Friday, March 31, 2006, 2:00 pm — Small Seminar Room, Bldg. 510
Spontaneous chiral symmetry breaking plays an important role in the low-energy dynamics of QCD. The nonzero chiral condensate is related to the non-zero density of small Dirac eigenvalues through the Banks-Casher relation.
Further, the low-energy Dirac spectrum has to satisfy a family of consistency relations called Leutwyler-Smilga (LS) spectral sum rules. These sum rules are universal, and the original LS derivation was based on quite general arguments.
I will discuss these sum rules in the closely related to (1-flavor) QCD but much simpler 2-dimensional Schwinger model. The dynamics of the two theories share chiral anomaly, topologically non-trivial vacuum, instantons, dynamical mass generation and confinement. While LS sum rules are the same for both theories, in the Schwinger model it is possible to achieve more detailed microscopic
understanding of them.
Three different ways to derive LS sum rules in the Schwinger Model will be discussed. The first is based on the clustering property of fermionic correlators and is also valid for 1-flavor QCD. The second is an exact microscopic (field theory) derivation. The third relies on 2D bosonization. The clustering property for multi-flavor QCD, relations with Random Matrix Theory and relevance
to lattice studies will be also briefly discussed.
Hosted by: Anna Stasto
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