Topological strings, matrix integrals, and singularity theory

Nakatsu, Toshio; Kato, Atsushi; Noumi, Masatoshi; Takebe, Takashi

doi:10.1016/0370-2693(94)91106-1

Cited by 11 publications

(13 citation statements)

References 18 publications

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“…For this homogeneous solution, we can write the F -function in terms of the β-periods of the differentials dz i , dΩ ∞,n and dΩ ∞,n as follows. First notice that by homogeneity relation (17) and definition of F -function (14), F can be written as a sum of periods and residues of dS…”

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confidence: 99%

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Whitham-Toda Hierarchy and N=2 Supersymmetric Yang-Mills Theory

1996

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The exact solution of N = 2 supersymmetric SU (N ) Yang-Mills theory is studied in the framework of the Whitham hierarchies. The solution is identified with a homogeneous solution of a Whitham hierarchy. This integrable hierarchy (Whitham-Toda hierarchy) describes modulation of a quasi-periodic solution of the (generalized) Toda lattice hierarchy associated with the hyperelliptic curves over the quantum moduli space. The relation between the holomorphic pre-potential of the low energy effective action and the τ function of the (generalized) Toda lattice hierarchy is also clarified. †

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confidence: 99%

“…Hence constraints (35) now become precisely same as those on the free energy of the A N −1 topological string (in spherical limit) [16], [17]. In this topological string theory, time variables such as T n play the role of coupling constants of the chiral primary fields or their gravitational descendants.…”

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confidence: 99%

Whitham-Toda Hierarchy and N=2 Supersymmetric Yang-Mills Theory

1996

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“…Notice that relation (42) is now translated to the adjoint action of g on the relativistic fermions ψ q and ψ * q . Nextly let us consider the asymptotic forms of operators B n andB n (12). From the definitions of these operators (11) their actions on the nonrelativistic fermions are…”

Section: Euclidean Stringsmentioning

confidence: 99%

“…where 0 ≤ k ≤ p −1. The partition function of this model is given by a generalized matrix Airy function [10], [11] and several topological aspects appear through the asymptotic expansion of this function [10], [12]. This matrix integral representation of (p, 1) string…”

Section: Introductionmentioning

confidence: 99%

Quantum and classical aspects of deformed c = 1 strings

1995

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The quantum and classical aspects of a deformed c = 1 matrix model proposed by Jevicki and Yoneya are studied. String equations are formulated in the framework of the Toda lattice hierarchy. The Whittaker functions now play the role of generalized Airy functions in c < 1 strings. This matrix model has two distinct parameters. Identification of the string coupling constant is thereby not unique, and leads to several different perturbative interpretations of this model as a string theory. Two such possible interpretations are examined. In both cases, the classical limit of the string equations, which turns out to give a formal solution of Polchinski's scattering equations, shows that the classical scattering amplitudes of massless tachyons are insensitive to deformations of the parameters in the matrix model. †

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“…Theh−dependent term in (33) is crucial for the matrix integral realization of this topological string [5], [15]. And also, from the analysis of the above equation (33) some geometrical nature of the topological string has been revealed through the "genus expansion" [15]. Thus we can also expect that some geometry of c = 1 string theory appears from the study of the characteristic relations (29) and (31).This study will be reported elsewhere.…”

Section: Commentmentioning

confidence: 99%

ON THE STRING EQUATION AT c=1

Nakatsu

1994

Mod. Phys. Lett. A

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The analogue of the string equation which specifies the partition function of c = 1 string with a compactification radius β ∈ Z ≥1 is described in the framework of the Toda lattice hierarchy. 1Recently much attention has been paid to the understanding of c = 1 string theory from the view of integrable hierarchy. In paticular the tachyon dynamics of the theory has been described in the framework of the (dispersionless) Toda lattice hierarchy [1],[2], [3]. In spite of these developments our understanding of the nonperturbative aspects for c = 1 string still has a gap from that of non-critical string theory. In the non-critical string theory the full partition function is the τ function of Kadomtsev-Petriashivil (KP) hierarchy specified by the solution of string equation [4] : [ P, Q ] = 1 where P, Q are differential operators. These pairs can be given in terms of the Lax and Orlov operators of KP hierarchy [5]. On the other hand, even in the framework of the Toda lattice (TL) hierarchy, the analogue of the string equation at c = 1 has not been clarified yet. In this letter, by utilizing the concepts of these integrable hierarchies, we try to obtain this nonperturbative counterpart which characterizes the generating function for the tachyon correlation functions of c = 1 string with a compactification radius β ∈ Z ≥1 .

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Topological strings, matrix integrals, and singularity theory

Cited by 11 publications

References 18 publications

Whitham-Toda Hierarchy and N=2 Supersymmetric Yang-Mills Theory

Whitham-Toda Hierarchy and N=2 Supersymmetric Yang-Mills Theory

Quantum and classical aspects of deformed c = 1 strings

ON THE STRING EQUATION AT c=1

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