theory (Parity) (SO(8) Triality) • Inequivalent theories only for • w does not affect action terms up to second order in the fluctuations about the N=8 vacuum (mass spectrum). • Possible relation to compactifiation of D=11 SUGRA on with torsion (w) (ABJ) [Aharony, Bergman, Jafferis, 0807. 4924]

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 G 2 vacuum to N=8 SO(8) one (both stable Ad. S 4)