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Twistor Actions for Integrable Systems
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Twistor Actions for Integrable Systems
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Many integrable systems can be reformulated as holomorphic vector bundles on twistor space. This is a powerful organizing principle in the theory of integrable systems. One shortcoming is that it is formulated at the level of the equations of motion. From this perspective, it is mysterious that integrable systems have Lagrangians. In this paper, we study a Chern-Simons action on twistor space and use it to derive the Lagrangians of some integrable sigma models. Our focus is on examples that come from dimensionally reduced gravity and supergravity. The dimensional reduction of general relativity to two spacetime dimensions is an integrable coset sigma model coupled to a dilaton and 2d gravity. The dimensional reduction of supergravity to two spacetime dimensions is an integrable coset sigma model coupled to matter fermions, a dilaton, and 2d supergravity. We derive Lax operators and Lagrangians for these 2d integrable systems using the Chern-Simons theory on twistor space. In the supergravity example, we use an extended setup in which twistor Chern-Simons theory is coupled to a pair of matter fermions.
Forward citations
Cited by 4 Pith papers
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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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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 Yang-Baxter Sigma Model from Twistor Space
A 4D analogue of the Yang-Baxter sigma model is derived from 6D twistor-space Chern-Simons theory via symmetry reduction, with its 2D equations embedded in anti-self-dual Yang-Mills.
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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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