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

Equivalent Fixed-Points in the Effective Average Action Formalism

Starting from a modified version of Polchinski's equation, Morris' fixed-point equation for the effective average action is derived. Since an expression for the line of equivalent fixed-points associated with every critical fixed-point is known in the former case, this link allows us to find, for the first time, the analogous expression in the latter case.Comment: 30 pages; v2: 29 pages - major improvements to section 3; v3: published in J. Phys. A - minor change

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

Observable consequences of quantum gravity: Can light fermions exist?

Any theory of quantum gravity must ultimately be connected to observations. This demand is difficult to be met due to the high energies at which we expect the quantum nature of gravity to become manifest. Here we study, how viable quantum gravity proposals can be restricted by investigating the interplay of gravitational and matter degrees of freedom. Specifically we demand that a valid quantum theory of gravity must allow for the existence of light (compared to the Planck scale) fermions, since we observe these in our universe. Within the effective theory framework, we can thus show that UV completions for gravity are restricted, regardless of the details of the microscopic theory. Specialising to asymptotically safe quantum gravity, we find indications that universes with light fermions are favoured within this UV completion for gravity.Comment: 4 pages, based on a talk given at Loops '11, Madrid, to appear in Journal of Physics: Conference Series (JPCS

Strain control of superlattice implies weak charge-lattice coupling in La0.5_{0.5}Ca0.5_{0.5}MnO3_3

We have recently argued that manganites do not possess stripes of charge order, implying that the electron-lattice coupling is weak [Phys Rev Lett \textbf{94} (2005) 097202]. Here we independently argue the same conclusion based on transmission electron microscopy measurements of a nanopatterned epitaxial film of La$_{0.5}$Ca$_{0.5}$MnO$_3$. In strain relaxed regions, the superlattice period is modified by 2-3% with respect to the parent lattice, suggesting that the two are not strongly tied.Comment: 4 pages, 4 figures It is now explained why the work provides evidence to support weak-coupling, and rule out charge orde

Functional renormalization group with a compactly supported smooth regulator function

The functional renormalization group equation with a compactly supported smooth (CSS) regulator function is considered. It is demonstrated that in an appropriate limit the CSS regulator recovers the optimized one and it has derivatives of all orders. The more generalized form of the CSS regulator is shown to reduce to all major type of regulator functions (exponential, power-law) in appropriate limits. The CSS regulator function is tested by studying the critical behavior of the bosonized two-dimensional quantum electrodynamics in the local potential approximation and the sine-Gordon scalar theory for d<2 dimensions beyond the local potential approximation. It is shown that a similar smoothing problem in nuclear physics has already been solved by introducing the so called Salamon-Vertse potential which can be related to the CSS regulator.Comment: JHEP style, 11 pages, 2 figures, proofs corrected, accepted for publication by JHE

Quantum Einstein Gravity

We give a pedagogical introduction to the basic ideas and concepts of the Asymptotic Safety program in Quantum Einstein Gravity. Using the continuum approach based upon the effective average action, we summarize the state of the art of the field with a particular focus on the evidence supporting the existence of the non-trivial renormalization group fixed point at the heart of the construction. As an application, the multifractal structure of the emerging space-times is discussed in detail. In particular, we compare the continuum prediction for their spectral dimension with Monte Carlo data from the Causal Dynamical Triangulation approach.Comment: 87 pages, 13 figures, review article prepared for the New Journal of Physics focus issue on Quantum Einstein Gravit

Simplicial Complex based Point Correspondence between Images warped onto Manifolds

Recent increase in the availability of warped images projected onto a manifold (e.g., omnidirectional spherical images), coupled with the success of higher-order assignment methods, has sparked an interest in the search for improved higher-order matching algorithms on warped images due to projection. Although currently, several existing methods "flatten" such 3D images to use planar graph / hypergraph matching methods, they still suffer from severe distortions and other undesired artifacts, which result in inaccurate matching. Alternatively, current planar methods cannot be trivially extended to effectively match points on images warped onto manifolds. Hence, matching on these warped images persists as a formidable challenge. In this paper, we pose the assignment problem as finding a bijective map between two graph induced simplicial complexes, which are higher-order analogues of graphs. We propose a constrained quadratic assignment problem (QAP) that matches each p-skeleton of the simplicial complexes, iterating from the highest to the lowest dimension. The accuracy and robustness of our approach are illustrated on both synthetic and real-world spherical / warped (projected) images with known ground-truth correspondences. We significantly outperform existing state-of-the-art spherical matching methods on a diverse set of datasets.Comment: Accepted at ECCV 202

Asymptotic Safety, Emergence and Minimal Length

There seems to be a common prejudice that asymptotic safety is either incompatible with, or at best unrelated to, the other topics in the title. This is not the case. In fact, we show that 1) the existence of a fixed point with suitable properties is a promising way of deriving emergent properties of gravity, and 2) there is a sense in which asymptotic safety implies a minimal length. In so doing we also discuss possible signatures of asymptotic safety in scattering experiments.Comment: LaTEX, 20 pages, 2 figures; v.2: minor changes, reflecting published versio