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Two-dimensional QCD on the sphere and on the cylinder
High Energy Physics - Theory · Submitted 20 Sep 1993
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Using this language, we derive some new results: we give an alternative description of the Douglas-Kazakov phase transition on the sphere, and we argue that an analogous phase transition exists on the cylinder.
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The abstract, sentence by sentence
The partition functions of QCD2 on simple surfaces admit representations in terms of exponentials of the inverse coupling, that are modular transforms of the usual character expansions. We review the construction of such a representation in the case of the cylinder, and show how it leads to a formulation of QCD2 as a $c=1$ matrix model of the Kazakov-Migdal type. The eigenvalues describe the positions of $N$ Sutherland fermions on a circle, while their discretized momenta label the representations in the corresponding character expansion. Using this language, we derive some new results: we give an alternative description of the Douglas-Kazakov phase transition on the sphere, and we argue that an analogous phase transition exists on the cylinder. We calculate the large $N$ limit of the partition function on the cylinder with boundary conditions given by semicircular distributions of eigenvalues, and we find an explicit expression for the large $N$ limit of the Itzykson-Zuber integral with the same boundary conditions. (Talk given at the ``Workshop on high energy physics and cosmology'' at Trieste, July 1993.)
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The partition functions of QCD2 on simple surfaces admit representations in terms of exponentials of the inverse coupling, that are modular transforms of the usual character expansions. | background 0.94 | 0.18 | 0.16 | asserted 1.00 |
| s1 | We review the construction of such a representation in the case of the cylinder, and show how it leads to a formulation of QCD2 as a $c=1$ matrix model of the Kazakov-Migdal type. | contribution 0.81 | 0.77 | 0.20 | asserted 1.00 |
| s2 | The eigenvalues describe the positions of $N$ Sutherland fermions on a circle, while their discretized momenta label the representations in the corresponding character expansion. | interpretation 0.52 | 0.33 | 0.07 | asserted 1.00 |
| s3 | Using this language, we derive some new results: we give an alternative description of the Douglas-Kazakov phase transition on the sphere, and we argue that an analogous phase transition exists on the cylinder. | result 0.61 | 0.95 | 0.46 | asserted 0.57 |
| s4 | We calculate the large $N$ limit of the partition function on the cylinder with boundary conditions given by semicircular distributions of eigenvalues, and we find an explicit expression for the large $N$ limit of the Itzykson-Zuber integral with the same boundary conditions. | result 0.93 | 0.95 | 0.18 | asserted 1.00 |
| s5 | (Talk given at the ``Workshop on high energy physics and cosmology'' at Trieste, July 1993.) | background 0.98 | 0.04 | 0.01 | unclear 0.86 |
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The paper
Original abstract
The partition functions of QCD2 on simple surfaces admit representations in terms of exponentials of the inverse coupling, that are modular transforms of the usual character expansions. We review the construction of such a representation in the case of the cylinder, and show how it leads to a formulation of QCD2 as a $c=1$ matrix model of the Kazakov-Migdal type. The eigenvalues describe the positions of $N$ Sutherland fermions on a circle, while their discretized momenta label the representations in the corresponding character expansion. Using this language, we derive some new results: we give an alternative description of the Douglas-Kazakov phase transition on the sphere, and we argue that an analogous phase transition exists on the cylinder. We calculate the large $N$ limit of the partition function on the cylinder with boundary conditions given by semicircular distributions of eigenvalues, and we find an explicit expression for the large $N$ limit of the Itzykson-Zuber integral with the same boundary conditions. (Talk given at the ``Workshop on high energy physics and cosmology'' at Trieste, July 1993.)
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4 arXiv papers cite this in 5 sentences
Papers citing it · 4 sentences without a confident label
Cites it as background 1 paper
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New light on this phenomenon was shed in [ref] , where Yang–Mills theory on the two-sphere was reformulated as a nonrelativistic fermionic system, and from the interpretation of the theory as a string theory, by expressing the partition function as a weighted sum over maps from a two-dimensional worldsheet into the manifold [ref] (see also the review [ref] and the recent [ref] ).
Large $N$ phase transition in $T \overline{T}$-deformed $2d$ Yang-Mills theory on the sphere · Two-dimensional Yang–Mills theory and its $TT$ -deformation · 0.95
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