Lattice results on QCDstrings - PowerPoint PPT Presentation

Title: Lattice results on QCDstrings


1
Lattice results on QCD-strings

• N.D. Hari Dass
• Institute of Mathematical Sciences
• Chennai
• In collaboration with Dr Pushan Majumdar, U.
  Muenster

2
(No Transcript)
3
More on KABRU

• 144 Dual Xeons _at_ 2.4 GHz, 533 MHz FSB, 266 MHz
  DDRAM memory (2GB per node on 120 nodes and 4GB
  per node on 24 nodes totaling 336 GB)
• Networking is through 3D torus SCI (Dolphinics)
  (6x6x4)
• Network attached storage 1.5 TB
• Sustained Node to Node Bandwidth 318 MB/s
• Bandwidth between processors on same node 864
  MB/s
• Latency 3.8 ms between different nodes and 0.7
  ms on same node
• HPL performance 1.002 Teraflop sustained (Peak
  1382)
• Scaling on MILC codes ks_imp_dyn1 (75-80) on
  pure_gauge (85)

4
Understanding nuclear forces

• The challenge in the beginning was to understand
  the structure and stability of atomic nucleus.
• Initially it was thought that protons, neutrons
  and pions were the elementary constituents and
  that the exchange of pions between protons and
  neutrons gave rise to the attractive nuclear
  forces.

5
Proliferation of particles.

• But with higher and higher energy collisions more
  and more particles other than the protons,
  neutrons and pions were produced.
• The simple picture of protons, neutrons and pions
  as the elementary constituents of nuclear matter
  was not viable.
• Two proposals came to be made almost concurrently
  to face the situation.

6
The hadronic string

• Chew and Frautschi observed that all the new
  particles produced lay on parallel lines (Regge
  trajectories) when their masses(or squared
  masses) were plotted against their angular
  momenta.
• Veneziano proposed a simple formula for the
  scattering amplitudes for the new particles.
• Nambu, Nielsen and Susskind made the astonishing
  proposal that both the Veneziano formula and the
  Regge trajectories could be understood if the
  particles were states of excitation of a
  relativistic string.

7
Problems with hadronic strings

• The full consistency of the hadronic string model
  required space-time to have 10 dimensions.
• Closer inspection of the spectrum of these
  strings revealed states that could not be
  hadronic states e.g massless spin-2 states.
• Such states would violate the so called Froissart
  bound for scattering amplitudes.
• Subsequently it was proposed not to use string
  theories to explain hadronic physics but as a
  means of unifying all interactions including
  gravity.

8
Quark model

• At around the same time Gellmann and Zweig
  independently proposed the quark model.
• According to this protons are constituted by 3
  quarks, 2 u-quarks of 2/3 electric charge and
  one d-quark of -1/3 charge. Likewise neutron
  constituents were 2 d-quarks and one u-quark.
• Pions were made up of a quark and anti-quark
  pair.
• The quarks were taken to be spin ½ particles.

9
Quark model..

• To overcome problems with Pauli exclusion
  principle, Nambu proposed that each quark comes
  with 3 different colours .
• This model was extremely succesful as
  book-keeping for the myriad of particles and
  could even explain some features like the
  observed magnetic moments.
• Attention then turned to constructing a theory
  for the interaction between quarks.
• Gellmann, Minkowski and Fritzsch proposed QCD
  with vector interactions motivated by the
  observed chiral symmetry among hadrons.

10
What is QCD? More technically

• QCD is a non-Abelian Gauge Theory.
• The gauge group is SU(3).
• The Quarks carry the fundamental representation
  3.
• The Gluons, which transmit the forces between
  quarks, carry the adjoint representation 8.
• 3 has triality, 8 has no triality.
• The theory in its nonperturbative domain has
  defied analytical approach despite the best
  efforts for more than 25 years.
• It is an outstanding problem of theoretical
  physics.

11
Quarks and Gluons of SU(3) QCD
12
(No Transcript)
13
Quark Confinement

• Quarks are not liberated even in very high energy
  collisions!
• The theory of Quarks must be such that they can
  never be free!

14
The dual superconductor idea
15
(No Transcript)
16
Lattice
17
Lattice QCD
18
(No Transcript)
19
Wilson Loop
20
Numerical Evidence For Flux Tubes
21
Our Simulations

• We measure the qqbar-potential of d4 su(3) pure
  gauge theory extremely accurately on 243x32 and
  324 lattices at b 5.7
• Lattice spacing a 1/6 fm so temporal extent is
  nearly 5.3 fm while spatial extent is 4fm3.
• We use Polyakov Loop Correlation Function to
  measure the potential.
• We use the Luscher-Weisz Multilevel algorithm.
• We also use the analytical multihit method to
  achieve speedup(60).

