Dimensional Reduction of Eleven Dimensional Supergravity - PowerPoint Presentation

Slide1

Dimensional Reduction

of Eleven Dimensional Supergravity

on SU(2) Group Manifold

and N=4 Gauged Supergravity

Patharadanai Nuchino Dr. Parinya Karndumri

June 8, 2016 Room Anek, Baansuan-Khunta and Golf Resort Hotel, Ubon Ratchathani, Thailand

Department of Physics, Faculty of Science, Chulalongkorn University

Siam Physics Congress 2016

Introduction of Supergravity theory

Supergravity

= +

General relativity (gravity)

Supersymmetry

symmetry between

boson

and

fermion

graviton(Spin=2)

gravitino

(Spin=3/2)

Supergravity multiplet

The simplest case in 4D, N=1

Supergravity can be extend

Higher dimensional theory

with extra dimensions

D=11 is maximum

N>1 theory

with more fields

N=8 is maximum for 4D

2

Supercharge

http://jac_leon.perso.neuf.fr/gravitation/images/space-time.gif

3

Gauged Supergravity

= +

N>1 Supergravity

contentsVector (gauge) fields

Gauge symmetry

4D N=4

SO(4) gauged Supergravity multiplet

a graviton (Spin=2)

4 gravitinos (Spin=3/2)

6 gauge fields

(Spin=1)

2 scalar fields

(Spin=0)

4 spinor fields

(Spin=1/2)

Ex.

SO(4) gauge symmetry

equipped

4

Gauged Supergravity in AdS/CFT

http://quantum-bits.org/wp-content/uploads/2015/09/ads-cft.png

AdS/CFT correspondence

[1, 2, 3]the new duality relating Supergravities

anti-de Sitter (AdS) background

Superconformal field theories on the AdS boundary

in D dimensional

D-1 dimensions

Dimensional reduction

lower dimensional

gauged supergravity

admit AdS background

higher dimensional

ungauged

supergravity

Derivation are

important

Λ

<1

quantum

5

What is Dimensional

Reduction ?

Consideration

gives rise

with

gauge symmetry

corresponds

a gravitational theory

in D spacetime dimensions

with additional

scalar fields&

vector fields

a gravitational theory

in D+n spacetime dimensions

where n spatial dimensions are

compactified to be

a very small compact space

symmetry on compact space

http://

www.pbs.org/wgbh/nova/assets/img/full-size/imagining-other-dimensions-merl.jpg

http://

www.vcharkarn.com/uploads/17/17496.jpg

http://

www.diffusion.ens.fr/vip/images/10.11.jpg

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some

notable cases

gauged supergravity in 7D11 dimensional

supergravitygauged supergravity in 5D

IIB (10 dimensional)

supergravity

gauged supergravity in 4D

S

5

reduction

S

7

reduction

S

4

reduction

[7]

[8]

[5, 6]

reduction

on n-dimensional sphere (S

n

)

lower dimensional

gauged supergravity

admit AdS vacuum solutions

11D or IIB

(10D)

supergravity

[4]

7

Objective

11 dimensional

supergravity

N=4 SO(4) gauged supergravity in 4 dimensionsS

7 reduction

[10]

Study

the unique maximal-dimensional supergravity

(the most fundamental)

the half-maximal 4D supergravity

[9]

Conformal Field Theory

in 3 dimensional spacetime

AdS/CFT correspondence

the quantum field theory on 2 dimensional surface

now used for

study the superconductivity of 2D superconductor [11,12]

the compact space

S7 ~ R

× S3 × S3

from the fact that S3

is a group manifold of Lie group SU(2)

The reduction ansatze (expressions of higher dimensional fields in terms of lower dimensional fields)

8

Dimensional Reduction Procedure

11D

Supergravity

Equations of motion

N = 4 SO(4)

gauged supergravity

in 4 dimensions

Equations of motion

yield

Substitute

These two theory are

Consistent!

SU(2)

SU(2)

Consistent dimensional reduction

of

the eleven dimensional supergravity

giving rise to the N=4 gauged supergravity in 4 dimensions was obtainedThe two SU(2)s form SO(4) ~ SU(2) x SU(2) gauge group of the lower dimensional theory

9Conclusions

10

Application

11D

Supergravity

solutionsEquations of motion

N = 4 SO(4)

gauged supergravity in 4 dimensions

solutions

Equations of motion

Lift up

-> Lift lower dimensional solutions up to the 11 dimensional theory

Reduction ansatze

Consistent

satisfy

satisfy

Ex.

Lift up

[13]

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AdS Black Hole

M2

(2D membrane)

inversely

11

References

[1]

Maldacena

, J. 1998. “The large N limit of superconformal field theories and supergravity”. Advances in Theoretical and Mathematical Physics. 2: 231-252. [2] Gubser, S. S., Klebanov, I. R., and Polyakov, A. M. 1998. “Gauge theory correlators from noncritical string theory”. Physics Letters B. 428: 105-114.[3] Witten, E. 1998. “Anti-de Sitter space and holography”. Advances in Theoretical and Mathematical Physics

. 2: 253-291.[4] Cvetic, M., et al. 1999. “Embedding AdS Black Holes in Ten and Eleven Dimensions”. Nuclear Physics B

. 558: 96-126.[5] Nastase, H., Vaman, D., and Nieuwenhuizen

, P. V. 1999. “Consistent nonlinear KK reduction of 11d supergravity on AdS7×S4 and self-duality in odd dimensions”. Physics Letters B

. 469: 96-102.[6] Nastase, H., Vaman, D., and Nieuwenhuizen, P. V. 2000. “Consistent of the AdS

7×S4 reduction and the origin of self-duality in odd dimensions”. Nuclear Physics B. 581: 179-239.

[7] De Witt, B. and Nicolai, H. 1987. “The consistency of the S7 truncation in D=11 supergravity”. Nuclear Physics B. 281: 211-240.

[8] Baguet, A., Hohm, O., and Samtleben, H. 2015. “Consistency type IIB reductions to maximal 5D supergravity”.

Physical Review D

. 92: 065004.

[9]

Cremmer

, E., Julia, B., and Scherk, J. 1978. “Supergravity Theory in Eleven-Dimensions”.

Physics Letters B

. 76: 409-412

[10]

Cvetic

, M., Lu, H. and Pope, C. N. 2000. “Four-dimensional N=4 SO(4) Gauged Supergravity from D=11”.

Nuclear Physics B

. 574: 761-781.

[11]

Gubster

, S. S., Pufu, S. S., and Rocha, F. D. 2010. “Quantum critical superconductors in string theory and M-theory”. Physical Letter B

. 683: 201-204. [12] Gauntlett, J., Sonner, J., and Wiseman, T. 2010. ”Quantum Criticality and Holographic Superconductors in M-theory”

Journal of High Energy Physics. 2010: 60.[13] Lu, H. and Zhang, X. 2014. “Exact Collapse Solutions in D=4, N=4 Gauged Supergravity and Their Generalizations” Journal of High Energy Physics

. 2014: 099.

12

Thank you

Every questions and comments

are welcome

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SAST

Science Achievement Scholarship of Thailand