1,393 research outputs found
Phase transition in matrix model with logarithmic action: Toy-model for gluons in baryons
We study the competing effects of gluon self-coupling and their interactions
with quarks in a baryon, using the very simple setting of a hermitian 1-matrix
model with action tr A^4 - log det(nu + A^2). The logarithmic term comes from
integrating out N quarks. The model is a caricature of 2d QCD coupled to
adjoint scalars, which are the transversely polarized gluons in a dimensional
reduction. nu is a dimensionless ratio of quark mass to coupling constant. The
model interpolates between gluons in the vacuum (nu=infinity), gluons weakly
coupled to heavy quarks (large nu) and strongly coupled to light quarks in a
baryon (nu to 0). It's solution in the large-N limit exhibits a phase
transition from a weakly coupled 1-cut phase to a strongly coupled 2-cut phase
as nu is decreased below nu_c = 0.27. Free energy and correlation functions are
discontinuous in their third and second derivatives at nu_c. The transition to
a two-cut phase forces eigenvalues of A away from zero, making glue-ring
correlations grow as nu is decreased. In particular, they are enhanced in a
baryon compared to the vacuum. This investigation is motivated by a desire to
understand why half the proton's momentum is contributed by gluons.Comment: 20 pages, 7 figure
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