22
Type of accuracies needed

• The polyakov loop correlator is a stochastic
  variable of nearly unit magnitude.
• At a separation of r8 the average value of this
  is around 10 -26
• It roughly falls by two orders of magnitude with
  every increase in r by unity.
• This too needs to be measured at fraction of a
  percent if string-like behaviour is to be
  extracted.
• Without the multihit and multilevel methods this
  would be a hopeless task.

23
Polyakov Loop Correlators
24
Luscher-Weisz Multilevel Algorithm
25
(No Transcript)
26
Some string actions and potentials
27
Results of Luscher and Weisz
28
Initial Conclusions of Luscher and Weisz

• The coefficient of the 1/r term in the qqbar
  potential agrees to within 15 from that of the
  free bosonic string theory in the distance range
  0.5-1.0 fm.
• They argued that the discrepancy could be due to
  boundary terms and other interaction terms.
• They found that a boundary term with b.04 could
  accommadate the data well.
• They found it surprising that even at 0.5fm there
  was evidence for string behaviour.

29
The Work of Kuti et al

• Kuti et al have undertaken very detailed studies
  of the spectrum of string excitations.
• They use the extended Wilson loops for this
  purpose.
• They use 242x30x60 lattice with as 0.2 fm and
  at .04 fm so that their longest time extent is
  2.4 fm.

30
Wilson Loops for Spectrum Studies
31
Results of Kuti et al
32
Spectrum according to Kuti et al
33
Summary of Results of Kuti et al

• The ordering of the spectrum does not agree with
  that of the bosonic string even upto nearly 3fm.
• There is a systematic overshooting of the string
  results as one goes to larger and larger
  distances.
• The data fits the free bosonic string ground
  state energy very well in the range 0.5-1.0 fm.

34
Our Simulation Results
35
Force vs Distance
36
(No Transcript)
37
(No Transcript)
38
Summary of Our Results

• We do not see any obvious convergence to either
  Nambu-Goto or free bosonic string to even upto
  0.75 fm.
• As r approaches 1 fm we see clear convergence to
  the Nambu-Goto potential.
• We see very clear discrepancy with the free
  bosonic string expectations. In fact a fit to
  this behaviour produces very poor c2

39
Luscher-weisz Revisited

• How then do we reconcile our conclusions with
  those of Luscher-Weisz who had suggested onset of
  string behaviour as early as 0.5 fm by ascribing
  the differences over free string behaviour to
  boundary terms?
• In 2004 they showed that Open String Closed
  String duality forbids boundary terms of the type
  considered before.
• It is better to interpret the results as string
  behaviour not setting so soon.

40
(No Transcript)
41
(No Transcript)
42
But Nambu-Goto string is inconsistent in d4

• Though the data picks the Nambu-Goto potential so
  accurately, there is a serious problem!
• This string theory can be consistently quantised
  only in d26
• The Luscher term is a consequence of such
  quantisations, so why should one place too much
  weight on its occurrence?

43
Effective string theories

• Polchinski and Strominger in 1992 set out to
  formulate effective string theories and their
  quantisations.
• This is similar in spirit to effective theories
  like chiral models for the description of pions.
• Non-polynomial, non-renormalisable.
• Designed so that quantisation preserves Lorentz
  Invariance.
• Leading correction to the linear potential is
  again exactly the old Luscher term.
• What are the corrections and how well does data
  fit them? Tachyons?

44
Are string and gauge theories dual to each

• Polyakov and others believe that gauge and string
  descriptions are dual to each other.
• This is also the content of Maldacenas AdS/CFT
  correspondence.
• This is expected to hold even for
  non-supersymmetric theories like QCD.
• Satchi Naik (HRI) showed how all these theories
  give the conventional Luscher term.
• The d3 case is more straightforward in this
  picture.

45
What Next?

• Push the simulations to larger and larger
  distances.
• Very time consuming! With each dr 1 the
  simulation time increases by 2 and already at r7
  it takes a day for 3 meas and for good statistics
  one needs about 500 meas!
• Probe effective string theories as well as
  AdS/CFT correspondence deeper.
• Extrinsic curvature strings.
• Investigate the Center issue investigate adjoint
  strings (large memory and large simulation time).
• Investigate Center-less groups like SO(3), G2 etc
• Investigate z(3) gauge theories.
• Investigate baryons and effective string
  coupling. Construct an effective QCD String
  Theory.
• The eventual goal is solving the Quark
  Confinement Problem