2008/09/30 by Marcos Mariño, Marcos Marino, Ricardo Schiappa +1 · 5 citations
Mathematics · Physics and Astronomy · #Amplitude #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Instanton #Matrix (chemical analysis) #Noncommutative and Quantum Gravity Theories #Partition (number theory) #Partition function (quantum field theory) #Quantum #Quantum field theory #String (physics) #cond-mat.stat-mech #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1063/1.3097755
published as J.Math.Phys.50:052301,2009 · 34 pages, 3 figures, JHEP3.cls; v2: added references, minor changes; v3: added 1 reference, more minor changes, final version for JMP; v4: more typos corrected
arxiv created 2009/03/17 · openalex publication_date 2009/05/01 · arxiv updated 2011/11/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We discuss various aspects of multi-instanton configurations in generic multicut matrix models. Explicit formulas are presented in the two-cut case and, in particular, we obtain general formulas for multi-instanton amplitudes in the one-cut matrix model case as a degeneration of the two-cut case. These formulas show that the instanton gas is ultradilute due to the repulsion among the matrix model eigenvalues. We exemplify and test our general results in the cubic matrix model, where multi-instanton amplitudes can be also computed with orthogonal polynomials. As an application, we derive general expressions for multi-instanton contributions in two-dimensional quantum gravity, verifying them by computing the instanton corrections to the string equation. The resulting amplitudes can be interpreted as regularized partition functions for multiple ZZ-branes, which take into full account their backreaction on the target geometry. Finally, we also derive structural properties of the trans-series solution to the Painlevé I equation.