Power-counting theorem for non-local matrix models and renormalisation

Solving the exact renormalisation group equation a la Wilson-Polchinski perturbatively, we derive a power-counting theorem for general matrix models with arbitrarily non-local propagators. The power-counting degree is determined by two scaling dimensions of the cut-off propagator and various topological data of ribbon graphs. As a necessary condition for the renormalisability of a model, the two scaling dimensions have to be large enough relative to the dimension of the underlying space. In order to have a renormalisable model one needs additional locality properties--typically arising from orthogonal polynomials--which relate the relevant and marginal interaction coefficients to a finite number of base couplings. The main application of our power-counting theorem is the renormalisation of field theories on noncommutative R^D in matrix formulation.Comment: 35 pages, 70 figures, LaTeX with svjour macros. v2: proof simplified because a discussion originally designed for \phi^4 on noncommutative R^2 was actually not necessary, see hep-th/0307017. v3: consistency conditions removed because models of interest relate automatically the relevant/marginal interactions to a finite number of base couplings, see hep-th/0401128. v4: integration procedure improved so that the initial cut-off can be directly removed; to appear in Commun. Math. Phy

On membrane interaction in matrix theory

We compute the interaction potential between two parallel transversely boosted wrapped membranes (with fixed momentum $p_-$) in D=11 supergravity with compact light-like direction. We show that the supergravity result is in exact agreement with the potential following from the all-order Born-Infeld-type action conjectured to be the leading planar infra-red part of the quantum super Yang-Mills effective action. This provides a non-trivial test of consistency of the arguments relating Matrix theory to a special limit of type II string theory. We also find the potential between two (2+0) D-brane bound states in D=10 supergravity (corresponding to the case of boosted membrane configuration in 11-dimensional theory compactified on a space-like direction). We demonstrate that the result reduces to the SYM expression for the potential in the special low-energy (\a'\to 0) limit, in agreement with previous suggestions. In appendix we derive the action obtained from the D=11 membrane action by the world-volume duality transformation of the light-like coordinate $x^-$ into a 3-vector.Comment: 18 pages, latex. v2: Some clarifying remarks and references added. v3: Further minor corrections and reference

Renormalization of the energy-momentum tensor in noncommutative complex scalar field theory

We study the renormalization of dimension four composite operators and the energy-momentum tensor in noncommutative complex scalar field theory. The proper operator basis is defined and it is proved that the bare composite operators are expressed via renormalized ones with the help of an appropriate mixing matrix which is calculated in the one-loop approximation. The number and form of the operators in the basis and the structure of the mixing matrix essentially differ from those in the corresponding commutative theory and in noncommutative real scalar field theory. We show that the energy-momentum tensor in the noncommutative complex scalar field theory is defined up to six arbitrary constants. The canonically defined energy-momentum tensor is not finite and must be replaced by the "improved" one, in order to provide finiteness. Suitable "improving" terms are found. Renormalization of dimension four composite operators at zero momentum transfer is also studied. It is shown that the mixing matrices are different for the cases of arbitrary and zero momentum transfer. The energy-momentum vector, unlike the energy-momentum tensor, is defined unambigously and does not require "improving", in order to be conserved and finite, at least in the one-loop approximation.Comment: 23 pages, pictures using axodraw, references are adde

Quantitative substantiation of pedogenesis model key components

The presented structure of humus soil horizon formation model in time for automorphic conditions includes all the factors of soil formation. The maximum thickness of humus soil horizon is justified in terms of its dependence from climatic energy costs on soil formation and the characteristics of parent rock granulometric content (expressed in terms of particle content lesser than 0.01 mm). This allows to predict the trends of pedogenesis and speed of humus horizon soils formation in relation to global climate changes, the age of which makes a country or more than a centuryyesBelgorod State Universit

Medical 3D printing: methods to standardize terminology and report trends.

BackgroundMedical 3D printing is expanding exponentially, with tremendous potential yet to be realized in nearly all facets of medicine. Unfortunately, multiple informal subdomain-specific isolated terminological 'silos' where disparate terminology is used for similar concepts are also arising as rapidly. It is imperative to formalize the foundational terminology at this early stage to facilitate future knowledge integration, collaborative research, and appropriate reimbursement. The purpose of this work is to develop objective, literature-based consensus-building methodology for the medical 3D printing domain to support expert consensus.ResultsWe first quantitatively survey the temporal, conceptual, and geographic diversity of all existing published applications within medical 3D printing literature and establish the existence of self-isolating research clusters. We then demonstrate an automated objective methodology to aid in establishing a terminological consensus for the field based on objective analysis of the existing literature. The resultant analysis provides a rich overview of the 3D printing literature, including publication statistics and trends globally, chronologically, technologically, and within each major medical discipline. The proposed methodology is used to objectively establish the dominance of the term "3D printing" to represent a collection of technologies that produce physical models in the medical setting. We demonstrate that specific domains do not use this term in line with objective consensus and call for its universal adoption.ConclusionOur methodology can be applied to the entirety of medical 3D printing literature to obtain a complete, validated, and objective set of recommended and synonymous definitions to aid expert bodies in building ontological consensus

The longitudinal fivebrane and tachyon condensation in matrix theory

We study a configuration in matrix theory carying longitudinal fivebrane charge, i.e. a D0-D4 bound state. We calculate the one-loop effective potential between a D0-D4 bound state and a D0-anti-D4 bound state and compare our results to a supergravity calculation. Next, we identify the tachyonic fluctuations in the D0-D4 and D0-anti-D4 system. We analyse classically the action for these tachyons and find solutions to the equations of motion corresponding to tachyon condensation.Comment: 19 page