does 4d space-time emerge dynamically from the ikkt matrix model ? numerical approaches to ads/cft,...
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![Page 1: 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,](https://reader036.vdocuments.net/reader036/viewer/2022062804/5697bf731a28abf838c7f087/html5/thumbnails/1.jpg)
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)
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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.)
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0. Introduction
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
4
QCD string theory
strong interactions what theory describes all the interactions including gravity
free quarks perturbation theory 10d space-time
confinement non-perturbative vacuum invisible extra dim. lattice theory non-perturbative formulation matrix models (Wilson ’74) (BFSS,IKKT ’96) properties of hadrons goal black holes, early universe, derivation of SM
Comparing string theory to QCD
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
5
QCD string theory
strong interactions what theory describes all the interactions including gravity
free quarks perturbation theory 10d space-time
confinement non-perturbative vacuum invisible extra dim. lattice theory non-perturbative formulation matrix models (Wilson ’74) (BFSS,IKKT ’96) properties of hadrons goal black holes, early universe, derivation of SM
Comparing string theory to QCD
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Jun Nishimura (KEK) 09.10.1 Imperial College London
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
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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Dynamical generation of 4d space-time
Eigenvalues :
in the limit
The order parameter forthe spontaneous breaking of the SO(10) symmetry
e.g.) SO(10) → SO(4)
c.f.) spontaneous breaking of Lorentz symmetry from tachyonic instability in bosonic SFT Kostelecky and Samuel (1988)
“moment of inertia” tensor
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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Plan of the talk
0. Introduction
1. Complex fermion determinant
2. Gaussian expansion method
3. Monte Carlo studies of one-loop effective theory
4. Full Monte Carlo studies (preliminary)
5. Summary
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1. Complex fermion determinant
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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Complex fermion determinant fermion determinant
reweighting method simulate the phase quenched model
cannot be treated as the Boltzmann weight
complex in general
suppressed as
effective sampling becomes difficult
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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Remarkable properties of the phase J.N.-Vernizzi (’00)
Stationarityof the phaseincreasesfor lower d
This effect compensates the entropy loss for lower d !
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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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)
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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Cousins of the IKKT matrix model
6d IKKT model
4d IKKT model
complex fermion determinant
10d IKKT model
We mostly focus on this modelfor technical simplicity
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2. Gaussian expansion method
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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Gaussian expansion methode.g.) one-matrix model
Consider the Gaussian action
free parameter
free propagator
interaction vertex
one-loopcounterterm
Perform perturbative expansion using
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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Self-consistency equation
self-consistency eq.:
How to identify the plateau ?
Search for concentration of solutions
plateau
Results of GEM depends on the free parameter
e.g.) free energy of the one-matrix model
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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GEM applied to 6d IKKT model Gaussian action
Aoyama-J.N.-Okubo, in prep.
Various symmetry breaking patterns
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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Results of GEM for the 6d IKKT model Aoyama-J.N.-Okubo, in prep.
Krauth-Nicolai-Staudacher (’98)
magnify this region
SO(5) SO(4) SO(3) SO(5) SO(4) SO(3) SO(5) SO(4) SO(3)
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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Results of GEM for the 6d IKKT model (cont’d)
SO(4)
SO(3) SO(4) SO(3)
SO(5)
SO(5)
concentration of solutions identified
SO(6) SO(3) SSB
suggesting :
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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Results of GEM for the 6d IKKT model
SO(5), extended
SO(4), extended
SO(3), extended
extent of the eigenvalue distributionin the extended/shrunk direction
finite in units of
shrunk directions
(cont’d)
0.18
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3. Monte Carlo studies ofone-loop effective theory
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Jun Nishimura (KEK) 09.10.1 Imperial College London
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One-loop effective theory
treat them as small fluctuationsand keep only quadratic terms
valid when
long distance behavior
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Jun Nishimura (KEK) 09.10.1 Imperial College London
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Branched-polymer-like structure Aoki-Iso-Kawai-Kitazawa-Tada(’98)
due to SUSY0
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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One-loop IKKT model with
No SSB of SO(10) symmetry
Ambjorn-Anagnostopoulos-Bietenholz-Hotta-J.N.(’00)
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Jun Nishimura (KEK) 09.10.1 Imperial College London
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One-loop 6d IKKT model with
No SSB of SO(6) symmetry
Ambjorn-Anagnostopoulos-Bietenholz-Hotta-J.N.(’00)
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Jun Nishimura (KEK) 09.10.1 Imperial College London
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Distribution of the normalized eigenvalues in the phase-quenched model
in the full model
How to include the effects of the phase
In order to see the net effects of the phase, we use the normalized variables:
finite N effects
Results in the phase-quenched model :
represents the effectsof the phase
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Jun Nishimura (KEK) 09.10.1 Imperial College London
Does 4d space-time emerge dynamically from the IKKT matrix model ?
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The behavior of the correction factor
no. of d.o.f.
favourscollapsed configs.
Anagnostopoulos-J.N. (’02)
one-loop6d IKKT model
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Factorization methodAnagnostopoulos-J.N. (’02)
Distribution of the normalized eigenvalues
has a double-peak structure !
scales ! scales !
L.h.s. is 1/N suppressed !
consistent withbranched polymer
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4. Full Monte Carlo studies (preliminary)
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Small x behavior of in full 6dIKKT modelphase space suppression :
Large-N extrapolation reveals the existence of a “hard-core potential”
Anagnostopoulos-Aoyama-Azuma-Hanada-J.N., in prog.
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Determination of the peak position
(at small x)
Precise position of the peak can be obtainedby more careful large-N extrapolation of
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Jun Nishimura (KEK) 09.10.1 Imperial College London
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Comparison of the peak heights
turned out to be negligible !
The information of comes in onlythrough the determination of
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Effects of the phase at
As far as , the left peak dominates !
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0.6
GEM result translates to
Prediction from GEM
consistent with MC !
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5. Summary
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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
SO(6) SO(3) SSB
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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 gravity Kawai’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.