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A New Type of Loop Equations
, 1999
"... We derive a new form of loop equations for lightlike 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 lightlike Wilson loop. Upon dimensional reduction to N = 4 SYM in four dimensions, t ..."
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Cited by 2 (0 self)
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We derive a new form of loop equations for lightlike 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 lightlike Wilson loop. Upon dimensional reduction to N = 4 SYM in four dimensions
Exact Renormalization Group and Loop Equation
, 1999
"... We propose a gauge invariant formulation of the exact renormalization group equation for nonsupersymmetric pure U(N) YangMills 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) YangMills 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
SPT09/015 Determinantal formulae and loop equations
, 901
"... We prove that the correlations functions, generated by the determinantal process of the ChristoffelDarboux kernel of an arbitrary order 2 ODE, do satisfy loop equations. 1 ..."
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Cited by 7 (2 self)
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We prove that the correlations functions, generated by the determinantal process of the ChristoffelDarboux kernel of an arbitrary order 2 ODE, do satisfy loop equations. 1
Loop Equations and Virasoro Constraints in Nonperturbative 2D Quantum Gravity
, 1990
"... We give a derivation of the loop equation for twodimensional 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 ..."
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Cited by 77 (4 self)
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We give a derivation of the loop equation for twodimensional 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 Antide Sitter supergravity
 PHYS. J. C22
"... Maldacena has put forward large N correspondence between superconformal field theories on the brane and antide Sitter supergravity in spacetime. We study some aspects of the correspondence between N = 4 superconformal gauge theory on D3brane and maximal supergravity on adS5 × S5 by introducing mac ..."
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Cited by 508 (1 self)
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potential and again find agreements between the gauge theory and the supergravity results. By turning on RamondRamond zeroform 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
Loop equations for the semiclassical 2matrix model . . .
, 2005
"... The 2matrix 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 ..."
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Cited by 15 (1 self)
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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
 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 ..."
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Cited by 738 (14 self)
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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
"... 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 SchwingerDyson 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 SchwingerDyson equation of the one and two hermitian matrix models, and of the Opnq model appear
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 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 ..."
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Cited by 540 (59 self)
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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
Results 1  10
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