Scheme Independence to all Loops

The immense freedom in the construction of Exact Renormalization Groups means that the many non-universal details of the formalism need never be exactly specified, instead satisfying only general constraints. In the context of a manifestly gauge invariant Exact Renormalization Group for SU(N) Yang-Mills, we outline a proof that, to all orders in perturbation theory, all explicit dependence of beta function coefficients on both the seed action and details of the covariantization cancels out. Further, we speculate that, within the infinite number of renormalization schemes implicit within our approach, the perturbative beta function depends only on the universal details of the setup, to all orders.Comment: 18 pages, 8 figures; Proceedings of Renormalization Group 2005, Helsinki, Finland, 30th August - 3 September 2005. v2: Published in jphysa; minor changes / refinements; refs. adde

Sensitivity of Nonrenormalizable Trajectories to the Bare Scale

Working in scalar field theory, we consider RG trajectories which correspond to nonrenormalizable theories, in the Wilsonian sense. An interesting question to ask of such trajectories is, given some fixed starting point in parameter space, how the effective action at the effective scale, Lambda, changes as the bare scale (and hence the duration of the flow down to Lambda) is changed. When the effective action satisfies Polchinski's version of the Exact Renormalization Group equation, we prove, directly from the path integral, that the dependence of the effective action on the bare scale, keeping the interaction part of the bare action fixed, is given by an equation of the same form as the Polchinski equation but with a kernel of the opposite sign. We then investigate whether similar equations exist for various generalizations of the Polchinski equation. Using nonperturbative, diagrammatic arguments we find that an action can always be constructed which satisfies the Polchinski-like equation under variation of the bare scale. For the family of flow equations in which the field is renormalized, but the blocking functional is the simplest allowed, this action is essentially identified with the effective action at Lambda = 0. This does not seem to hold for more elaborate generalizations.Comment: v1: 23 pages, 5 figures, v2: intro extended, refs added, published in jphy

Conformal anomaly from gauge fields without gauge fixing

We show how the Weyl anomaly generated by gauge fields, can be computed from manifestly gauge invariant and diffeomorphism invariant exact renormalization group equations, without having to fix the gauge at any stage. Regularisation is provided by covariant higher derivatives and by embedding the Maxwell field into a spontaneously broken $U(1|1)$ supergauge theory. We first provide a realisation that leaves behind two versions of the original $U(1)$ gauge field, and then construct a manifestly $U(1|1)$ supergauge invariant flow equation which leaves behind only the original Maxwell field in the spontaneously broken regime.Comment: 24 page

Progress towards therapies for disease modification in Parkinson's disease

The development of interventions to slow or halt the progression of Parkinson's disease remains a priority for patients and researchers alike. To date, no agents have been shown to have unequivocal evidence of disease-modifying effects in Parkinson's disease. The absence of disease-modifying treatments might relate not only to inadequate approaches for the selection of therapeutic candidates but also to insufficient attention to detail in clinical trial design. Better understanding of Parkinson's disease pathogenesis associated with advances in laboratory models, the use of objective biomarkers of disease progression and target engagement, and a focus on agents known to be safe for human use, alongside the use of precision medicine approaches, should together greatly increase the likelihood for successful identification of disease-modifying treatments for Parkinson's disease

Frame-dragging effects on magnetic fields near a rotating black hole

We discuss the role of general relativity frame dragging acting on magnetic field lines near a rotating (Kerr) black hole. Near ergosphere the magnetic structure becomes strongly influenced and magnetic null points can develop. We consider aligned magnetic fields as well as fields inclined with respect to the rotation axis, and the two cases are shown to behave in profoundly different ways. Further, we construct surfaces of equal values of local electric and magnetic intensities, which have not yet been discussed in the full generality of a boosted rotating black hole.Comment: to appear in the proceedings of "The Central Kiloparsec in Galactic Nuclei (AHAR 2011)", Journal of Physics: Conference Series (JPCS), IOP Publishin

Optimization of the derivative expansion in the nonperturbative renormalization group

We study the optimization of nonperturbative renormalization group equations truncated both in fields and derivatives. On the example of the Ising model in three dimensions, we show that the Principle of Minimal Sensitivity can be unambiguously implemented at order $\partial^2$ of the derivative expansion. This approach allows us to select optimized cut-off functions and to improve the accuracy of the critical exponents $\nu$ and $\eta$. The convergence of the field expansion is also analyzed. We show in particular that its optimization does not coincide with optimization of the accuracy of the critical exponents.Comment: 13 pages, 9 PS figures, published versio

Self-energy and critical temperature of weakly interacting bosons

Using the exact renormalization group we calculate the momentum-dependent self-energy Sigma (k) at zero frequency of weakly interacting bosons at the critical temperature T_c of Bose-Einstein condensation in dimensions 3 <= D < 4. We obtain the complete crossover function interpolating between the critical regime k << k_c, where Sigma (k) propto k^{2 - eta}, and the short-wavelength regime k >> k_c, where Sigma (k) propto k^{2 (D-3)} in D> 3 and Sigma (k) \propto ln (k/k_c) in D=3. Our approach yields the crossover scale k_c on the same footing with a reasonable estimate for the critical exponent eta in D=3. From our Sigma (k) we find for the interaction-induced shift of T_c in three dimensions Delta T_c / T_c approx 1.23 a n^{1/3}, where a is the s-wave scattering length and n is the density.Comment: 4 pages,1 figur

A hierarchy of bound states in the 1D ferromagnetic Ising chain CoNb2_2O6_6 investigated by high resolution time-domain terahertz spectroscopy

Kink bound states in the one dimensional ferromagnetic Ising chain compound CoNb$_2$O$_6$ have been studied using high resolution time-domain terahertz spectroscopy in zero applied magnetic field. When magnetic order develops at low temperature, nine bound states of kinks become visible. Their energies can be modeled exceedingly well by the Airy function solutions to a 1D Schr\"odinger equation with a linear confining potential. This sequence of bound states terminates at a threshold energy near two times the energy of the lowest bound state. Above this energy scale we observe a broad feature consistent with the onset of the two particle continuum. At energies just below this threshold we observe a prominent excitation that we interpret as a novel bound state of bound states -- two pairs of kinks on neighboring chains