1. Kaluza-Klein non-compactification to dS
6/27/2018 4:11 AM
Kaluza-Klein non-compactification
to dS
Inyong park
CQUeST, Sogang University
Philander Smith College
2012 International workshop on
String theory and cosmology, June 2012
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

2. This talk /22
Is based on part of on-going project (with E. Hatefi and A. Nurmagambetov), selected for wider audience
Will focus on motivation and direction
Reviews and contrasts two approaches to dS:
Calaby-Yau type compactification and explicit KK non-compactification
Towards the end, Issues to study in KK non-compactification
Comments/feedbacks are welcomed

3. Calaby-Yau type compactification
Original CY compactification
Flux compactifcation (successful but implicit,
KK non-compactification as an alternative)

4. Original CY compactification
M10 = M4 × M6 metric ansatz
To see residual susy in 4D, analyze
δε (fermionic fields) = 0
Heterotic context, N=1 susy in 4D with 6D CY manifold
Description of CY: in terms of Hodge numbers (cohomological specification),
Given Hodge numbers there can be infinitely many different metrics, they can be even topologically distinct spaces, one would not put some of them
together if explicit forms of metrics were known

5. Flux compactification
Turn on various RR gauge field strengths
Internal manifold differs from CY by a warp factor in some cases, in other cases non-Kahler manifolds appear

6. Flux compactification: cont’d
Flux plays multiple roles (reduces susy, converts AdS to dS, e.g., in KKLT)
Involve warped geometry
For a compact, non-singular internal manifold without brane source, the warp factor must be trivial , dS cannot be realized,
requires brane sources or higher derivative corrections to sugra to go around no-go’s
Larger than realistic amount of susy initially,
further breaking by turning on flux,
CY manifold not sacred (may be sacred but not for susy reason)

7. Flux compactification: cont’d
Seems that the issue of consistent truncation is obscured (due to lack of explicit form of the metric)
(consistent truncation means reduced theory is decoupled from the infinite tower of the rest of the modes, therefore, “self-contained”; we assume that it is a desirable property)

8. possible ways to go around no-go, such as adding stringy effects
Led to
no-go theorems
possible ways to go around no-go, such as adding stringy effects
Provides no-go theorems
Possible ways to circumvent no-go

9. Flux compactification: adding branes
No-go theorem can be evaded by adding branes
E.g., D7 branes wrapping four cycle, acts as D3 source
Bianchi identity in the presence of fluxes
D3 brane charge density
Integrating over the internal manifold ,one ges
(called IIB “tadpole cancellation condition”)
What about back reaction? (effect of the additional branes to metric)

10. KKLT type approach Add anti-D3 branes to lift AdS to dS
Seems that back-reaction issue only implicitly dealt with at best

11. Calaby-Yau type compactification: cont’d
6/27/2018 4:11 AM
Calaby-Yau type compactification: cont’d
undesirable feature
No explicit forms of metric known other than a few simple cases
inevitably
“Generic” approach (generic discussion, could be much more informative if explicit forms of CYs are known )
Large number of moduli moduli stabilization procedure required “top-down approach”
some of the moduli could be against consistent truncation, would be better to be put off
since consistent truncation obscured in this approach, this issue cannot be addressed
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

12. Could one hope to do better?

13. Explicit KK (non)-compactification
6/27/2018 4:11 AM
Explicit KK (non)-compactification
Explicit form of internal manifold
Such as torus (ungauged sugra), sphere (gauged sugra)
Consistent truncation: solution of reduced theory becomes automatically solution of mother theory
reduction on a hyperboliodal space (our main interest)
Explicit procedure to potential (may lead to inflationary models)
“Bottom-up” approach, much smaller moduli
space, potential risk of pathology, in such cases try to amend by considering e.g. stringy effects etc
© 2007 Microsoft Corporation. All rights reserved. Microsoft, Windows, Windows Vista and other product names are or may be registered trademarks and/or trademarks in the U.S. and/or other countries.
The information herein is for informational purposes only and represents the current view of Microsoft Corporation as of the date of this presentation. Because Microsoft must respond to changing market conditions, it should not be interpreted to be a commitment on the part of Microsoft, and Microsoft cannot guarantee the accuracy of any information provided after the date of this presentation. MICROSOFT MAKES NO WARRANTIES, EXPRESS, IMPLIED OR STATUTORY, AS TO THE INFORMATION IN THIS PRESENTATION.

14. Example: IIB S^5 reduction

15. Sphere reduction in general
When scalars vanish (i.e. a ground state)
Scalar part of the ansatze is usually the most difficult
The vevs may be fixed by extremizing the scalar potential of reduced theory, (Some of the scalars become moduli of the potential of the reduced theory)

16. Work of Cvetic, Gibbons and Pope (CGP)
Hyperboloidal reduction, inhomogeneous space (not a coset space)
Bosonic sectors worked out (but not the fermonic sector), led to gauged dS sugra in lower D
Non-compactification
typically leads to theories with ghosts
No ghosts in CGP work but extrema in a saddle point of potential This is a problem
Could stringy effects cure this?
(This will be one of the directions that we will look into)

17. P and q are number of 1’s and -1’s respectively
For trivial scalar configurations
SO(p)xSO(q) isometry group (common subgroup of SO(p+q) and SO(p,q)), compact group
Positive definite metric

18. Comparison with homogeneous hyperbolic plane H^2
H^2 is a coset
with isometry group O(2,1)
H^2 non-compactification leads to theories with ghosts (wrong sign kinetic terms)

19. (including ) does not lead to ghosts
However, led to saddle point in the work of CGP

20. Interesting issues to study in
Could one amend the saddle point problem?
1. start small number of scalars in the metric ansatz,
and increase subsequently (try to freeze the wrong modes that cause saddle shape potential)
2. add stringy effect (add R^2 term to the IIB sugra)
Amount of susy of reduced theory (was not analyzed by CGP)
δε (fermionic fields) = 0, find Killing spinor(s)
Brane contents from 10D view point, possible connection with flux compactification (can check presence of the added stuff such as anti D3’s)
Inflationary models?

21. We are looking at
IIB 10D -> 5D -> 4D sequence
Will report progress in the near future