Multiinstantons and multicuts
Abstract
We discuss various aspects of multiinstanton configurations in generic multicut matrix models. Explicit formulas are presented in the twocut case and, in particular, we obtain general formulas for multiinstanton amplitudes in the onecut matrix model case as a degeneration of the twocut 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 multiinstanton amplitudes can be also computed with orthogonal polynomials. As an application, we derive general expressions for multiinstanton contributions in twodimensional 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 ZZbranes, which take into full account their backreaction on the target geometry. Finally, we also derive structural properties of the transseries solution to the Painlevé I equation.
 Publication:

Journal of Mathematical Physics
 Pub Date:
 May 2009
 DOI:
 10.1063/1.3097755
 arXiv:
 arXiv:0809.2619
 Bibcode:
 2009JMP....50e2301M
 Keywords:

 11.25.Yb;
 02.40.k;
 02.10.Ud;
 02.10.De;
 04.60.m;
 M theory;
 Geometry differential geometry and topology;
 Linear algebra;
 Algebraic structures and number theory;
 Quantum gravity;
 High Energy Physics  Theory;
 Condensed Matter  Statistical Mechanics;
 Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 34 pages, 3 figures, JHEP3.cls