相关论文: Finiteness in N=1 SYM Theories

The concept of symmetries in physics is briefly reviewed. In the first part of these lecture notes, some of the basic mathematical tools needed for the understanding of symmetries in nature are presented, namely group theory, Lie groups and…

In this paper, we consider mixed sums of generalized polygonal numbers. Specifically, we obtain a finiteness condition for universality of such sums; this means that it suffices to check representability of a finite subset of the positive…

We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations…

In this paper we study quadratic forms which are universal when restricted to almost prime inputs, establishing finiteness theorems akin to the Conway--Schneeberger 15 theorem.

A rigorous algebraic proof of the full finiteness in all orders of perturbation theory is given for the Yang-Mills-Chern-Simons theory in a general three-dimensional Riemannian manifold. We show the validity of a trace identity, playing the…

Different notions for order convergence have been considered by various authors. Associated to every notion of order convergence corresponds a topology, defined by taking as the closed sets those subsets of the poset satisfying that no net…

We present a concept of uniform encodability of theories and develop tools related to this concept. As an application we obtain general undecidability results which are uniform for large families of structures. In the way, we define…

Recent development in numerical simulations of supersymmetric Yang-Mills (SYM) theories on the lattice is reviewed.

In a classical case, orthogonal polynomial sequences are in such a way that the $ n $th polynomial has the exact degree $n$. Such sequences are complete and form a basis of the space for any arbitrary polynomial. In this paper, we introduce…

In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals

Besides solving the spectral problem of $\mathcal{N}=4$ Super-Yang-Mills (SYM) theory, integrability also provides us with tools to compute the structure constants of the theory, most prominently through the hexagon formalism. We show that,…

We show that the relational theory of intersection types known as BCD has the finite model property; that is, BCD is complete for its finite models. Our proof uses rewriting techniques which have as an immediate by-product the polynomial…

We consider one-plaquette unitary matrix model at finite $N$ using exact expression of the partition function for both SU($N$) and U($N$) groups.

We give sufficient conditions to find all subtypes isomorphic to a subtype in a finite generalized ordered type.

N = 1, all-loop Finite Unified Theories (FUTs) are very interesting not only since they realize an old theoretical dream, but also due the remarkable predictive power of particular models as well as for providing candidates that might shed…

This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible…

The first part is expository: it explains how finite fields may be used to prove theorems on infinite fields by a reduction mod p process. The second part gives a variant of P.Smith's fixed point theorem which applies in any characteristic.

We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.

Finite Turing computation has a fundamental symmetry between inputs, outputs, programs, time, and storage space. Standard models of transfinite computational break this symmetry; we consider ways to recover it and study the resulting model…

We review the calculation and properties of the supersymmetric index for four dimensional N=1 theories, illustrating its physical significance in several examples.