# 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

On instantons and 4-manifolds:

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:

1. J. Topology, 4 (2011), 737-789

2. J. Amer. Math. Soc. 26 (2013), 595-644

3. Annals of Mathematics, Volume 174 (2011) 947-1007

• Dirac families for loop groups as matrix factorizations,

Comptes Rendus Mathematique, Volume 353, Issue 5, May 2015, Pages 415-419

On the cobordism hypothesis:

• Daniel S. Freed, Short-range entanglement and invertible field theories $[$arXiv:1406.7278 $]$
category: people

Last revised on August 17, 2022 at 06:17:16. See the history of this page for a list of all contributions to it.