SUPERSYMMETRICNON-LINEAR SIGMA MODEL

IN THE WARPED SPACE

Jingsheng LiJohns Hopkins University

Work with J. Bagger: arxiv: 1106.2343

May 8 2012 Pheno 2012 Symposium

2

Outlook

• Non-linear σ Model in Flat Extra Dimension

• Non-linear σ Model in Warped Extra Dimension

• Examples

• Summary

3

Flat Extra Dimension

4

Flat Extra Dimension (d=5)• Hypermultiplet

• Action

5

Flat Extra Dimension (d=5)

• Transformation

• Constraints

6

Warped Extra Dimension

7

• ε → Killing Spinor1

• New Scalar Potential V2

• New Constraints on X3

From Flat to Warped Space

8

5-d Anti-de Sitter• Metric

• Killing Spinor

9

5-d Anti-de Sitter• Hypermultiplet

• Action

10

5-d Anti-de Sitter• Transformation

• Constraints

11

• Pick up (M, g, Ω)1

• Solve X2

• Construct G, V3

Model Building Procedure

12

EXAMPLES

13

Flat HyperKahler Space• Flat Geometry

• Solve Constraints

• Determine Scalar Potential

14

Flat HyperKahler Space• “Massless” Case

Mass Spectrum

15

Flat HyperKahler Space• Massive Case

16

HyperKahler Cone•

• Solve Constraints

• If

17

Summary

• The Target Space of Non-linear Sigma Model in AdS5 is HyperKahler Manifold.

• Killing Vector X Satisfies Inhomogeneous Tri-holomophic Condition.

• Target Space Tri-holomorphic Isometries Can be Gauged.

• Ready For Phenomenological Study.

18

THANK YOU!