Radius stabilization in 5D SUGRA models on orbifold

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Radius stabilization in Radius stabilization in 5D SUGRA 5D SUGRA models on orbifold models on orbifold Yutaka Sakamura (Osaka Uni v.) in collaboration with Hiroyuki A be (YITP) arXiv:0708.xxxx July 31, 2007@SUSY07

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Radius stabilization in 5D SUGRA models on orbifold. Yutaka Sakamura (Osaka Univ.) in collaboration with Hiroyuki Abe (YITP) arXiv:0708.xxxx July 31, 2007@SUSY07. Introduction. Models with extra dimensions: Randall-Sundrum model hierarchy (Randall & Sundrum, 1999) - PowerPoint PPT Presentation

Transcript of Radius stabilization in 5D SUGRA models on orbifold

Page 1: Radius stabilization in 5D SUGRA  models on orbifold

Radius stabilization in 5D SUGRA Radius stabilization in 5D SUGRA

models on orbifold models on orbifold

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

arXiv:0708.xxxx

July 31, 2007@SUSY07

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Introduction

Models with extra dimensions:• Randall-Sundrum model hierarchy (Randall & Sundrum, 1999)

• Split fermions Yukawa hierarchy (Arkani-Hamed & Schmaltz, 2000) • Gauge symmetry breaking by B.C. (Kawamura, 2000; Csaki, et.al, 2003,…)

• SUSY breaking by B.C. (Scherk-Schwarz, 1979)

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5D SUGRA on S /Z : the simplest setup for extra-dimensional modele.g.,• SUSY Randall-Sundrum model

• 5D effective theory of the heterotic M theory

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Gherghetta & Pomarol, NPB586 (2000) 141; Falkowski et.al, PLB491 (2000) 172; Altendorfer et.al, PRD63 (2001) 125025.

Horava & Witten, NPB460 (1996) 506; Lukas et.al, PRD59 (1999) 086001

(compactified on 6D Calabi-Yau manifold)

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Spacetime

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Randall-Sundrum model

5D effective theory of the heterotic M theory

These backgrounds are realized in the 5D gauged SUGRA.

Background metric:

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We introduce a hypermultiplet whose manifold is SU(2,1)/U(2). (the “universal hypermultiplet’’ in 5D heterotic M theory)

We obtain both RS model & 5D heterotic M theory by gauging different isometries.

Isometry group: SU(2,1)

In 5D heterotic M theory, Re S: Calabi-Yau volume

S: Z -even: Z -odd

2

2(N=1 chiral multiplets)

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We consider the following gaugings (by the graviphoton). • -gauging

• -gauging

5D heterotic M theory

SUSY RS model

(Falkowski, Lalak, Pokorski, PLB491 (2000) 172)

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No boundary terms Radius R is undetermined (at tree level)

We introduce the boundary superpotentials.

In the RS background, R can be stabilized by(Maru & Okada, PRD70 (2004) 025002)

W= (constant)+(linear term for S) at y=0, R. Thus we consider this type of boundary superpotentials.

The radius R must be stabilized at some finite value.

We analyze the scalar potential in the 4D effective theory.

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Derivation of 4D effective theoryPaccetti Correia, Schmidt, Tavartkiladze, NPB751 (2006) 222; Abe & Sakamura, PRD75 (2007) 025018

N=1 superfield description of off-shell 5D SUGRA action

N=1 superfield description of off-shell 4D SUGRA action

Integrating out Z -odd superfields& Dimensional reduction

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Physical fields: ( S, T ) + (4D gravitational multiplet)

radion multiplet

By this method, we obtain

keeping N=1off-shell structure

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Scalar potential

SUSY condition

SUSY point is a stationary point of V, but not always a local minimum.

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-gauging

For simplicity, we assume that

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SUSY condition:

SUSY point

non-SUSY point

This is a saddle point.

This is a local minimum.

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-gauging(SUSY RS model)

Here we assume that

(warp factor superfield)

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SUSY point

non-SUSY point

This is a local minimum.

This is a saddle point.

(Maru & Okada, PRD70 (2004) 025002)

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()-gauging

incomplete gamma function

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ln(ReS)

ln|

0

0

Stationary points

SUSY

SUSY

local minimum

saddle point

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ln(ReS)

ln|

0

0

Stationary points

SUSY

SUSY

local minimum

saddle point

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ln(ReS)

ln|

0

0

Stationary points

SUSYSUSY

local minimum

saddle point

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ln(ReS)

ln|

0

0

Stationary points

SUSY

local minimum

saddle point

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ln(ReS)

ln|

0

0

Stationary points

SUSY

SUSY

local minimum

saddle point

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ln(ReS)

ln|

0

0

Stationary points

SUSY

SUSY

local minimum

saddle point

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gauging vacuum

pure SUSY Minkowski

> SUSY AdS

< SUSY AdS4

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mass terms in W may change a saddle point to a local minimum.

So far, we consider

SUSY mass at boundariesComment 1

W= (constant)+(linear term for S) at boundaries.

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Uplift of AdS vacuum

SUSY AdS SUSY Minkowski

For > , by fine-tuning ,

Assume SUSY sector that decouples from (S,T).

Total potential:

4V Vtotal

Comment 2

( K.Choi, arXiv:0705.3330)

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Summary

• Radius stabilization in 5D gauged SUGRA with the universal hypermultiplet.

• Boundary superpotential:W= (constant)+(linear term for S) at y=0, R.

gauging vacuum pure SUSY Minkowski > SUSY AdS< SUSY AdS4

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Future Plan

• More general superpotential at boundaries

• Gauging other isometries(e.g., SUSY bulk mass)

• SUSY spectrum after uplifting AdS vacuum