Density via duality

AbstractWe present an unexpected correspondence between homomorphism duality theorems and gaps in the poset of graphs and their homomorphisms. This gives a new proof of the density theorem for undirected graphs and solves the density problem for directed graphs

3+1D Massless Weyl spinors from bosonic scalar-tensor duality

We consider the fermionization of a bosonic free theory characterized by the 3+1D scalar - tensor duality. This duality can be interpreted as the dimensional reduction, via a planar boundary, of the 4+1D topological BF theory. In this model, adopting the Sommerfield tomographic representation of quantized bosonic fields, we explicitly build a fermionic operator and its associated Klein factor such that it satisfies the correct anticommutation relations. Interestingly, we demonstrate that this operator satisfies the massless Dirac equation and that it can be identified with a 3+1D Weyl spinor. Finally, as an explicit example, we write the integrated charge density in terms of the tomographic transformed bosonic degrees of freedom

Duality for convex monoids

Every C*-algebra gives rise to an effect module and a convex space of states, which are connected via Kadison duality. We explore this duality in several examples, where the C*-algebra is equipped with the structure of a finite-dimensional Hopf algebra. When the Hopf algebra is the function algebra or group algebra of a finite group, the resulting state spaces form convex monoids. We will prove that both these convex monoids can be obtained from the other one by taking a coproduct of density matrices on the irreducible representations. We will also show that the same holds for a tensor product of a group and a function algebra.Comment: 13 page

Simulating Dense Matter

I review the Sign Problem hindering lattice QCD simulations of dense baryonic matter, focussing where possible on its physical relevance. The possibility of avoiding the Sign Problem via a duality transformation is also briefly considered. Finally, I review evidence for deconfinement at non-zero quark density in recent simulations of Two Color QCD.Comment: Talk at "New Frontiers in QCD", Yukawa International Seminar 2006 (Kyoto), 8 pages, 7 figure

The effect of three matters on KSS bound

Our goal in this manuscript is to introduce black brane solutions in AdS 4-dimensional (4D) Einstein-Gauss-Bonnet-Yang-Mills theory in presence of string cloud and quintessence. Shear viscosity to entropy density ratio is computed via fluid-gravity duality, as a transport coefficient for this model.Comment: 10 pages, no figur

Schrodinger Fermi Liquids

A class of strongly interacting many-body fermionic systems in 2+1D non-relativistic conformal field theory is examined via the gauge-gravity duality correspondence. The 5D charged black hole with asymptotic Schrodinger isometry in the bulk gravity side introduces parameters of background density and finite particle number into the boundary field theory. We propose the holographic dictionary, and realize a quantum phase transition of this fermionic liquid with fixed particle number by tuning the background density $\beta$ at zero temperature. On the larger $\beta$ side, we find the signal of a sharp quasiparticle pole on the spectral function A(k,w), indicating a well-defined Fermi surface. On the smaller $\beta$ side, we find only a hump with no sharp peak for A(k,w), indicating the disappearance of Fermi surface. The dynamical exponent $z$ of quasiparticle dispersion goes from being Fermi-liquid-like $z\simeq1$ scaling at larger $\beta$ to a non-Fermi-liquid scaling $z\simeq 3/2$ at smaller $\beta$. By comparing the structure of Green's function with Landau Fermi liquid theory and Senthil's scaling ansatz, we further investigate the behavior of this quantum phase transition.Comment: 26 pages, many figures of spectral functions A(k,w). v2: add a new Fig, several clarifications, and discussions about holographic renormalization. Program code shared via a URL link in the manuscrip

Elliptic flow of gluon matter in ultrarelativistic heavy-ion collisions

Employing a perturbative QCD based parton cascade we calculate the elliptic flow $v_2$ and its transverse momentum dependence $v_2(p_T)$ for the gluon matter created in Au+Au collisions at $\sqrt{s_{NN}}=200$ GeV. To make comparisons with the experimental data at the BNL Relativistic Heavy Ion Collider (RHIC), parton-hadron duality is assumed. We find that whereas the integrated $v_2$ matches the experimental data, the gluon (or pion) $v_2(p_T)$ is about 20-50% smaller than the experimental data. Hadronization via gluon fragmentation and quark recombination seems to be the key to explaining the necessary jump of $v_2(p_T)$ from the partonic to the hadronic phase. We also show that the elliptic flow values moderately depend on the chosen freezeout condition, which will thus constrain the shear viscosity to the entropy density ratio of the quark gluon plasma created at RHIC.Comment: 20 pages, 7 figures, minor corrections, published versio