Scherk-Schwarz SUSY breaking Scherk-Schwarz SUSY breaking frfrom the viewpoint ofom the viewpoint of 5D conformal supergravity5D conformal supergravity

Yutaka Sakamura 　 (Osaka Univ.) in collaboration with Hiroyuki Abe (YITP)

JHEP0602 (2006) 014 (hep-th/051 ２３２６ )

8/29/2006@SI06

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

Conformal SUGRA (off-shell formulation of SUGRA)useful and powerful to describe the SUGRA action with boundaries

In conformal SUGRA, various properties of SS mechanism can be easily understood.

SS twist in 5D SUGRA

5D SUGRA on with the radiusIt has symmetry. Orbifold b.c. : We choose as Twisting b.c. for

Consistency condition:

This requires 　　　　　　　　　 .

5D conformal supergravity Symmetries:

Field content: Weyl multiplet: Hypermultiplet:

Vector multiplet:

（ Kugo & Ohashi ）

compensatorPhysical fields

Superconformal gauge fixing Extra symmetries: Ordinary gauge fixing conditions

Combining and gauge fixings,

We will modify this as

while the physical fields remain periodic.

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, …)

SUSY breaking terms:

All SUSY terms are proportional to .

gravitino gaugino

hyperscalar

Singular gauge fixingWe take a gauge fixing parameter as

Namely,

Thus becomes boundary terms.

SS twist

⇔ Boundary Constant superpotential

provided that .

SS SUSY breaking is spontaneous.

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 .

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.

-even case:Boundary tension terms come from

Then,

SUSY condition:

Randall-Sundrum condition:

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.

Future works The case that both SS twist and bounda

ry constant superpotentials exist (model of Altendorfer,Bagger,Nemeschansky?)

Extension to two-compensator case(e.g. effective theory of heterotic M theory)

In the flat case, SS twist ⇔ b.d. constant superpotential

Is it possible to restore SUSY by tuning ?

The answer is NO. SS twist does not lead to the b.d. tensions.

Relation to the ABN model is still an open question.