nLab Daniel Freed

Daniel Freed is a mathematician at University of Texas, Austin.

Freed’s work revolves around the mathematical ingredients and foundations of modern quantum field theory and of string theory, notably in its more subtle aspects related to quantum anomaly cancellation (which he was maybe the first to write a clean mathematical account of). In the article Higher Algebraic Structures and Quantization (1992) he envisioned much of the use of higher category theory and higher algebra in quantum field theory and specifically in the problem of quantization, which has – and still is – becoming more widely recognized only much later. He recognized and emphasized the role of differential cohomology in physics for the description of higher gauge fields and their anomaly cancellation. Much of his work focuses on the nature of the Freed-Witten anomaly in the quantization of the superstring and the development of the relevant tools in supergeometry, and notably in K-theory and differential K-theory. More recently Freed aims to mathematically capture the 6d (2,0)-superconformal QFT.

Selected writings

Dedicated entries:

On spin geometry, Dirac operators and index theory:

On quantum anomalies via index theory:

On instantons and 4-manifolds:

On topological quantum field theory:

On twisted equivariant K-theory with an eye towards twisted ad-equivariant K-theory:

On quantization of the electromagnetic field in view of Dirac charge quantization:

On twisted ad-equivariant K-theory of compact Lie groups and the identification with the Verlinde ring of positive energy representations of their loop group:

On the cobordism hypothesis:

On formalizing short-range entanglement in topological phases of matter via invertible topological field theories:

On classification of invertible TQFTs via reflection positivity:

On spectral networks and Chern-Simons theory with complex gauge group:

category: people

Last revised on October 29, 2023 at 10:43:21. See the history of this page for a list of all contributions to it.