منابع مشابه
On Expansion and Topological Overlap
We give a detailed and easily accessible proof of Gromov’s Topological Overlap Theorem. Let X be a finite simplicial complex or, more generally, a finite polyhedral cell complex of dimension d. Informally, the theorem states that if X has sufficiently strong higher-dimensional expansion properties (which generalize edge expansion of graphs and are defined in terms of cellular cochains of X) the...
متن کاملTopological susceptibility from the overlap
The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge. Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the top...
متن کاملThe Overlap Formalism and Topological Susceptibility on the Lattice ∗
Two recent methods[1,2] for measuring the topological susceptibility, χt = 〈Q〉 V , in pure SU(2) gauge theory using the lattice regularization are considered to be in disagreement. In one method[1], the gauge fields are smoothed with an improved cooling technique while the topological charge Q is calculated using a lattice discretization. In the other method[2], inverse-blocking is employed to ...
متن کاملTopological expansion and boundary conditions
In this article, we compute the topological expansion of all possible mixed-traces in a hermitian two matrix model. In other words we give a recipe to compute the number of discrete surfaces of given genus, carrying an Ising model, and with all possible given boundary conditions. The method is recursive, and amounts to recursively cutting surfaces along interfaces. The result is best represente...
متن کاملTransiting topological sectors with the overlap
The overlap operator provides an elegant definition for the winding number of lattice gauge field configurations. Only for a set of configurations of measure zero is this procedure undefined. Without restrictions on the lattice fields, however, the space of gauge fields is simply connected. I present a simple low dimensional illustration of how the eigenvalues of a truncated overlap operator fl...
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ژورنال
عنوان ژورنال: Geometriae Dedicata
سال: 2017
ISSN: 0046-5755,1572-9168
DOI: 10.1007/s10711-017-0291-4