• Introduction instanton molecules and topological susceptibility • Random matrix model • Chiral condensate and Dirac spectrum •A modified model and Topological susceptibility • Summary Topological susceptibility at finite temperature Topological susceptibility at finite temperature in a random matrix model in a random matrix model Chiral 07, 14 Nov. @ RCN Munehisa Ohtani (Univ. Regensburg) with C. Lehner, T. Wettig (Univ. Regensburg) T. Hatsuda (Univ. of Tokyo)
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Introduction instanton molecules and topological susceptibility Random matrix model
Topological susceptibility at finite temperature in a random matrix model. Munehisa Ohtani ( Univ. Regensburg ) with C . Lehner, T . Wettig ( Univ. Regensburg ) T. H atsuda ( Univ. of Tokyo ). Introduction instanton molecules and topological susceptibility - PowerPoint PPT Presentation
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• Introduction instanton molecules and topological susceptibility
• Random matrix model• Chiral condensate and Dirac spectrum• A modified model and Topological susceptibility • Summary
Topological susceptibility at finite Topological susceptibility at finite temperaturetemperature
in a random matrix modelin a random matrix model
Chiral 07, 14 Nov. @ RCNP
Munehisa Ohtani (Univ. Regensburg) with C. Lehner, T. Wettig (Univ.
Regensburg)
T. Hatsuda (Univ. of Tokyo)
IntroductionIntroduction
_ Banks-Casher rel: = (0)
where () = 1/V (n) = 1/ Im Tr( D+i)1
E.-M.Ilgenfritz & E.V.Shuryak PLB325(1994)263
Chiral symmetry breaking and instanton molecules
_
_
: chiral restoration
# of I-I : Formation of instanton molecules
?
?
Index Theorem: 1 tr FF = N+ N
~
32 2
0 mode of +() chirality associatedwith an isolated (anti-) instanton
tune NQ so as to cancel the factor at the saddle point.
Modified Random Matrix modelModified Random Matrix model
ZmRM = DZL-S(Q,) eN/2 2tr2det(2 + 2T2)N/2
Q
We propose a modified model:
where _ in the conventional model is reproduced.
cancelled factor =1 at Q = 0 i.e. saddle pt. eq. does not change
(
at T = 0 in the conventional model is reproduced.
(
cancelled factor =1 also at T = 0 i.e. quantities at T = 0 do not change
at T > 0 is not suppressed in the thermodynamic limit.
T / Tc
m
topological susceptibility in the modified model topological susceptibility in the modified model
1
+ Nf
11
m(m+0)
where0 : saddle pt. value
m
m
· Decreasing as T · Comparable with lattice results
B.Alles, M.D’Elia, A.Di Giacomo, PLB483(2000)
Summary and outlookSummary and outlook Chiral restoration and topological susceptibility are studied in a random matrix model formation of instanton molecules connects them via Banks-Casher relation and the index theorem.
Conventional random matrix model : 2nd order chiral transition &
unphysical suppression of for T >0 in the thermodynamic limit.
We propose a modified model in which
& are same as in the original model, at T >0 is well-defined and decreases as T increases.
consistent with instanton molecule formation, lattice results
Outlook: To find out the random matrix before H-S transformation from which the modified model are derived, Extension to finite chemical potential, Nf dependence …