On the complete perturbative solution of one-matrix models
We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear group GL(N), and arbitrary correlators in the Gaussian phase...
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Elsevier
2017-08-01
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| Series: | Physics Letters B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S0370269317304574 |
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doaj-03e8c9f9a9c0469fb9671d26697502cc2020-11-24T21:23:59ZengElsevierPhysics Letters B0370-26932017-08-01771503507On the complete perturbative solution of one-matrix modelsA. Mironov0A. Morozov1Lebedev Physics Institute, Moscow 119991, Russia; ITEP, Moscow 117218, Russia; Institute for Information Transmission Problems, Moscow 127994, Russia; Corresponding author.ITEP, Moscow 117218, Russia; Institute for Information Transmission Problems, Moscow 127994, RussiaWe summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear group GL(N), and arbitrary correlators in the Gaussian phase are given by finite sums over Young diagrams of a given size, which involve also the well known characters of symmetric group. The previously known integrability and Virasoro constraints are simple corollaries, but no vice versa: complete solvability is a peculiar property of the matrix model (hypergeometric) τ-functions, which is actually a combination of these two complementary requirements.http://www.sciencedirect.com/science/article/pii/S0370269317304574 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. Mironov A. Morozov |
| spellingShingle |
A. Mironov A. Morozov On the complete perturbative solution of one-matrix models Physics Letters B |
| author_facet |
A. Mironov A. Morozov |
| author_sort |
A. Mironov |
| title |
On the complete perturbative solution of one-matrix models |
| title_short |
On the complete perturbative solution of one-matrix models |
| title_full |
On the complete perturbative solution of one-matrix models |
| title_fullStr |
On the complete perturbative solution of one-matrix models |
| title_full_unstemmed |
On the complete perturbative solution of one-matrix models |
| title_sort |
on the complete perturbative solution of one-matrix models |
| publisher |
Elsevier |
| series |
Physics Letters B |
| issn |
0370-2693 |
| publishDate |
2017-08-01 |
| description |
We summarize the recent results about complete solvability of Hermitian and rectangular complex matrix models. Partition functions have very simple character expansions with coefficients made from dimensions of representation of the linear group GL(N), and arbitrary correlators in the Gaussian phase are given by finite sums over Young diagrams of a given size, which involve also the well known characters of symmetric group. The previously known integrability and Virasoro constraints are simple corollaries, but no vice versa: complete solvability is a peculiar property of the matrix model (hypergeometric) τ-functions, which is actually a combination of these two complementary requirements. |
| url |
http://www.sciencedirect.com/science/article/pii/S0370269317304574 |
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AT amironov onthecompleteperturbativesolutionofonematrixmodels AT amorozov onthecompleteperturbativesolutionofonematrixmodels |
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