Two dimensional Yang-Mills theory via stochastic differential equations

Gross, Leonard; King, Christopher; Sengupta, Ambar N.

doi:10.1016/0003-4916(89)90032-8

Cited by 76 publications

(60 citation statements)

References 26 publications

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“…This result is agreement with the results obtained by Bralic, 5 Gross et al 4 and Klimek et al and Kazakov. 28 However, even for this special case, our method of arriving at the result is different.…”

Section: ͑Iv14͒supporting

confidence: 93%

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SU( N ) Quantum Yang–Mills theory in two dimensions: A complete solution

Ashtekar

Lewandowski

Marolf

et al. 1997

Journal of Mathematical Physics

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A closed expression of the Euclidean Wilson-loop functionals is derived for pure Yang-Mills continuum theories with gauge groups SU(N) and U(1) and spacetime topologies R 1 ϫR 1 and R 1 ϫS 1 . ͑For the U(1) theory, we also consider the S 1 ϫS 1 topology.͒ The treatment is rigorous, manifestly gauge invariant, manifestly invariant under area preserving diffeomorphisms and handles all ͑piecewise analytic͒ loops in one stroke. Equivalence between the resulting Euclidean theory and and the Hamiltonian framework is then established. Finally, an extension of the Osterwalder-Schrader axioms for gauge theories is proposed. These axioms are satisfied in the present model.

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Section: ͑Iv14͒supporting

confidence: 93%

“…͑See also Refs. 2, 3.͒ Similarly, Gross and co-authors 4 have used stochastic methods to obtain closed expressions for non-overlapping Wilson loops. While these methods have yielded a wealth of insights, to the best of our knowledge, a closed expression for generic Wilson loops has not yet appeared in the literature.…”

Section: Introductionmentioning

confidence: 99%

SU( N ) Quantum Yang–Mills theory in two dimensions: A complete solution

Ashtekar

Lewandowski

Marolf

et al. 1997

Journal of Mathematical Physics

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“…The following result (Gross et al [5] and Driver [4]) summarizes the main facts about stochastic holonomy under the Yang-Mills measure:…”

Section: Stochastic Holonomymentioning

confidence: 95%

“…where we used (5). Note that h(t) is the holonomy of the loop which travels up from o along the y-axis to (0, y(0)), then proceeds along the path s → s, y(s) up to time t, then travels down parallel to the y-axis till hits y = 0, and then returns to the origin along the x-axis.…”

Section: Parallel Transport and Holonomymentioning

confidence: 99%

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The Large-N Yang-Mills Field on the plane and free noise

Sengupta¹

2008

AIP Conference Proceedings

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SO(N) Lattice Gauge Theory, planar and beyond

Basu

Ganguly

2018

Comm Pure Appl Math

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Lattice gauge theories have been studied in the physics literature as discrete approximations to quantum Yang-Mills theory for a long time. Primary statistics of interest in these models are expectations of the so-called Wilson loop variables. In this article we continue the program initiated by Chatterjee [3] to understand Wilson loop expectations in lattice gauge theories in a certain limit through gauge-string duality. The objective in this paper is to better understand the underlying combinatorics in the strong coupling regime by giving a more geometric picture of string trajectories involving correspondence to objects such as decorated trees and noncrossing partitions. Using connections with free probability theory, we provide an elaborate description of loop expectations in the planar setting, which provides certain insights into structures of higher-dimensional trajectories as well. Exploiting this, we construct an example showing that in any dimension, the Wilson loop area law lower bound does not hold in full generality.

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Two dimensional Yang-Mills theory via stochastic differential equations

Cited by 76 publications

References 26 publications

SU( N ) Quantum Yang–Mills theory in two dimensions: A complete solution

SU( N ) Quantum Yang–Mills theory in two dimensions: A complete solution

The Large-N Yang-Mills Field on the plane and free noise

SO(N) Lattice Gauge Theory, planar and beyond

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