Two-dimensional gauge theories of the symmetric group Sn and branched n-coverings of Riemann surfaces in the large-n limit

D’Adda, A.; Provero, Paolo

doi:10.1016/s0920-5632(02)01308-7

Cited by 4 publications

(3 citation statements)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Since ramified S(N )-bundles are in bijection with ramified coverings with N sheets, one recovers the link explained by A. D'Adda and P. Provero in [9] and [10] between S(N )-Yang-Mills measure and random branched S(N ) coverings. It has to be noticed that this link is different from the U (N )-Yang-Mills measure/ramified coverings partly explained in [19] and also known as the Yang-Mills/String duality.…”

Section: Intoductionsupporting

confidence: 68%

A combinatorial theory of random matrices III: random walks on $\mathfrak{S}(N)$, ramified coverings and the $\mathfrak{S}(\infty)$ Yang-Mills measure

Gabriel

2015

Preprint

View full text Add to dashboard Cite

The aim of this article is to study some asymptotics of a natural model of random ramified coverings on the disk of degree N . We prove that the monodromy field, called also the holonomy field, converges in probability to a non-random continuous field as N goes to infinity. In order to do so, we use the fact that the monodromy field of random uniform labelled simple ramified coverings on the disk of degree N has the same law as the S(N )-Yang-Mills measure associated with the random walk by transpositions on S(N ).This allows us to restrict our study to random walks on S(N ): we prove theorems about asymptotics of random walks on S(N ) in a new framework based on the geometric study of partitions and the Schur-Weyl-Jones's dualities. In particular, given a sequence of conjugacy classes (λN ⊂ S(N )) N∈N , we define a notion of convergence for (λN ) N∈N which implies the convergence in non-commutative distribution and in P-distribution of the λN -random walk to a multiplicative P-Lévy process. This limiting process is shown not to be a free multiplicative Lévy process and we compute its log-cumulant transform. We give also a criterion on (λN ) N∈N in order to know if the limit is random or not.

show abstract

Section: Intoductionsupporting

confidence: 68%

A combinatorial theory of random matrices III: random walks on $\mathfrak{S}(N)$, ramified coverings and the $\mathfrak{S}(\infty)$ Yang-Mills measure

Gabriel

2015

Preprint

View full text Add to dashboard Cite

show abstract

“…This question has been addressed in recent interesting papers [46,47] It is also interesting to ask whether the phase transition that we have identified is related to recent work which studied phase transitions for statistical systems of random walks on discrete groups like the permutation group. [48,49]…”

Section: Discussionmentioning

confidence: 99%

Matrix Model Thermodynamics

Semenoff¹

2004

Quantum Theory and Symmetries

View full text Add to dashboard Cite

Some recent work on the thermodynamic behavior of the matrix model of M-theory on a pp-wave background is reviewed. We examine a weak coupling limit where computations can be done explicitly. In the large N limit, we find a phase transition between two distinct phases which resembles a "confinement-deconfinement" transition in gauge theory and which we speculate must be related to a geometric transition in M-theory. We review arguments that the phase transition is also related to the Hagedorn transition of little string theory in a certain limit of the 5-brane geometry.

show abstract

“…The S n lattice gauge theory perspective for U(N) gauge theory at large N is emphasized in [30]. Computations of 2dYM partition functions for general Riemann surfaces with boundaries expressed in the symmetric group basis, and the connection with Hurwitz space counting is given in [4,6,26].…”

Section: 2mentioning

confidence: 99%

Strings from Feynman graph counting: Without largeN

Koch

Ramgoolam²

2012

Phys. Rev. D

View full text Add to dashboard Cite

A well-known connection between n strings winding around a circle and permutations of n objects plays a fundamental role in the string theory of large N two dimensional Yang Mills theory and elsewhere in topological and physical string theories. Basic questions in the enumeration of Feynman graphs can be expressed elegantly in terms of permutation groups. We show that these permutation techniques for Feynman graph enumeration, along with the Burnside counting lemma, lead to equalities between counting problems of Feynman graphs in scalar field theories and Quantum Electrodynamics with the counting of amplitudes in a string theory with torus or cylinder target space. This string theory arises in the large N expansion of two dimensional Yang Mills and is closely related to lattice gauge theory with S n gauge group. We collect and extend results on generating functions for Feynman graph counting, which connect directly with the string picture. We propose that the connection between string combinatorics and permutations has implications for QFT-string dualities, beyond the framework of large N gauge theory.1 robert@neo.phys.wits.ac.za

show abstract

Two-dimensional gauge theories of the symmetric group Sn and branched n-coverings of Riemann surfaces in the large-n limit

Cited by 4 publications

References 14 publications

A combinatorial theory of random matrices III: random walks on $\mathfrak{S}(N)$, ramified coverings and the $\mathfrak{S}(\infty)$ Yang-Mills measure

A combinatorial theory of random matrices III: random walks on $\mathfrak{S}(N)$, ramified coverings and the $\mathfrak{S}(\infty)$ Yang-Mills measure

Matrix Model Thermodynamics

Strings from Feynman graph counting: Without largeN

Contact Info

Product

Resources

About