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183
The dS/CFT correspondence
- JHEP
, 2001
"... A holographic duality is proposed relating quantum gravity on dSD (D-dimensional de Sitter space) to conformal field theory on a single SD−1 ((D-1)-sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I + (the future bou ..."
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Cited by 196 (7 self)
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A holographic duality is proposed relating quantum gravity on dSD (D-dimensional de Sitter space) to conformal field theory on a single SD−1 ((D-1)-sphere), in which bulk de Sitter correlators with points on the boundary are related to CFT correlators on the sphere, and points on I + (the future boundary of dSD) are mapped to the antipodal points on SD−1 relative to those on I −. For the case of dS3, which is analyzed in some detail, the central charge of the CFT2 is computed in an analysis of the asymptotic symmetry group at I ±. This dS/CFT proposal is supported by the computation of correlation functions of a massive scalar field. In general the dual CFT may be non-unitary and (if for example there are sufficently massive stable scalars) contain complex conformal weights. We also consider the physical region O − of dS3 corresponding to the causal past of a timelike observer, whose holographic dual lives on a plane rather than a sphere. O − can be foliated by asymptotically flat spacelike slices. Time evolution along these slices is generated by
Strings from tachyons: The c = 1 matrix reloaded
- JHEP
"... We propose a new interpretation of the c=1 matrix model as the world-line theory of N unstable D-particles, in which the hermitian matrix is provided by the non-abelian open string tachyon. For D-particles in 1+1-d string theory, we find a direct quantitative match between the closed string emission ..."
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Cited by 130 (1 self)
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We propose a new interpretation of the c=1 matrix model as the world-line theory of N unstable D-particles, in which the hermitian matrix is provided by the non-abelian open string tachyon. For D-particles in 1+1-d string theory, we find a direct quantitative match between the closed string emission due to a rolling tachyon and that due to a rolling eigenvalue in the matrix model. We explain the origin of the double-scaling limit, and interpret it as an extreme representative of a large equivalence class of dual theories. Finally, we define a concrete decoupling limit of unstable D-particles in IIB string theory that reduces to the c=1 matrix model, suggesting that The duality between open and closed string theory has led to various deep and surprising insights into the fundamental structure of both systems. A relatively recent, but still incompletely understood, example of such a duality is Sen’s observation that unstable D-branes can completely decay into closed strings via open string tachyon condensation [1]. Both the full time
Liouville bootstrap via harmonic analysis on a noncompact quantum group
"... Abstract. The purpose of this short note is to announce results that amount to a verification of the bootstrap for Liouville theory in the generic case under certain assumptions concerning existence and properties of fusion transformations. Under these assumptions one may characterize the fusion and ..."
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Cited by 93 (12 self)
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Abstract. The purpose of this short note is to announce results that amount to a verification of the bootstrap for Liouville theory in the generic case under certain assumptions concerning existence and properties of fusion transformations. Under these assumptions one may characterize the fusion and braiding coefficients as solutions of a system of functional equations that follows from the combination of consistency requirements and known results. This system of equations has a unique solution for irrational central charge c> 25. The solution is constructed by solving the Clebsch-Gordan problem for a certain continuous series of quantum group representations and constructing the associated Racah-coefficients. This gives an explicit expression for the fusion coefficients. Moreover, the expressions can be continued into the strong coupling region 1 < c < 25, providing a solution of the bootstrap also for this region. 1.
Notes on Topological String Theory and 2D Quantum Gravity
, 1990
"... In these notes we give a review of topological string theory. We discuss twodimensional topological field theories, which represent its classical backgrounds. We describe their symmetries and the properties of the physical amplitudes. In the particular context of d < 1 we explain how topological ..."
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Cited by 75 (3 self)
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In these notes we give a review of topological string theory. We discuss twodimensional topological field theories, which represent its classical backgrounds. We describe their symmetries and the properties of the physical amplitudes. In the particular context of d < 1 we explain how topological string theory can be exactly solved, by deriving Schwinger-Dyson equations in the form of recursion relations between world-sheet correlation functions at different genera.
Unitary and complex matrix models as 1-d type 0 strings
, 2003
"... We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to ĉ < 1 matter coupled to super-Liouville theory. We examine in detail the ĉ = 0 ..."
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Cited by 69 (10 self)
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We propose that the double scaling behavior of the unitary matrix models, and that of the complex matrix models, is related to type 0B and 0A fermionic string theories. The particular backgrounds involved correspond to ĉ < 1 matter coupled to super-Liouville theory. We examine in detail the ĉ = 0 or pure supergravity case, which is related to the double scaling limit around the Gross-Witten transition, and find that reversing the sign of the Liouville superpotential interchanges the 0A and 0B theories. We also find smooth transitions between weakly coupled string backgrounds with D-branes, and backgrounds with Ramond-Ramond fluxes only. Finally, we discuss matrix models with multicritical potentials that are conjectured to correspond to 0A/0B string theories based on (2, 4k) super-minimal models.
