607 research outputs found
Chiral Random Matrix Model at Finite Chemical Potential: Characteristic Determinant and Edge Universality
We derive an exact formula for the stochastic evolution of the characteristic
determinant of a class of deformed Wishart matrices following from a chiral
random matrix model of QCD at finite chemical potential. In the WKB
approximation, the characteristic determinant describes a sharp droplet of
eigenvalues that deforms and expands at large stochastic times. Beyond the WKB
limit, the edges of the droplet are fuzzy and described by universal edge
functions. At the chiral point, the characteristic determinant in the
microscopic limit is universal. Remarkably, the physical chiral condensate at
finite chemical potential may be extracted from current and quenched lattice
Dirac spectra using the universal edge scaling laws, without having to solve
the QCD sign problem.Comment: 16 pages, 4 figure
Heavy Hadrons and QCD Instantons
Heavy hadrons are analyzed in a random and dilute gas of instantons. We
derive the instanton-induced interactions between heavy and light quarks at
next to leading order in the heavy quark mass and in the planar approximation,
and discuss their effects on the hadronic spectrum. The role of these
interactions in the formation of exotic hadrons is also discussed.Comment: 26 pages, REVTeX, 2 tables, 5 figures, uses FEYNMAN.st
Heavy Holographic Exotics: Tetraquarks as Efimov States
We provide a holographic description of non-strange multiquark exotics as
compact topological molecules by binding heavy-light mesons to a tunneling
configuration in D8-D that is homotopic to the vacuum state with fixed
Chern-Simons number. In the tunneling process, the heavy-light mesons transmute
to fermions. Their binding is generic and arises from a trade-off between the
dipole attraction induced by the Chern-Simons term and the U(1) fermionic
repulsion. In the heavy quark limit, the open-flavor tetraquark exotics and , emerge as bound Efimov states in a degenerate
multiplet with opposite intrinsic Chern-Simons numbers
. The hidden-flavor tetraquark exotics such as ,
and as compact topological molecules are
unbound. Other exotics are also discussed.Comment: 16 pages, 13 figure
Disorder in the Sachdev-Yee-Kitaev Model
We give qualitative arguments for the mesoscopic nature of the
Sachdev-Yee-Kitaev (SYK) model in the holographic regime with with
Majorana particles coupled by antisymmetric and random interactions of
range . Using a stochastic deformation of the SYK model, we show that its
characteristic determinant obeys a viscid Burgers equation with a small
spectral viscosity in the opposite regime with , in leading order. The
stochastic evolution of the SYK model can be mapped onto that of random matrix
theory, with universal Airy oscillations at the edges. A spectral
hydrodynamical estimate for the relaxation of the collective modes is made.Comment: 7 pages, 1 figur
Critical Scaling at Zero Virtuality in QCD
We show that at the critical point of chiral random matrix models, novel
scaling laws for the inverse moments of the eigenvalues are expected. We
evaluate explicitly the pertinent microscopic spectral density, and found it in
agreement with numerical calculations. We suggest that similar sum rules are of
relevance to QCD at the critical temperature, and even above if the transition
is amenable to a Landau-Ginzburg description.Comment: 4 pages with 3 eps figures included; small changes, typos correcte
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