1 / 37

Does 4d space-time emerge dynamically from the IKKT matrix model ?

Does 4d space-time emerge dynamically from the IKKT matrix model ?. Numerical Approaches to AdS/CFT, Large N and Gravity, Sep 28-Oct 2, 2009, Imperial College, London Jun Nishimura (KEK Theory Center). based on collaborations with Konstantinos Anagnostopoulos

toril
Télécharger la présentation

Does 4d space-time emerge dynamically from the IKKT matrix model ?

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Does 4d space-time emerge dynamicallyfrom the IKKT matrix model ? Numerical Approaches to AdS/CFT, Large N and Gravity, Sep 28-Oct 2, 2009, Imperial College, London Jun Nishimura (KEK Theory Center)

  2. based on collaborations with • Konstantinos Anagnostopoulos • (National Technical University, Athens) • Tatsumi Aoyama (KEK) • Takehiro Azuma　（Setsunan U.） • Masanori Hanada (Weizmann Inst.) • Toshiyuki Okubo (Meijo U.) • Fumihiko Sugino (Okayama Inst.) Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  3. 0. Introduction

  4. Comparing string theory to QCD QCD string theory strong interactionswhat theory describesall the interactions including gravity free quarksperturbation theory10d space-time confinementnon-perturbative vacuum invisible extra dim. lattice theory non-perturbative formulation matrix models (Wilson ’74) (BFSS,IKKT ’96) properties of hadronsgoal black holes, early universe, derivation of SM Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  5. Comparing string theory to QCD QCD string theory strong interactionswhat theory describesall the interactions including gravity free quarksperturbation theory10d space-time confinementnon-perturbative vacuum invisible extra dim. lattice theory non-perturbative formulation matrix models (Wilson ’74) (BFSS,IKKT ’96) properties of hadronsgoal black holes, early universe, derivation of SM Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  6. IKKT matrix model (Ishibashi-Kawai-Kitazawa-Tsuchiya ’96) a non-perturbative formulation of type IIB superstring theory in 10 dim. (conjecture) • Similarity to the Green-Schwarz worldsheet action in the Schild gauge • c.f.) Matrix Theory membrane action in the light cone gauge • Interactions between D-branes • Attempt to derive string field theory from SD eqs. for Wilson loops Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  7. in the limit Dynamical generation of 4d space-time c.f.) spontaneous breaking of Lorentz symmetry from tachyonic instability in bosonic SFT Kostelecky and Samuel (1988) The order parameter for the spontaneous breaking of the SO(10) symmetry “moment of inertia” tensor Eigenvalues : e.g.) SO(10) → SO(4) Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  8. Plan of the talk • 0. Introduction • Complex fermion determinant • 2. Gaussian expansion method • 3. Monte Carlo studies of one-loop effective theory • 4. Full Monte Carlo studies (preliminary) • 5. Summary Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  9. Complex fermion determinant

  10. Complex fermion determinant • fermion determinant • reweighting method simulate the phase quenched model complex in general cannot be treated as the Boltzmann weight suppressed as effective sampling becomes difficult Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  11. Remarkable properties of the phase J.N.-Vernizzi (’00) Stationarity of the phase increases for lower d This effect compensates the entropy loss for lower d ! Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  12. This is a dilemma ! • Phase of the fermion determinant • important for the possible SSB of SO(10) • difficult to include in Monte Carlo simulation Gaussian expansion method Section 2 Sugino-J.N. (’00), Kawai et al. (’01),… New Monte Carlo technique Section 3 Anagnostopoulos-J.N. (’01) Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  13. We mostly focus on this model for technical simplicity Cousins of the IKKT matrix model 10d IKKT model 6d IKKT model complex fermion determinant 4d IKKT model Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  14. 2. Gaussian expansion method

