## 10 Citations

### Four Chapters on Low-Dimensional Gauge Theories

- Mathematics
- 2015

This is the written version of a set of four lectures given at the CIB in Lausanne in April 2015. The aim of these lectures was to present some of the mathematical-physical ideas underlying…

### The $1/N$ expansion for SO(N) lattice gauge theory at strong coupling

- Mathematics, Physics
- 2016

The $1/N$ expansion is an asymptotic series expansion for certain quantities in large-$N$ lattice gauge theories. This article gives a rigorous formulation and proof of the $1/N$ expansion for Wilson…

### Wilson loop expectations in $SU(N)$ lattice gauge theory

- Physics
- 2016

This article gives a rigorous formulation and proof of the $1/N$ expansion for Wilson loop expectations in strongly coupled $SU(N)$ lattice gauge theory in any dimension. The coefficients of the…

### Yang–Mills for Probabilists

- MathematicsProbability and Analysis in Interacting Physical Systems
- 2019

The rigorous construction of quantum Yang-Mills theories, especially in dimension four, is one of the central open problems of mathematical physics. Construction of Euclidean Yang-Mills theories is…

### A stochastic analysis approach to lattice Yang--Mills at strong coupling

- Mathematics
- 2022

. We develop a new stochastic analysis approach to the lattice Yang–Mills model at strong coupling in any dimension d > 1, with t’ Hooft scaling βN for the inverse coupling strength. We study their…

### Canonical quantization of 1+1-dimensional Yang-Mills theory: An operator-algebraic approach

- Mathematics
- 2019

We present a mathematically rigorous canonical quantization of Yang-Mills theory in 1+1 dimensions (YM$_{1+1}$) by operator-algebraic methods. The latter are based on Hamiltonian lattice gauge theory…

### Yang–Mills Measure and the Master Field on the Sphere

- MathematicsCommunications in Mathematical Physics
- 2020

We study the Yang–Mills measure on the sphere with unitary structure group. In the limit where the structure group has high dimension, we show that the traces of loop holonomies converge in…

### Yang–Mills Measure on the Two-Dimensional Torus as a Random Distribution

- MathematicsCommunications in Mathematical Physics
- 2019

We introduce a space of distributional 1-forms $$\Omega ^1_\alpha $$Ωα1 on the torus $$\mathbf {T}^2$$T2 for which holonomies along axis paths are well-defined and induce Hölder continuous functions…

### What is a random surface?

- Mathematics
- 2022

Given 2n unit equilateral triangles, there are finitely many ways to glue each edge to a partner. We obtain a random sphere-homeomorphic surface by sampling uniformly from the gluings that produce a…

### A Functional Integral Approaches to the Makeenko–Migdal Equations

- MathematicsCommunications in Mathematical Physics
- 2019

Makeenko and Migdal (1979) gave heuristic identities involving the expectation of the product of two Wilson loop functionals associated to splitting a single loop at a self-intersection point.…

## References

SHOWING 1-10 OF 66 REFERENCES

### Ultraviolet stability of three-dimensional lattice pure gauge field theories

- Physics
- 1985

We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on…

### Ultraviolet Stability of Three-Dimensional Lattice Pure Gauge Field Theories *

- Physics
- 2005

We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on…

### The variational problem and background fields in renormalization group method for lattice gauge theories

- Physics, Mathematics
- 1985

We consider the action of a lattice gauge theory on a space of regular gauge field configurations with fixed averages, and we prove that there exists a minimum of this action. The minimum is unique…

### The U(1) Higgs model

- Physics
- 1986

By using rigorous renormalization group methods we construct the continuum limit of the finite-volume lattice U(1) Higgs model in two and three dimensions. The method relies on a proof of the…

### Convergent renormalization expansions for lattice gauge theories

- Physics
- 1988

In this paper we introduce an inductive description of the complete effective densities including large field domains, and we show that the renormalization transformations preserve the form of the…

### Propagators and renormalization transformations for lattice gauge theories. I

- Physics
- 1984

Lattice gauge theories may be looked at as perturbations of the theory of a vector field with a Gaussian action. We study this theory here and in following papers obtaining crucial results for…

### On the construction of quantized gauge fields

- Mathematics
- 1980

In this paper the construction of the two-dimensional abelian Higgs model begun in two earlier articles is completed. First we show how to remove the remaining ultraviolet cutoff on the gauge field,…

### Exact computation of loop averages in two-dimensional Yang-Mills theory

- Mathematics
- 1980

We present an explicit algorithm that allows the exact computation of all nonlocal gauge-invariant correlation functions in two-dimensional Yang-Mills theory. Explicit expressions are given for the…

### Renormalization group approach to lattice gauge field theories

- Physics
- 1987

We study four-dimensional pure gauge field theories by the renormalization group approach. The analysis is restricted to small field approximation. In this region we construct a sequence of localized…

### Large field renormalization. I. The basic step of the ℝ operation

- Physics
- 1989

We construct the renormalization operation of the expressions connected with the large field regions. This operation, denoted by ℝ, removes the main obstacle to prove the ultraviolet stability of…