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Radius stabilization in 5D SUGRA models on orbifold

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)

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Radius stabilization in 5D SUGRA models on orbifold

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  1. 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

  2. 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)

  3. 1 • 5D SUGRA on S /Z : • the simplest setup for extra-dimensional model • e.g., • SUSY Randall-Sundrum model • 5Deffective theory of the heterotic M theory 2 Gherghetta & Pomarol, NPB586 (2000) 141; Falkowski et.al, PLB491 (2000) 172; Altendorfer et.al, PRD63 (2001) 125025. (compactified on 6D Calabi-Yau manifold) Horava & Witten, NPB460 (1996) 506; Lukas et.al, PRD59 (1999) 086001

  4. Spacetime

  5. Background metric: Randall-Sundrum model 5D effective theory of the heterotic M theory These backgrounds are realized in the 5D gauged SUGRA.

  6. 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) S: Z -even x: Z -odd 2 (N=1 chiral multiplets) 2 In 5D heterotic M theory, Re S: Calabi-Yau volume

  7. We consider the following gaugings (by the graviphoton). • a-gauging • b-gauging (Falkowski, Lalak, Pokorski, PLB491 (2000) 172) 5D heterotic M theory SUSY RS model

  8. The radius R must be stabilized at some finite value. No boundary terms Radius R is undetermined (at tree level) We introduce the boundary superpotentials. In the RS background, Rcan be stabilized by (Maru & Okada, PRD70 (2004) 025002) W= (constant)+(linear term for S) at y=0, pR. Thus we consider this type of boundary superpotentials. We analyze the scalar potential in the 4D effective theory.

  9. Derivation of 4D effective theory Paccetti Correia, Schmidt, Tavartkiladze, NPB751 (2006) 222; Abe & Sakamura, PRD75 (2007) 025018 N=1 superfield description of off-shell 5D SUGRA action keeping N=1 off-shell structure Integrating out Z -odd superfields & Dimensional reduction 2 N=1 superfield description of off-shell 4D SUGRA action Physical fields:( S, T ) + (4D gravitational multiplet) radion multiplet By this method, we obtain

  10. Scalar potential SUSY condition SUSY point is a stationary point of V, but not always a local minimum.

  11. a-gauging For simplicity, we assume that

  12. SUSY condition: SUSY point This is a saddle point. non-SUSY point This is a local minimum.

  13. b-gauging (SUSY RS model) (warp factor superfield) Here we assume that

  14. SUSY point This is a local minimum. (Maru & Okada, PRD70 (2004) 025002) non-SUSY point This is a saddle point.

  15. (a,b)-gauging incomplete gamma function

  16. Stationary points local minimum ln|W| saddle point 0 SUSY SUSY 0 ln(ReS)

  17. Stationary points local minimum ln|W| saddle point 0 SUSY SUSY 0 ln(ReS)

  18. Stationary points local minimum ln|W| saddle point 0 SUSY SUSY 0 ln(ReS)

  19. Stationary points local minimum ln|W| saddle point 0 SUSY 0 ln(ReS)

  20. Stationary points local minimum ln|W| saddle point 0 SUSY SUSY 0 ln(ReS)

  21. Stationary points local minimum ln|W| saddle point 0 SUSY SUSY 0 ln(ReS)

  22. gauging vacuum pure b SUSY Minkowski b > a SUSY AdS b < a SUSY AdS 4 4

  23. Comment 1 SUSY mass at boundaries So far, we consider W= (constant)+(linear term for S) at boundaries. mass terms inWmay change a saddle point to a local minimum.

  24. Comment 2 Uplift of AdS vacuum Assume SUSY sector that decouples from (S,T). ( K.Choi, arXiv:0705.3330) Total potential: For b > a , by fine-tuning z , V SUSY Minkowski V SUSY AdS total 4

  25. Summary • Radius stabilization in 5D gauged SUGRA with the universal hypermultiplet. • Boundary superpotential:W= (constant)+(linear term for S) at y=0, pR. gauging vacuum pure b SUSY Minkowski b > a SUSY AdS b < a SUSY AdS 4 4

  26. Future Plan • More general superpotential at boundaries • Gauging other isometries(e.g., SUSY bulk mass) • SUSY spectrum after uplifting AdS vacuum

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