Twistor! Spring 2022

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The goal of this seminar is to understand twistor theory and some of its relations to other parts of mathematical physics.

Time and location information

Organisers: Sam DeHority, Zoe Himwich, Davis Lazowski
Time/date: Wednesday 11am-12:15pm EST
Location: Math 622

Please email zmh2110@columbia.edu if you would like to be on the mailing list.

Plan/references

Beginning with an introduciton to twistors and spinors, the plan is to understand some parts of

  1. Scattering amplitudes and their relation to holomorphic curves in twistor space, starting from the work https://arxiv.org/abs/hep-th/0312171 and other developments including https://arxiv.org/abs/hep-th/0402045, https://arxiv.org/abs/1309.0885.
  2. Developments in ambitwistor theory, perhaps from https://arxiv.org/pdf/1311.2564.pdf https://arxiv.org/pdf/1606.05636.pdf.
  3. Understanding the quantization of certain twistor field theories in https://arxiv.org/abs/2111.08879 and https://arxiv.org/abs/2201.02595 after a slow introduction to the BV formalism.

Virtual attendance

List of talks

Date Talk Info
Tuesday
Mar. 8
Speaker: Davis Lazowski
Title: Twistor theory and the Penrose-Ward Correspondence
Abstract: I will give a basic introduction to spinors, twistors and some of their applications to the study of gauge theory.
Thursday
Mar. 17
Speaker: Zoe Himwich
Title: Perturbative Gauge Theory as String Theory in Twistor Space
Abstract: I will be presenting Witten’s paper “ Perturbative Gauge Theory as String Theory in Twistor Space”
Wednesday
Mar. 23
Speaker: Sam DeHority
Title: Holomorphic curves and scattering amplitudes
Abstract: Continuing with Witten’s paper, we will discuss scattering amplitudes under the Fourier transform to twistor space. We will demonstrate in examples, including the Parke-Taylor formula discussed last week, that the amplitudes are supported on holomorphic curves in twistor space whose degree and genus are related to the helicity violation and loop order of the amplitude.
Wednesday
Mar. 30
Speaker: Davis Lazowski
Title: Scattering amplitudes and ambitwistor string theories
Abstract: I will sketch the basics of ambitwistor string theories and how they lead to the Cachazo-He-Yuan formula for tree level scattering amplitudes.
Wednesday
Apr. 6
Speaker: Davis Lazowski
Title: Scattering amplitudes and ambitwistor string theories II
Abstract: Continuing from last time, I will sketch the basics of ambitwistor string theories and how they lead to the Cachazo-He-Yuan formula for tree level scattering amplitudes.
Hiatus  
Wednesday
Apr. 27
Speaker: Zoe Himwich
Title: ASDYM and KdV
Abstract: I will explain reductions of the ASDYM equation and the connection between the Penrose-Ward correspondence and the reduction to KdV.