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Scherk-Schwarz twist in 5D conformal SUGRA

This paper explores the Scherk-Schwarz twist in 5D conformal supergravity (SUGRA) as a solution for the hierarchy problem. It discusses the necessity of SUSY breaking and the simplest case of 5D SUGRA with different boundary conditions for bosons and fermions. The concept of Scherk-Schwarz SUSY breaking and its relationship to boundary constant superpotentials are explained. The paper also discusses the gauging of the graviphoton and the consistency conditions required for twisted gauge fixings.

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Scherk-Schwarz twist in 5D conformal SUGRA

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  1. Scherk-Schwarz twist in 5D conformal SUGRA Yutaka Sakamura(Osaka Univ.) in collaboration with Hiroyuki Abe (YITP) JHEP0602 (2006) 014 (hep-th/051２３２６) 31 Oct. 2006@Honolulu

  2. Introduction SUSY: a solution of hierarchy problem • SUSY breaking is necessary • Scherk-Schwarz SUSY breaking: • the simplest case is 5D theory on or • different b.c. on bosons and fermions

  3. Conformal SUGRA(off-shell formulation of SUGRA)useful and powerful to describe the SUGRA action with boundariesIn conformal SUGRA, various properties of SS mechanism can be easily understood.

  4. SS twist in 5D SUGRA 5D SUGRA on with the radius It has symmetry. • Orbifold b.c. : We choose as • Twisting b.c. for

  5. Consistency condition: This requires .

  6. 5D conformal supergravity （Kugo & Ohashi） • Symmetries: • Field content: • Weyl multiplet: • Hypermultiplet: • Vector multiplet: compensator Physical fields

  7. Superconformal gauge fixing • Extra symmetries: • Ordinary gauge fixing conditions

  8. Combining and gauge fixings, We will modify this as while the physical fields remain periodic.

  9. gauge field on-shell is given by is shifted and This corresponds to the nonvanishing F-term of the radion superfield in the superfield formalism. (G.v. Gersdorff, M.Quiros, …)

  10. gravitino gaugino SUSY breaking terms: All SUSY terms are proportional to . hyperscalar

  11. Singular gauge fixing We take a gauge fixing parameter as

  12. Namely, Thus becomes boundary terms. SS twist ⇔ Boundary Constant superpotential provided that . SS SUSY breaking is spontaneous.

  13. SS twist and warped geometry SS twist yields an inconsistency on the warped geometry. (Hall,Nomura,Okui,Oliver (2004)) • Gauging of by graviphoton is necessary to realize geometry. • From , a graviphoton mass term appears, which is proportional to .

  14. Consistency condition: • Models of (Gherghetta,Pomarol;Falkowski,Lalak,Pokorski) gauging with odd couplingi.e., • Model of (Altendorfer,Bagger,Nemeschansky) gauging with even coupling i.e., SS twisting seems possible. But this model is not derived from known off-shell SUGRA.

  15. -even case: Boundary tension terms come from Then, • SUSY condition: • Randall-Sundrum condition:

  16. Summary From the viewpoint of 5D conformal SUGRA, • SS twisting for is understood as twisted gauge fixing. • SS twist ⇔ Boundary constant superpotential • SS twist in leads to massive graviphoton.

  17. Future works • The case that both SS twist and boundary constant superpotentials exist • Extension to two-compensator case(e.g. effective theory of heterotic M theory)

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