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Tachikawa Lab
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The lab explores the mathematical aspects of quantum field theory and string theory.
AboutAbout the lab
From theoretical physics to new mathematics.
The Tachikawa Lab studies the mathematical aspects of quantum field theory and string theory.
Its main research subjects are symmetries and anomalies, and the geometric and algebraic structures associated with supersymmetric quantum field theories.
With supersymmetry, the strongly coupled regime of quantum field theory can be investigated theoretically, using just pen, paper, and a little computing.
In the course of this research, a wide variety of mathematical concepts arise naturally.
Key terms
- Quantum field theory
- A theory that treats particles as "fields" spread across space, combining quantum mechanics and relativity to describe elementary particles
- Supersymmetry
- A symmetry that exchanges the particles that make up matter (fermions) with the particles that carry forces (bosons)
- Anomaly
- A phenomenon in which a symmetry that holds in a classical theory is broken when the theory is quantized
ResearchResearch themes
The lab studies various mathematical aspects of quantum field theory and string theory. Its main subjects are symmetries and anomalies, and the geometric and algebraic structures associated with supersymmetric quantum field theories.
*Illustrative imageThe strongly coupled regime of supersymmetric quantum field theories
Quantum field theory, which describes the world of elementary particles, exhibits a wide range of properties in the strongly coupled regime. Supersymmetry makes it possible to investigate this regime theoretically, so the lab takes it as its main subject and also studies the related superstring theory.
*Illustrative imageThe relationship between quantum field theory and mathematics
The lab studies the connection between quantum field theory and mathematics through three kinds of relationships: developing new mathematics in order to investigate quantum field theory, doing mathematics by using quantum field theory, and applying existing mathematics in order to learn quantum field theory.
MembersFaculty
- ProfessorYuji TachikawaPublications ↗
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Hopf Fibration” Niles Johnson / CC BY 4.0 (cropped)
- The strongly coupled regime of supersymmetric quantum field theories: “Quintic 1” The original uploader was Floriang at German Wikipedia. / CC BY-SA 3.0 (cropped)
- The relationship between quantum field theory and mathematics: “Circules in the three sphere” Brnbrnz / CC BY-SA 4.0 (cropped)
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