Random super matrices with an external source

Autor: Shinobu Hikami, Edouard Brézin
Přispěvatelé: Laboratoire de Physique Théorique de l'ENS (LPTENS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Théorique de l'ENS ( LPTENS ), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris ( FRDPENS ), Centre National de la Recherche Scientifique ( CNRS ) -École normale supérieure - Paris ( ENS Paris ) -Centre National de la Recherche Scientifique ( CNRS ) -École normale supérieure - Paris ( ENS Paris ) -Université Pierre et Marie Curie - Paris 6 ( UPMC ) -Centre National de la Recherche Scientifique ( CNRS )
Rok vydání: 2018
Předmět:
Surface (mathematics)
High Energy Physics - Theory
Nuclear and High Energy Physics
Pure mathematics
n-point function
Gaussian
[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]
Duality (optimization)
FOS: Physical sciences
01 natural sciences
010305 fluids & plasmas
[ PHYS.HTHE ] Physics [physics]/High Energy Physics - Theory [hep-th]
Superspaces
symbols.namesake
Matrix (mathematics)
Mathematics - Algebraic Geometry
Intersection
0103 physical sciences
FOS: Mathematics
surface
lcsh:Nuclear and particle physics. Atomic energy. Radioactivity
U(N|M)
010306 general physics
Algebraic Geometry (math.AG)
Eigenvalues and eigenvectors
Mathematical Physics
Physics
Matrix Models
[PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]
matrix model: random
Mathematical Physics (math-ph)
boundary condition
Moduli space
High Energy Physics - Theory (hep-th)
Topological Field Theories
symbols
lcsh:QC770-798
moduli space
duality
[ PHYS.MPHY ] Physics [physics]/Mathematical Physics [math-ph]
Kontsevich model
Random matrix
Zdroj: JHEP
JHEP, 2018, 08, pp.086. ⟨10.1007/JHEP08(2018)086⟩
Journal of High Energy Physics
Journal of High Energy Physics, Springer, 2018, 08, pp.086. ⟨10.1007/JHEP08(2018)086⟩
Journal of High Energy Physics, Vol 2018, Iss 8, Pp 1-12 (2018)
ISSN: 1126-6708
1029-8479
DOI: 10.48550/arxiv.1805.04240
Popis: In the past we have considered Gaussian random matrix ensembles in the presence of an external matrix source. The reason was that it allowed, through an appropriate tuning of the eigenvalues of the source, to obtain results on non-trivial dual models, such as Kontsevich's Airy matrix models and generalizations. The techniques relied on explicit computations of the k-point functions for arbitrary N (the size of the matrices) and on an N-k duality. Numerous results on the intersection numbers of the moduli space of curves were obtained by this technique. In order to generalize these results to include surfaces with boundaries, we have extended these techniques to supermatrices. Again we have obtained quite remarkable explicit expressions for the k-point functions, as well as a duality. Although supermatrix models a priori lead to the same matrix models of 2d-gravity, the external source extensions considered in this article lead to new geometric results.
Comment: 12 pages
Databáze: OpenAIRE
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