The Schwarzschild metric is derived as a Kähler metric on a holomorphic 'coincidence locus' within the twistor space of self-dual Taub-NUT, solving the googly problem for this specific spacetime.
Integrable Deformations from Twistor Space
6 Pith papers cite this work. Polarity classification is still indexing.
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abstract
Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons in 6 dimensions. We provide the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. Starting from 6d holomorphic Chern-Simons theory on twistor space with a particular meromorphic 3-form $\Omega$, we construct the defect theory to find a novel 4d integrable field theory, whose equations of motion can be recast as the 4d anti-self-dual Yang-Mills equations. Symmetry reducing, we find a multi-parameter 2d integrable model, which specialises to the $\lambda$-deformation at a certain point in parameter space. The same model is recovered by first symmetry reducing, to give 4d Chern-Simons with generalised boundary conditions, and then constructing the defect theory.
fields
hep-th 6representative citing papers
Integrable (d+1)-dimensional field theories are obtained via homotopy transfer from cyclic L_infinity-algebras describing topological-holomorphic higher Chern-Simons theories on M × CP¹, with integrability encoded in a map to higher Lax connections.
Non-commutative 5d Chern-Simons theory on the spinor bundle compactifies to the KP equation, with vanishing tree amplitudes and W_{1+∞} defect algebra reducing to w_{1+∞} in the dispersionless limit.
Derives μ-frame auxiliary deformation of 2D BM model and uplifts both ν- and μ-frames to 4D higher-derivative theory lacking manifest diffeomorphism invariance.
Intersecting surface operators in 6d holomorphic Chern-Simons and BF theories produce local R-matrix-like operators with evidence for Yang-Baxter relations and derived coproducts from OPEs.
Twistor-space 6d Chern-Simons theory with Yang-Baxter boundary conditions yields a 4d integrable field theory whose symmetry reduction is the 2d Yang-Baxter sigma model.
citing papers explorer
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Schwarzschild black holes from twistor space
The Schwarzschild metric is derived as a Kähler metric on a holomorphic 'coincidence locus' within the twistor space of self-dual Taub-NUT, solving the googly problem for this specific spacetime.
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On the structure of higher-dimensional integrable field theories
Integrable (d+1)-dimensional field theories are obtained via homotopy transfer from cyclic L_infinity-algebras describing topological-holomorphic higher Chern-Simons theories on M × CP¹, with integrability encoded in a map to higher Lax connections.
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Non-Commutative Gauge Theory at the Beach
Non-commutative 5d Chern-Simons theory on the spinor bundle compactifies to the KP equation, with vanishing tree amplitudes and W_{1+∞} defect algebra reducing to w_{1+∞} in the dispersionless limit.
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The auxiliary-deformed Breitenlohner-Maison model: duality frames and higher-dimensional origin
Derives μ-frame auxiliary deformation of 2D BM model and uplifts both ν- and μ-frames to 4D higher-derivative theory lacking manifest diffeomorphism invariance.
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Intersecting Surface Operators in 6d Holomorphic Field Theories
Intersecting surface operators in 6d holomorphic Chern-Simons and BF theories produce local R-matrix-like operators with evidence for Yang-Baxter relations and derived coproducts from OPEs.
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The Yang-Baxter Sigma Model from Twistor Space
Twistor-space 6d Chern-Simons theory with Yang-Baxter boundary conditions yields a 4d integrable field theory whose symmetry reduction is the 2d Yang-Baxter sigma model.