  15. Gaussian expansion method e.g.) one-matrix model Consider the Gaussian action free parameter Perform perturbative expansion using free propagator interaction vertex one-loop counterterm Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  16. Self-consistency equation Results of GEM depends on the free parameter e.g.) free energy of the one-matrix model plateau How to identify the plateau ? self-consistency eq.: Search for concentration of solutions Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  17. GEM applied to 6d IKKT model Aoyama-J.N.-Okubo, in prep. • Gaussian action Various symmetry breaking patterns Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  18. magnify this region Results of GEM for the 6d IKKT model Aoyama-J.N.-Okubo, in prep. SO(5) SO(4) SO(3) SO(5) SO(4) SO(3) SO(5) SO(4) SO(3) Krauth-Nicolai- Staudacher (’98) Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  19. SO(6) SO(3) SSB Results of GEM for the 6d IKKT model (cont’d) concentration of solutions identified SO(5) SO(4) SO(5) SO(4) SO(3) SO(3) suggesting : Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  20. Results of GEM for the 6d IKKT model (cont’d) extent of the eigenvalue distribution in the extended/shrunk direction SO(5), extended SO(4), extended SO(3), extended shrunk directions 0.18 finite in units of Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  21. 3. Monte Carlo studies ofone-loop effective theory

  22. One-loop effective theory treat them as small fluctuations and keep only quadratic terms valid when long distance behavior Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  23. Branched-polymer-like structure Aoki-Iso-Kawai-Kitazawa-Tada(’98) 0 due to SUSY Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  24. One-loop IKKT model with Ambjorn-Anagnostopoulos-Bietenholz-Hotta-J.N.(’00) • No SSB of SO(10) symmetry Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  25. One-loop 6d IKKT model with Ambjorn-Anagnostopoulos-Bietenholz-Hotta-J.N.(’00) • No SSB of SO(6) symmetry Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  26. How to include the effects of the phase Results in the phase-quenched model : finite N effects In order to see the net effects of the phase, we use the normalized variables: • Distribution of the normalized eigenvalues • in the phase-quenched model • in the full model represents the effects of the phase Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  27. favours collapsed configs. The behavior of the correction factor Anagnostopoulos-J.N. (’02) one-loop 6d IKKT model no. of d.o.f. Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  28. Factorization method Anagnostopoulos-J.N. (’02) Distribution of the normalized eigenvalues has a double-peak structure ! scales ! scales ! consistent with branched polymer L.h.s. is 1/N suppressed ! Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  29. 4. Full Monte Carlo studies (preliminary)

  30. Anagnostopoulos- Aoyama-Azuma- Hanada-J.N., in prog. Small x behavior of in full 6dIKKT model phase space suppression : Large-N extrapolation reveals the existence of a “hard-core potential” Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  31. Determination of the peak position (at small x) Precise position of the peak can be obtained by more careful large-N extrapolation of Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  32. Comparison of the peak heights turned out to be negligible ! The information of comes in only through the determination of Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  33. As far as , the left peak dominates ! Effects of the phase at Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  34. Prediction from GEM 0.6 GEM result translates to consistent with MC ! Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  35. 5. Summary

  36. SO(6) SO(3) SSB Summary and future prospects • IKKT matrix model non-perturbative definition of superstring the dynamical origin of space-time dim. • 6d IKKT model complex fermion determinant • Gaussian expansion method • MC studies with factorization method large-N extrapolation for each factor of the distribution so far, consistent with GEM prediction • Extension to IKKT model, straightforward Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

  37. Some comments • D0 brane system Hanada and Wiseman’s talk The phase of the fermion determinant can be neglected. agreement with the gauge/gravity duality the reason needs to be understood SSB of SO(9) seems unlikely to happen… studies based on GEM Aoyama-J.N.-Okubo-Takeuchi, in prog • IKKT model appearance of 4d gravityKawai’s talk spontaneous breaking of SUSY ?Sugino’s talk How to think about the Euclidean time Ambjorn’s talk How to read off the Standard Model d.o.f. Does 4d space-time emerge dynamically 　from the IKKT matrix model ?

More Related