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Abstract
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We compute the large
limit of several objects related to the two-dimensional Euclidean
Yang–Mills measure on closed, connected, orientable surfaces
with
genus
,
when a structure group is taken among the classical groups of order
. We
first generalise to all classical groups the convergence of partitions functions obtained
by the second author for unitary groups. We then apply this result to prove
convergence of Wilson loop observables for loops included within a topological disc of
. This
convergence solves a conjecture of B. Hall and shows moreover that the limit is independent of
the topology of
and is equal to an evaluation of the planar master field. Using similar arguments, we
show that Wilson loops vanish asymptotically for all noncontractible simple
loops.
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Keywords
two-dimensional Yang–Mills measure, Wilson loops, master
field, random matrices
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Mathematical Subject Classification
Primary: 60B15, 60B20, 60K35, 81T13, 81T32
Secondary: 46L54, 57R56, 60D05
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Milestones
Received: 6 April 2022
Revised: 7 May 2023
Accepted: 7 June 2023
Published: 29 November 2023
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© 2023 MSP (Mathematical Sciences
Publishers). |
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