1. as holographic description of String Field Theory inspired models
p-adic models
as holographic description of
String Field Theory inspired models
(SFT/p-adic Strings Duality)
Irina Aref'eva
Steklov Mathematical Institute, RAN, Moscow
It is my pleasure to give the talk here.
I would like to thank organizers for invitation.
The short title of my talk is
“SFT/p-adic Strings Duality”
International Workshop "p -Adic Methods for Modelling of Complex Systems“
ZiF, Bielefeld University, Bielefeld, Germany
April 15–19, 2013

2. Outlook Holography for p-adic effective action
SFT(String Field Theory) Inspired Action
SFT Inspired Action for Physical Problems
SFT/p-adic Duality
Cosmology
Quark Gluon Plasma in Heavy Ion Collisions

3. We
String theory(ies) is UV complete theory
No UV divergences

4. SFT action for tachyons (boson string)
Kostelecky, Samuel, 1988
ABGKM, review arXiv: , 2001

5. Cosmological Models with SFT Inspired Actions
String inspired

6. P-adics non-local models
Homogeneous case
V.S.Vladimirov

7. String Field Inspired Nonlocal Models in Cosmology
Later cosmology
w<-1
Inflation
steep potential,
non-gaussianity
Bouncing solutions
I.A., astro-ph/
I.A., L.Joukovkaya, JHEP,05109 (2005) 087
I.A., A.Koshelev, JHEP, (2007) 041
L.Joukovskaya, PR D76 (2007) ;
JHEP (2009 ) 
G. Calcagni, M.Montobbio,G.Nardelli,
; ;
Calcagni, Nardelli, ……..
N. Barnaby, T. Biswas, J.M. Cline, hep-th/ ,
J.Lidsey, hep-th/ ;
Nunes, Mulryne, ;
I. A., I.Volovich, arXiv: ,
works in progress
I.A., L.Joukovskaya, S.Vernov, JHEP 0707 (2007) 087
…….
Nonlocality has been applied to several problems in cosmology.

8. Holography and duality.
D=5 Susskind, 1994
D=3 ‘t Hooft, 1993
D=4
D=3
Duality:
D=4 Gauge theory
N=4 YM with SU(Nc)
String theory
on AdS5xS5
Gravity
in AdS5
Maldacena 1997:
‘t Hooft, “dimensional reduction in quantum gravity” gr-qc/
Susskind, “The World as a hologram” hep-th/

9. Simplest Holographic Models. Plane version of GKPW duality
Gubser,Klebanov,Polyakov; Witten, 1998
IA, I.Volovich, 1998
Naked['neɪkɪd] holography
Proof

10. Holographic Models with SFT Inspired Actions

11. Simplest Holographic Models

12. GKPW Holographic Model
panch

13. Nonlocal Holographic Model

14. p-adic as Holography for SFT inspired Model
P-adic action
SFT inspired action

15. Theories with Infinite # of derivatives
Speculative =['spekjələtɪv]

16. Conclusion
P-adic effective models in AdS produce the SFT-inspired models on the holograpic boundary of AdS

17. BACKUP slides

18. Cosmological Singularity
Classical versions of the Friedmann Big Bang cosmological models of the universe
contain a singularity at the start of time.
Here we restrict ourself with a simple approach by considering the time variable t
running over the half-line with regular boundary conditions at t = 0.

19. Cosmological Daemon I. A., I.Volovich, arXiv: 1103.0273
Nonlocal string field theory equations with infinite number of derivatives.
We use the heat equation method and show that on the half-line in addition to the usual initial data a new arbitrary function (external source) occurs that is called the daemon function.
The daemon function governs the evolution of the universe similar to the Maxwell demon.
In the simplest case the nonlocal scalar field reduces to the usual local scalar field coupled with an external source.

20. The Heat Equation on the Whole Line

21. The heat equation of the half-line

22. Solutions to Linearized Nonlocal Equation on the Half-line
Dirichlet's daemon without source

23. Linearized Nonlocal Equation on the Half-line
Dirichlet's daemon – one mode
Energy and pressure on the solution

24. Dynamical system with Higgs potential
elliptic cosine function of modulus k