arXiv · hep-th/0602121
I review the theory of renormalization, as applied to weak-coupling perturbation theory in quantum field theories.
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John C. Collins. 2006-02-12. Renormalization: general theory. https://arxiv.org/abs/hep-th/0602121
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We explore anisotropic holographic superfluidity and find analytic solutions near critical point where superfluid/normalfluid phase transition appears in a holographic dual fluid system. In arXiv:hep-th/1109.4592, the authors obtained such an analytic solution in 5-dimensional Einstein-SU(2)Yang-Mills system, and it is asymptotically AdS$_5$. What is more in this note is that we get analytic solutions near the critical point in 3- and 4- dimensional Einstein-Scalar-U(1)$\times$SU(2)Yang-Mills systems, which become asymptotically hyperscaling violation geometry. We also get leading order back reactions to the background geometry, which clearly shows spatial anisotropy of the bulk geometry. To explore the properties of the spacetime, we compute holographic entanglement entropy and confirm that the superfluid/normalfluid phase transition must occur at the critical point.
The Drude-Kadanoff-Martin model is a simple low energy and long wavelength description of charge transport, parameterised by the current relaxation timescale $τ$, charge diffusivity $D$ and charge compressibility $χ$. We obtain sharp constraints on these parameters in terms of the microscopic energy and length scales of any underlying lattice model with local and bounded interactions. Our primary tools are upper bounds on the retarded Green's function for the charge density in such a setting. We first note that the Drude-Kadanoff-Martin model cannot pertain at microscopic energy scales because it is inconsistent with the exponential suppression of spectral weight at the highest frequencies in a lattice model. Secondly, under the assumption that the low energy dynamics is captured by the model, we obtain a lower bound on the collective mean free path $\ell \equiv \sqrt{τD}$. This bound is shown to imply a version of the Mott-Ioffe-Regel bound: systems with $\ell$ much shorter than the lattice length scale cannot have conventional Drude peaks, in the sense of being captured by the DKM model.
We compute the gluonic contribution to the gravitational form factors of the proton using the improved holographic QCD model, in which the proton is described in terms of bulk Dirac fermions. Model parameters are constrained using lattice and phenomenological input, allowing us to obtain estimates for the gravitational form factors and to compare them with results from other approaches. Using the extracted form factors, we analyze mechanical properties of the proton, including pressure and shear distributions. We obtain estimates for the mechanical and mass radii of the proton, $ρ_{\text{mech}} \approx 0.63$ fm, $ρ_{\text{mass}} \approx 0.65$ fm, and compare these values with radius estimates from other nonperturbative studies.