We clarify some peculiar aspects of the perturbative expansion around a classical fuzzy-sphere solution in matrix models with a cubic term. While the effective action in the large-N limit is saturated at the one-loop level, we find that the “one-loop dominance” does not hold for generic observables due to one-particle reducible diagrams. However, we may exploit the one-loop dominance for the ef...

The nonperturbative aspects of string theory are explored for noncritical string in two distinct formulations, loop equations and matrix models. The effects corresponding to the D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations cannot. This imp...

We find soliton-like solutions in a particular case of non-abelian loop Toda equations associated with general linear groups. We use the formalism of rational dressing based on appropriate block-matrix representation suggested by the Z-gradation under consideration. We present solutions in a form of a direct matrix generalization of the Hirota’s soliton constructions already well-known for the ...

We find new solutions, including soliton-like ones, for a special case of nonAbelian loop Toda equations associated with complex general linear groups. We use the method of rational dressing based on an appropriate block-matrix representation suggested by the Z-gradation under consideration. We present solutions in a form of a direct matrix generalization of the Hirota’s soliton solution alread...

We consider membranes of spherical topology in uncompactified Matrix theory. In general for large membranes Matrix theory reproduces the classical membrane dynamics up to 1/N corrections; for certain simple membrane configurations, the equations of motion agree exactly at finite N . We derive a general formula for the one-loop Matrix potential between two finite-sized objects at large separatio...

In recent years, several matrix-valued subdivisions have been proposed for triangular meshes. The matrix-valued subdivisions can simulate and extend the traditional scalar-valued subdivision, such as loop and 3 subdivision. In this paper, we study how to construct the matrix-valued subdivision wavelets, and propose the novel biorthogonal wavelet based on matrix-valued subdivisions on multiresol...

We extend earlier schemes for merging tree-level matrix elements with parton showers to include also merging with one-loop matrix elements. In this paper we make a first study on how to include one-loop corrections, not only for events with a given jet multiplicity, but simultaneously for several different jet multiplicities. Results are presented for the simplest non-trivial case of hadronic e...

We study the new boundary condition of the O(n) model proposed by Jacobsen and Saleur using the matrix model. The spectrum of boundary operators and their conformal weights are obtained by solving the loop equations. Using the diagrammatic expansion of the matrix model as well as the loop equations, we make an explicit correspondence between the new boundary condition of the O(n) model and the ...

The nonperturbative aspects of string theory are explored for noncritical string in two distinct formulations, loop equations and matrix models. The effects corresponding to the D-brane in these formulations are especially investigated in detail. It is shown that matrix models can universally yield a definite value of the chemical potential for an instanton while loop equations cannot. This imp...

Loop equations of matrix models express the invariance of the models under field redefinitions. We use loop equations to prove that it is possible to define continuum times for the generic hermitian 1-matrix model such that all correlation functions in the double scaling limit agree with the corresponding correlation functions of the Kontsevich model expressed in terms of kdV times. In addition...