Correlation functions in conformal Toda field theory II
, 2009
"... This is the second part of the paper [1]. Here we show that three-point correlation function with one semi-degenerate field in Toda field theory as well as fourpoint correlation function with one completely degenerate and one semi-degenerate field can be represented by the finite dimensional integr ..."
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Cited by 53 (8 self)
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This is the second part of the paper [1]. Here we show that three-point correlation function with one semi-degenerate field in Toda field theory as well as fourpoint correlation function with one completely degenerate and one semi-degenerate field can be represented by the finite dimensional integrals.
2D Gravity and Random Matrices
, 1994
"... We review recent progress in 2D gravity coupled to d < 1 conformal matter, based on a representation of discrete gravity in terms of random matrices. We discuss the saddle point approximation for these models, including a class of related O(n) matrix models. For d < 1 matter, the matrix proble ..."
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Cited by 40 (0 self)
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We review recent progress in 2D gravity coupled to d < 1 conformal matter, based on a representation of discrete gravity in terms of random matrices. We discuss the saddle point approximation for these models, including a class of related O(n) matrix models. For d < 1 matter, the matrix problem can be completely solved in many cases by the introduction of suitable orthogonal polynomials. Alternatively, in the continuum limit the orthogonal polynomial method can be shown to be equivalent to the construction of representations of the canonical commutation relations in terms of differential operators. In the case of pure gravity or discrete Ising–like matter, the sum over topologies is reduced to the solution of non-linear differential equations (the Painlevé equation in the pure gravity case) which can be shown to follow from an action principle. In the case of pure gravity and more generally all unitary models, the perturbation theory is not Borel summable and therefore alone does not define a unique solution. In the non-Borel summable case, the matrix model does not define the sum over topologies beyond perturbation theory. We also review the computation of correlation functions directly in the continuum formulation of matter coupled to 2D gravity, and compare with the matrix model results. Finally, we
The tachyon at the end of the universe
- JHEP
"... We show that a tachyon condensate phase replaces the spacelike singularity in certain cosmological and black hole spacetimes in string theory. We analyze explicitly a set of examples with flat spatial slices in various dimensions which have a winding tachyon condensate, using worldsheet path integra ..."
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Cited by 38 (6 self)
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We show that a tachyon condensate phase replaces the spacelike singularity in certain cosmological and black hole spacetimes in string theory. We analyze explicitly a set of examples with flat spatial slices in various dimensions which have a winding tachyon condensate, using worldsheet path integral methods from Liouville theory. In a vacuum with no excitations above the tachyon background in the would-be singular region, we analyze the production of closed strings in the resulting state in the bulk of spacetime. We find a thermal result reminiscent of the Hartle-Hawking state, with tunably small energy density. The amplitudes exhibit a self-consistent truncation of support to the weakly-coupled small-tachyon region of spacetime. We argue that the background is accordingly robust against back reaction, and that the resulting string theory amplitudes are perturbatively finite, indicating a resolution of the singularity and a mechanism to start or end time in string theory. Finally, we discuss the generalization of these methods to examples with positively curved spatial slices. July
Liouville quantum gravity and KPZ
, 2008
"... Consider a bounded planar domain D, an instance h of the Gaussian free field on D, with Dirichlet energy (2π) −1 ∇h(z) · ∇h(z)dz, and a constant 0 ≤ γ < 2. D The Liouville quantum gravity measure on D is the weak limit as ε → 0 of the measures ε γ2 /2 γhε(z) e dz, where dz is Lebesgue measure on ..."
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Cited by 37 (6 self)
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Consider a bounded planar domain D, an instance h of the Gaussian free field on D, with Dirichlet energy (2π) −1 ∇h(z) · ∇h(z)dz, and a constant 0 ≤ γ < 2. D The Liouville quantum gravity measure on D is the weak limit as ε → 0 of the measures ε γ2 /2 γhε(z) e dz, where dz is Lebesgue measure on D and hε(z) denotes the mean value of h on the circle of radius ε centered at z. Given a random (or deterministic) subset X of D one can define the scaling dimension of X using either Lebesgue measure or this random measure. We derive a general quadratic relation between these two dimensions, which we view as a probabilistic formulation of the KPZ relation from conformal field theory. We also present a boundary analog of KPZ (for subsets of ∂D). We illustrate (via heuristics and announced results) the connection between discrete and continuum quantum gravity and provide a framework for understanding Euclidean scaling exponents via quantum gravity.
Geometrical interpretation of d-branes in gauged wzw models
- JHEP
"... We show that one can construct D-branes in parafermionic and WZW theories (and their orbifolds) which have very natural geometrical interpretations, and yet are not automatically included in the standard Cardy construction of D-branes in rational conformal field theory. The relation between these th ..."
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Cited by 32 (0 self)
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We show that one can construct D-branes in parafermionic and WZW theories (and their orbifolds) which have very natural geometrical interpretations, and yet are not automatically included in the standard Cardy construction of D-branes in rational conformal field theory. The relation between these theories and their T-dual description leads to an analogy between these D-branes and the familiar A-branes and B-branes of N = 2 theories. May
