We establish an exact isomorphism between self-avoiding branched polymers in D + 2 continuum dimensions and the hard-core continuum gas at negative activity. We review conjectures and results on critical exponents for D + 2 = 2, 3, 4 and show that they are corollaries of our result. We explain the connection (first proposed by Parisi and Sourlas) between branched polymers in D + 2 dimensions an...

We elaborate an explicit example of dimensional reduction of the free massless Dirac operator with SU(3)-symmetry, defined on 12-dimensional manifold, which is the total space of principle SU(3)-bundle over 4-dimensional manifold. It turns out that after the dimensional reduction we obtain the “usual” Dirac operator, defined on 4-dimensional pseudo-Riemannian (non-flat) manifold but with mass t...

The requirement that physical phenomena associated with gravitational collapse should be duly reconciled with the postulates of quantum mechanics implies that at a Planckian scale our world is not 3+1 dimensional. Rather, the observable degrees of freedom can best be described as if they were Boolean variables defined on a two-dimensional lattice, evolving with time. This observation, deduced f...

A 3D-2D dimensional reduction analysis for supremal functionals is performed in the realm of Γ-convergence. We show that the limit functional still admits a supremal representation, and we provide a precise identification of its density in some particular cases. Our results rely on an abstract representation theorem for the Γ-limit of a family of supremal functionals. Mathematics Subject Classi...

There has been increased interest recently in feedback methods for reliable , robust, eecient computational methods in mechanics. We will outline the construction of such methods for a class of problems describing bending of plates for certain classes of loads. We emphasize the theoretical performance of this method, such as the selection of basis functions in the dimensional reduction { ensuri...

The dual theory describing the 4D Coulomb gas of point-like magnetically charged objects, which confines closed electric strings, is considered. The respective generalization of the theory of confining strings to confining membranes is further constructed. The same is done for the analogous SU(3)-inspired model. We then consider a combined model which confines both electric charges and closed s...

We consider the application of regularization by dimensional reduction to NLO corrections of hadronic processes. The general collinear singularity structure is discussed, the origin of the regularization-scheme dependence is identified and transition rules to other regularization schemes are derived. PACS: 11.10.Gh, 11.15.-q, 12.38.Bx, 12.60.Jv

We perform a generalised Scherk-Schwarz reduction of the effective action of the het-erotic string on T 6 to obtain a massive N = 4 supergravity theory in four dimensions. The local symmetry-group of the resulting d = 4 theory includes a Heisenberg group, which is a subgroup of the global O(6, 6 + n) obtained in the standard reduction. We show explicitly that the same theory can be obtained by ...

Abstract: The issue related to the so-called dimensional reduction procedure is revisited within the Euclidean formalism. First, it is shown that for symmetric spaces, the local exact heatkernel density is equal to the reduced one, once the harmonic sum has been successfully performed. In the general case, due to the impossibility to deal with exact results, the short t heat-kernel asymptotics ...

This paper is the first in a series of three, which analyze an adaptive approximate approach for solving (n + 1 (-dimensional boundary value problems by replacing them with systems of equations in n-dimensional space. In this approach the unknown functions of (n + 1) variables are projected onto finite linear combinations of functions of just n variables. This paper shows how the coefficients o...