Quantum and classical aspects of deformed c = 1 strings

Nakatsu, Toshio; Takasaki, Kanehisa; Tsujimaru, S.

doi:10.1016/0550-3213(95)00131-b

Cited by 29 publications

(52 citation statements)

References 45 publications

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“…The string equation in full genus is discussed in [18]. Quite recently the string equation of the deformed c = 1 string in the black hole background is also formulated in the framework of the Toda lattice hierarchy [19].…”

Section: Introductionmentioning

confidence: 99%

Topological strings with scaling violation and Toda lattice hierarchy

Kanno

Ohta

1995

Nuclear Physics B

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We show that there is a series of topological string theories whose integrable structure is described by the Toda lattice hierarchy. The monodromy group of the Frobenius manifold for the matter sector is an extension of the affine Weyl group W (A (1) N ) introduced by Dubrovin. These models are generalizations of the topological CP 1 string theory with scaling violation. The logarithmic Hamiltonians generate flows for the puncture operator and its descendants. We derive the string equation from the constraints on the Lax and the Orlov operators. The constraints are of different type from those for the c = 1 string theory. Higher genus expansion is obtained by considering the Lax operator in matrix form.

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Section: Introductionmentioning

confidence: 99%

Topological strings with scaling violation and Toda lattice hierarchy

Kanno

Ohta

1995

Nuclear Physics B

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“…which was also obtained in [18,20]. This equation is perfectly correct but its use in reaching the density of states is limited.…”

Section: Jhep12(2006)008mentioning

confidence: 53%

“…The integrable properties of the 0A matrix model were first studied using the Toda lattice hierarchy [17] in the early '90s [18], when it was known as the deformed matrix model [19]. More recently this has been discussed by [20,21].…”

Section: Jhep12(2006)008mentioning

confidence: 99%

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Integrable deformations of hat c = 1 strings in flux backgrounds

Davis

Larsen

O’Connell

et al. 2006

J. High Energy Phys.

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We study d = 2 0A string theory perturbed by tachyon momentum modes in backgrounds with non-trivial tachyon condensate and Ramond-Ramond (RR) flux. In the matrix model description, we uncover a complexified Toda lattice hierarchy constrained by a pair of novel holomorphic string equations. We solve these constraints in the classical limit for general RR flux and tachyon condensate. Due to the non-holomorphic nature of the tachyon perturbations, the transcendental equations which we derive for the string susceptibility are manifestly non-holomorphic. We explore the phase structure and critical behavior of the theory.

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“…It has been already pointed out that at the selfdual radius, the integrable structure of the c = 1 string theory is described by the Toda lattice hierarchy [20,21,22,23] We will see that this is the case for any compactification radius. For that we will need to write explicitly the GCE partition function in terms of the eigenvalues z 1 , ...z N of the twisting matrix Ω.…”

Section: Integrability Of the Scaling Limitmentioning

confidence: 60%

Matrix model of the (1+1) dimensional dilatonic black hole in the double scaling limit

Казаков¹,

Kostov²,

Kutasov³

2000

Proceedings of Non-Perturbative Quantum Effects 2000 — PoS(tmr2000)

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We construct a large N matrix matrix model describing two-dimensional Euclidean string theory compactified on a circle of radius R and perturbed by an operator creating winding modes (vortices) on the worldsheet. The matrix model is exactly solvable and posesses an integrable structure of the infinite Toda chain hierarchy. We give explicit expressions for its free energy in the sphere-and torus approximation. A conjecture by V. Fateev, A. and Al. Zamolodchikov about the equivalence of the sine-Liouville and SL(2, R)/U (1) conformal field theories implies that for particular values of the parameters (vanishing cosmological constant µ and compactification radius R = 3 4 R KT ) the matrix model can be used to study two-dimensional string theory in the Euclidean black hole background to all orders in string perturbation theory.

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Quantum and classical aspects of deformed c = 1 strings

Cited by 29 publications

References 45 publications

Topological strings with scaling violation and Toda lattice hierarchy

Topological strings with scaling violation and Toda lattice hierarchy

Integrable deformations of hat c = 1 strings in flux backgrounds

Matrix model of the (1+1) dimensional dilatonic black hole in the double scaling limit

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