Conformal algebra and multipoint correlation functions in 2D statistical models

Dotsenko, Victor; Fateev, V.A.

doi:10.1016/0550-3213(84)90269-4

Cited by 1,306 publications

(859 citation statements)

References 15 publications

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“…Note that after allowing for this factor, the new parameterization still contains one less independent function than that in eq. (13). The solution found by CZ does have this form, and we hope to illuminate the reason for this in our analysis.…”

Section: Chim-zamolodchikov Formmentioning

confidence: 64%

“…This is defined at least to all orders in perturbation theory. The perturbing "energy" operator corresponding to the Potts model is known as Φ 21 in the usual conventions of conformal theory [16,13] (although in [13] the subscripts are backwards from these now-accepted conventions). This definition is useful because it allows one to show that this massive field theory is integrable [24], even though the underlying Potts lattice model is not.…”

Section: The Minimal Models and The Rsos Modelsmentioning

confidence: 99%

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ExactS-matrices for supersymmetric sigma models and the Potts model

Fendley

Read

2002

J. Phys. A: Math. Gen.

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We study the algebraic formulation of exact factorizable S-matrices for integrable twodimensional field theories. We show that different formulations of the S-matrices for the Potts field theory are essentially equivalent, in the sense that they can be expressed in the same way as elements of the Temperley-Lieb algebra, in various representations. This enables us to construct the S-matrices for certain nonlinear sigma models that are invariant under the Lie "supersymmetry" algebras sl(m + n|n) (m = 1, 2, n > 0), both for the bulk and for the boundary, simply by using another representation of the same algebra. These Smatrices represent the perturbation of the conformal theory at θ = π by a small change in the topological angle θ. The m = 1, n = 1 theory has applications to the spin quantum Hall transition in disordered fermion systems. We also find S-matrices describing the flow from weak to strong coupling, both for θ = 0 and θ = π, in certain other supersymmetric sigma models.

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Section: Chim-zamolodchikov Formmentioning

confidence: 64%

Section: The Minimal Models and The Rsos Modelsmentioning

confidence: 99%

ExactS-matrices for supersymmetric sigma models and the Potts model

Fendley

Read

2002

J. Phys. A: Math. Gen.

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“…The induced gravity action I[g] being a non-local functional, it is natural to introduce one, or several fields in addition to the metric that render the action local. The minimal way to achieve this is by means of a single scalar field, B(x), as in Feigin-Fuks theory [68][69][70], which has a nonminimal coupling to the metric. Consider the following local action, invariant under general coordinate transformations applied to g µν and B:…”

Section: Jhep02(2016)167mentioning

confidence: 99%

The unitary conformal field theory behind 2D Asymptotic Safety

Nink

Reuter

2016

J. High Energ. Phys.

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Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in d > 2 dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge c = 25. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in d > 2 dimensions and Polyakov's induced gravity action in two dimensions.

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“…As a consequence, the field ∂X µ is not a conserved current, instead there is a so-called background charge, and correlation functions -which will not concern us in this paper -would have to be computed using screening operators, see [7,8] and also [5,6].…”

Section: The External Sectormentioning

confidence: 99%

Moduli stabilisation on the worldsheet

Deo

Lambert

Recknagel

2011

J. High Energ. Phys.

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We consider compactifications of type II string theory using exact internal CFT's with central charge c = 9 + , | | 1, leading to an effective potential for the dilaton. For > 0 the potential is positive and the dilaton is ultimately driven to weak coupling. For < 0 the dilaton is driven to strong coupling, but we can stabilise the background by including D-branes. The resulting minimum admits an AdS 4 solution where the cosmological constant is of the order 3 and the string coupling constant is of order . Furthermore these CFT's typically do not possess any massless or tachyonic modes. Thus these vacua provide exact CFT descriptions of moduli stabilisation in weakly coupled string theory.

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Conformal algebra and multipoint correlation functions in 2D statistical models

Cited by 1,306 publications

References 15 publications

ExactS-matrices for supersymmetric sigma models and the Potts model

ExactS-matrices for supersymmetric sigma models and the Potts model

The unitary conformal field theory behind 2D Asymptotic Safety

Moduli stabilisation on the worldsheet

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