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A New Type of Loop Equations

by Nadav Drukker , 1999
"... We derive a new form of loop equations for light-like Wilson loops. In bosonic theories those loop equations close only for straight lightlike Wilson lines. In the case of N = 1 in ten dimensions they close for any light-like Wilson loop. Upon dimensional reduction to N = 4 SYM in four dimensions, t ..."
Abstract - Cited by 2 (0 self) - Add to MetaCart
We derive a new form of loop equations for light-like Wilson loops. In bosonic theories those loop equations close only for straight lightlike Wilson lines. In the case of N = 1 in ten dimensions they close for any light-like Wilson loop. Upon dimensional reduction to N = 4 SYM in four dimensions

Exact Renormalization Group and Loop Equation

by Shinji Hirano , 1999
"... We propose a gauge invariant formulation of the exact renormalization group equation for nonsupersymmetric pure U(N) Yang-Mills theory, based on the construction by Tim Morris. In fact we show that our renormalization group equation amounts to a regularized version of the loop equation, thereby prov ..."
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We propose a gauge invariant formulation of the exact renormalization group equation for nonsupersymmetric pure U(N) Yang-Mills theory, based on the construction by Tim Morris. In fact we show that our renormalization group equation amounts to a regularized version of the loop equation, thereby

SPT-09/015 Determinantal formulae and loop equations

by M. Bergère, B. Eynard , 901
"... We prove that the correlations functions, generated by the determinantal process of the Christoffel-Darboux kernel of an arbitrary order 2 ODE, do satisfy loop equations. 1 ..."
Abstract - Cited by 7 (2 self) - Add to MetaCart
We prove that the correlations functions, generated by the determinantal process of the Christoffel-Darboux kernel of an arbitrary order 2 ODE, do satisfy loop equations. 1

Loop Equations and Virasoro Constraints in Non-perturbative 2-D Quantum Gravity

by Robbert Dijkgraaf, Herman Verlinde, Erik Verlinde , 1990
"... We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and the string equation of the one matrix model. We find that the loop equation is equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the Virasoro alg ..."
Abstract - Cited by 77 (4 self) - Add to MetaCart
We give a derivation of the loop equation for two-dimensional gravity from the KdV equations and the string equation of the one matrix model. We find that the loop equation is equivalent to an infinite set of linear constraints on the square root of the partition function satisfying the Virasoro

Macroscopic strings as heavy quarks in large N gauge theory and Anti-de Sitter supergravity

by Soo-jong Rey, Jung-tay Yee - PHYS. J. C22
"... Maldacena has put forward large N correspondence between superconformal field theories on the brane and anti-de Sitter supergravity in spacetime. We study some aspects of the correspondence between N = 4 superconformal gauge theory on D3-brane and maximal supergravity on adS5 × S5 by introducing mac ..."
Abstract - Cited by 508 (1 self) - Add to MetaCart
potential and again find agreements between the gauge theory and the supergravity results. By turning on Ramond-Ramond zero-form potential, we also study θ vacuum angle dependence of the static potential. We finally discuss dynamical realization of loop equation via turning on local electric field

Supermatrix models, loop equations, and duality

by Patrick Desrosiers, Bertrand Eynard - J. Math. Phys
"... ar ..."
Abstract - Cited by 4 (1 self) - Add to MetaCart
Abstract not found

Loop equations for the semiclassical 2-matrix model . . .

by B. Eynard , 2005
"... The 2-matrix model can be defined in a setting more general than polynomial potentials, namely, the semiclassical matrix model. In this case, the potentials are such that their derivatives are rational functions, and the integration paths for eigenvalues are arbitrary homology classes of paths for ..."
Abstract - Cited by 15 (1 self) - Add to MetaCart
for which the integral is convergent. This choice includes in particular the case where the integration path has fixed endpoints, called hard edges. The hard edges induce boundary contributions in the loop equations. The purpose of this article is to give the

Modeling and simulation of genetic regulatory systems: A literature review

by Hidde De Jong - JOURNAL OF COMPUTATIONAL BIOLOGY , 2002
"... In order to understand the functioning of organisms on the molecular level, we need to know which genes are expressed, when and where in the organism, and to which extent. The regulation of gene expression is achieved through genetic regulatory systems structured by networks of interactions between ..."
Abstract - Cited by 738 (14 self) - Add to MetaCart
DNA, RNA, proteins, and small molecules. As most genetic regulatory networks of interest involve many components connected through interlocking positive and negative feedback loops, an intuitive understanding of their dynamics is hard to obtain. As a consequence, formal methods and computer tools

Abstract loop equations, topological recursion and applications

by Nicolas Orantin
"... We formulate a notion of ”abstract loop equations”, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two hermitian matrix models, and of the Opnq model appear as sp ..."
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We formulate a notion of ”abstract loop equations”, and show that their solution is provided by a topological recursion under some assumptions, in particular the result takes a universal form. The Schwinger-Dyson equation of the one and two hermitian matrix models, and of the Opnq model appear

Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes

by M. Bershadsky, S. Cecotti, H. Ooguri, C. Vafa - Commun. Math. Phys , 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
Abstract - Cited by 540 (59 self) - Add to MetaCart
We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a
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