Download - 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. 9804056F.Cordaro, P.Frè, L.Gualtieri, P.Termonia, M.T. 9804056
Wit, Samtleben, M.T. 0311224Wit, Samtleben, M.T. 0311224; Dall’Agata, Inverso, M.T. 1209.0760Dall’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
• Conclusions
• Relevance of symplectic frames: New N=8 SUGRAs with SO(8) local symmetry
Introduction
• D=4 Supergravity from Superstring/M-theory:
SuperstringM-theory
M1,3 x MRicci flat
Flux = 0
D=4 ungaugedSupergravity
Global symmetriesDualities
•Minimal coupl.•mass. def.•V()
D=4 gaugedSupergravity
M1,3 x M
Flux 0
Embedding tensor
• Mass deformations: spontaneous SUSY breaking
•Scalar potential: moduli stabilization in Minkoswki, dS or AdS vacua
Ungauged (extended) Supergravities
• Electric-magnetic duality symmetry of Maxwell equations now must also involve the scalar fields (Gaillard-Zumino)
G = Isom(Mscal)Non-linear action on
Linear actionF
G
g¢F
G
Sp(2 nv, R) E/M duality promotes
G to global sym. of f.eqs. E B. ids.
g = 2 G A B
C D• Smaller symmetry of the action:
• Scalar fields (described by a non-lin. Sigma-model) are non-minimally coupled to the vector ones
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
• Coupling of scalar fields to vectors is fixed up to a symplectic transfomation on F and G (Symplectic FrameSymplectic Frame)
Parity as an anti-Symplectic Duality
• 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
• 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 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 ]
• Restore SUSY of the action:
Mass terms:
Scalar potential:
Fermion shifts:
Closure:
Locality
Linear:
• String/M-theory origin:
[D’Auria, Gargiulo, Ferrara, M.T., Vaulà 0303049; Angelantonj, Ferrara, M.T. 0306185; de Wit, Samtleben, M.T. 0311224…]
• Manifestly G-covariant formulation de Wit, Samtleben, M.T. 0507289
• Emb. tensor from E11 and tensor hiearachies [de Wit, Samtleben 0501243; Riccioni, West 0705.0752; de Wit, Nicolai, Samtleben, 0801.1294]
N=8, D=4 SUGRA
• Scalar fields in non-linear -model with target space
(1) g
A
(28) AAB
ABC
ABCD
gravitational
A,B 2 8 of SU(8)R
Mscal = =
32 supercharges
Linear constraints
Quad. constraints
• Looking for SO(8):
• First gauging:[de Wit, Nicolai ’82]
Original dWN gauging
Hull’s CSO(p,q,r)-gaugings
Same groups gauged by the magnetic vectors
Gaugings defined by
• 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 E7(7) for generic angle:
but not in SU(28) for generic
• analogue of de Roo-Wagemann’s angle in N=4, N=2: parametrizes inequivalent theories.
• Vacua of original dWN theory =0studied by Warner and recently by Fischbacher (found several critical points, not complete yet)
• Studied vacua with a G2 residual symmetry: suffices to restrict to G2 singlets
• Scalar potential:
where and de Wit, Samtleben, M.T. 0705.2101
Dall’Agata, Inverso, M.T. 1209.0760Borghese, Guarino, Roest, 1209.3003
• Discrete symmetries of Veff:
(Parity) (SO(8) Triality)
originate from non trivial symmetries of the whole theory
• 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 () (ABJ) [Aharony, Bergman, Jafferis, 0807.4924]
• Inequivalent theories only for
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)