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Integrable Classical and Quantum Gravity
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In these lectures we report recent work on the exact quantization of dimensionally reduced gravity, i.e. 2d non-linear (G/H)-coset space sigma-models coupled to gravity and a dilaton. Using methods developed in the context of flat space integrable systems, the Wheeler-DeWitt equations for these models can be reduced to a modified version of the Knizhnik-Zamolodchikov equations from conformal field theory, the insertions given by singularities in the spectral parameter plane. This basic result in principle permits the explicit construction of solutions, i.e. physical states of the quantized theory. In this way, we arrive at integrable models of quantum gravity with infinitely many self-interacting propagating degrees of freedom.
Forward citations
Cited by 3 Pith papers
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Time-Dependent Integrability from Gauge Theory, I
Spacetime-dependent 4d Chern-Simons theory generates time-dependent integrable field theories whose allowed time dependence coincides with one-loop RG flow while preserving Lax integrability.
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The auxiliary-deformed Breitenlohner-Maison model: duality frames and higher-dimensional origin
Extends auxiliary deformations of the 2D BM model to the μ-frame and uplifts both frames to a 4D higher-derivative theory without manifest diffeomorphism invariance.
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Integrable deformations of dimensionally reduced gravity
Auxiliary field and Yang-Baxter deformations of D=2 dimensionally reduced gravity are shown to admit flat Lax representations, with the auxiliary field case preserving the Hamiltonian integrability structure.
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