nLab bosonization

Idea

In (2d) conformal field theories, certain fermion-fields may be re-expressed as chiral boson fields – this is called bosonization.

The converse of bosonization explains for instance why chiral bosons have partition functions like Pfaffian line bundles in 2d, namely theta functions (…) (Alvares-Gaumé-, Bost, Moore, Nelson & Vafa 1987).

Related concepts

• condensed matter physics

• string theory

A related phenomenon in algebra is

• Radford-Majid bosonisation

References

Lecture notes and surveys include

• D. Sénéchal, An introduction to bosonization (arXiv:cond-mat/9908262)

See also:

• Wikipedia, Bosonization

• Luis Alvarez-Gaumé, Jean-Benoit Bost, Gregory Moore, Philip Nelson, Cumrun Vafa, Bosonization on higher genus Riemann surfaces, Communications in Mathematical Physics, Volume 112, Number 3 (1987), 503-552 (Euclid)

Discussion for 3d CFTs (such as the ABJM model):

• Amit Sever, Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions, talk at Strings 2022 [indico:4940843, slides, video]

On the difference between summing over spin structures and gauging $(-1)^F$:

• Philip Boyle Smith, Yunqin Zheng. Backfiring Bosonisation (2024). (arXiv:2403.03953).