Related papers: Good Towers of Function Fields
In these 4 lectures, I give a brief introduction to the principles of effective field theory and discuss their application via 3 examples: (i) the Standard Model as an effective theory; (ii) non-linear sigma models and the composite Higgs;…
In this paper a Kummer theory of division points over rank one Drinfeld A=Fq[T]-modules defined over global function fields was given. The results are in complete analogy with the classical Kummer theory of division points over the…
We examine the motion of light fields near the bottom of a potential valley in a multi-dimensional field space. In the case of two fields we identify three general scales, all of which must be large in order to justify an effective…
Wigner's irreducible positive energy representations of the Poincare group are often used to give additional justifications for the Lagrangian quantization formalism of standard QFT. Here we study another more recent aspect. We explain in…
We describe Taylor towers for spaces of knots arising from Goodwillie-Weiss calculus of the embedding functor and extend the configuration space integrals of Bott and Taubes from spaces of knots to the stages of the towers. We show that…
Physics beyond the standard model can affect top-quark physics indirectly. We describe the effective field theory approach to describing such physics, and contrast it with the vertex-function approach that has been pursued previously. We…
In this paper we derive a recursion for the zeta function of each function field in the second Garcia-Stichtenoth tower when $q=2$. We obtain our recursion by applying a theorem of Kani and Rosen that gives information about the…
We introduce normalized Drinfeld modular curves that parameterize rank $m$ Drinfeld modules compatible with a $T$-torsion structure arising from a given conjugacy class of nilpotent upper-triangular $n\times n$ matrices with rank $\geqslant…
We observe that successive applications of known results from the theory of positive systems lead to an {\it efficient general algorithm} for positive realizations of transfer functions. We give two examples to illustrate the algorithm, one…
Manifold learning and effective model building are generally viewed as fundamentally different types of procedure. After all, in one we build a simplified model of the data, in the other, we construct a simplified model of the another…
In the theory of operads we consider functors of generalized symmetric powers defined by sums of coinvariant modules under actions of symmetric groups. One observes classically that the construction of symmetric functors provides an…
Effective field theories offer a powerful method to unify diverse models under a small set of control parameters, allowing systematic expansions around well-established theories. These techniques, developed in particle physics, were…
Fix a nonzero level $\mathfrak{n} \in \mathbb{F}_q[T]$. In this paper, we first establish a function field analogue of Ligozat's theorem, which serves as our main result and provides a criterion for Drinfeld modular units on the Drinfeld…
We give a general construction of correlation functions in rational conformal field theory on a possibly non-orientable surface with boundary in terms of 3-dimensional topological quantum field theory. The construction applies to any…
I summarize the motivation for the effective field theory approach to nuclear physics, and highlight some of its recent accomplishments. The results are compared with those computed in potential models.
We employ the effective field theory approach to analyze the characteristics of Euclidean wormholes within axion theories. Using this approach, we obtain non-perturbative instantons in various complex scalar models with and without a…
It has been common wisdom among mathematicians that Extended Topological Field Theory in dimensions higher than two is naturally formulated in terms of n-categories with n> 1. Recently the physical meaning of these higher categorical…
This is the second paper in a series of papers aimed at providing a geometric construction of modular functors and topological quantum field theories from conformal field theory building on the constructions in [TUY] and [KNTY]. We give a…
In these lectures I first explain, in a rather basic fashion, the construction of effective field theories. I then discuss some recent developments in the application of such theories to two- and three-nucleon systems.
An effective field theory approach is developed for calculating the thermodynamic properties of a field theory at high temperature $T$ and weak coupling $g$. The effective theory is the 3-dimensional field theory obtained by dimensional…