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Results tagged with topological-quantum-field-theory
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user 1450
Topological quantum field theory.
19
votes
What are D-branes, really?
I'm going to attempt a short, partial answer written for pure mathematicians.
The word "brane" in high-energy physics means "submanifold". The word is short for "membrane". More precisely, it means …
- 56.6k
15
votes
When is a TQFT the dimensional reduction of a higher dimensional TQFT?
Asking for sufficient conditions that an $n$-dimensional TQFT lifts to $n+1$ dimensions is like asking for sufficient conditions that an egg will hatch into a bird. You might think of necessary condi …
- 56.6k
49
votes
Accepted
Why are fusion categories interesting?
Fusion categories (over $\mathbb{C}$) are a natural generalization of finite groups and their behavior over $\mathbb{C}$. The complex representation theory of a finite group is a fusion category, but …
10
votes
What do decategorification and "compactification on a circle" have to do with each other?
If you think of a TQFT as a functor from cobordisms to vector spaces, then $F(X \times S^1)$ will give you the dimension of the state space of $X$ (or the superdimension or whatever), because it is th …
- 56.6k
14
votes
What's the right way to think about "anomalies" in 3d TQFTs?
My own understanding of anomalies in TQFTs:
In cases that I have seen, "anomaly" in general refers to central extensions and line bundles. Physicists have long thought of these issues in a very expl …
- 56.6k