A causal alternative to the c=0 string

2. A causal alternative to the c=0 string Jan Ambjorn Niels Bohr and Univ. Utrecht W.W. Univ. Of Iceland Stefan Zohren Imperial College London Renate Loll Univ. Utrecht Yoshiyuki Watabiki Tokyo Inst. Tech. Zakopane 16 06 2008

3. Publications and preprints • Putting a cap on causality violations in CDT arXiv:0709.2784 JHEP 0712:017,2007 • A String Field Theory based on Causal Dynamical Triangulations arXiv:0802.0719 JHEP 0805:032,2008 • Topology change in causal quantum gravity arXiv:0802.0896 Conf.Proc. JGRG17 Nagoya, Japan • A Matrix Model for 2D Quantum Gravity defined by Causal Dynamical Triangulations arXiv:0804.0252 t.a. Phys. Lett. B provisional titles for papers to come that are covered in this talk: • Loop equations for CDT • The causal continuum limit for matrix model quantum gravity

4. What and Why? • Two dimensional quantum gravity • Non critical (bosonic) string theory= Strings living in target space with D≠26 • Toy model for 4d quantum gravity • Talks by J. Ambjorn and A. Goerlich

5. How? • Dynamical triangulations (DT): • Path integral over geometries  Discrete statistical sum over triangulations • Manifold is discretized with equilateral triangles • Geometry is encoded in the way triangles are glued together

6. Geometry of DT Flat space: a Positively curved space:

7. Two different theories? • Euclidean 2D quantum gravity • Causal 2D quantum gravity

8. Not on the discrete level • Euclidean 2D quantum gravity • Causal 2D quantum gravity

9. On the discrete level:Euclidean DT  Causal DT • Euclidean 2D quantum gravity • Causal 2D quantum gravity

10. Discrete:Euclidean DT  Causal DT • On the discrete level: • EDT = CDT + spatial topology change

11. Continuum:Euclidean DT ≠ Causal DT • In the continuum: • EDT ≠CDT + spatial topology change

12. Continuum:CDT is better behaved • EDT • Hausdorff dimension = 4 • Time scales non canonically • Spatial topology changes are everywhere and dominate the dynamics • No single string states • CDT • Hausdorff dimension = 2 • Time is measured in seconds as should be • Spatial topology changes controlled by a coupling constant • Fock space of multistring states can be explicitly defined

13. The old construction of CDT • The Transfer matrix

14. Causal quantum gravity • What do we compute? Z The disc function W(Z,T) T • Probability amplitude

15. Causal Dynamical Triangulations • Discrete path integral • Transfer matrix T=1 The disc function

16. Causal Dynamical Triangulations • Discrete path integral • Transfer matrix T=2 The disc function

17. Causal Dynamical Triangulations • Discrete path integral • Transfer matrix T=3 The disc function

18. Causal Dynamical Triangulations • Discrete path integral • Transfer matrix T=4 The disc function

19. Causal Dynamical Triangulations • Discrete path integral • Transfer matrix T=5 The disc function

20. Causal Dynamical Triangulations • Discrete path integral • Transfer matrix T=6 The disc function

21. NEW for CDT: • Loop equations

22. N The new CDT loop equations N N

23. N The new CDT loop equations N+1 N+1

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