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Results tagged with topological-quantum-field-theory
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user 115363
Topological quantum field theory.
6
votes
3
answers
306
views
Original reference for generators and relations of 2-dimensional TQFT
What is the original reference where it was first proven that the generators and relations of the 2-dimensional cobordism category are those of commutative Frobenius algebras?
I've seen this article b …
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4
votes
0
answers
172
views
Classification of special symmetric Frobenius algebras over real vector spaces
Is there a general classification of special symmetric Frobenius algebras over real vector spaces? I know that $n\times n$ matrix algebras, the quaternions, the complex numbers, the trivial algebra, a …
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10
votes
2
answers
577
views
What do "pivotal" and "spherical" mean for (unitary) fusion categories on the level of the $...
For me, a fusion category (over $\mathbb{C}$) is just a tensor $F$ (the associator, with $6$ simple-object labels and $4$ fusion space indices) and a tensor $d$ (the quantum dimensions, with one simpl …
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11
votes
1
answer
569
views
Importance of the principal bundle in Chern-Simons theory
This is a very basic beginners question about Chern-Simons theory. The configurations that we sum over to get the partition function are given by a Lie-algebra valued 1-form $A$ on a topological 3-man …
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0
votes
Are there examples of finite-dimensional complex non-semisimple non-commutative symmetric Fr...
I just realize that my question is actually rather trivial the way I posed it: There exist non-commutative semisimple examples (with the $2\times 2$ matrix algebra being the smallest example). There a …
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3
votes
2
answers
165
views
Classification of crossed $G$-algebras
Added later: As Viktor Ostrik points out in a comment, what I'm looking for is a classification of so-called crossed $G$-algebras corresponding to homotopy TQFTs with homotopy target space $K(G, 1)$ a …
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4
votes
2
answers
252
views
Are there examples of finite-dimensional complex non-semisimple non-commutative symmetric Fr...
Are there any examples of finite-dimensional complex non-semisimple non-commutative symmetric Frobenius algebras? Or can one show that none exist?
I went through this list of all complex associative a …
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9
votes
1
answer
302
views
Is there a simple argument that shows that two unitary fusion categories are Morita equivale...
By Morita equivalent I mean that there is an invertible bi-module between the two fusion categories. [Feel free to replace the Drinfeld centers being "equal" by an appropriate categorial notion of "eq …
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4
votes
Is a unitary Hamiltonian TQFT the same as a unitary axiomatic TQFT?
On the Hamiltonian level, the (axiomatic) TQFT tensors correspond to the imaginary time evolution of a microscopic system, not the real-time evolution (which would be a unitary operator). So there's n …
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4
votes
0
answers
184
views
Can non-chiral 3D TQFTs be extended to non-orientable manifolds whereas chiral ones cannot?
As far as I know, when talking about TQFT, one usually means TQFTs on oriented manifolds with boundary (cobordisms)
It appears to me that the Turaev-Viro-Barrett-Westbury state-sum construction can b …
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7
votes
2
answers
304
views
How do I calculate the modular fusion category from a given Lie algebra and level in Chern-S...
In Chern-Simons theory, one has modular fusion categories that are labelled by a Lie algebra and a "level", e.g. $SU(2)_2$ ("$SU(2)$ level $2$").
Physically this modular fusion category describes the …
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7
votes
0
answers
234
views
Why are Levin-Wen/Turaev-Viro models said to be non-chiral?
I'd like to bring together the following two notions of "non-chiral":
On the abstract algebraic side, a modular fusion category describing the anyon content of some physical system is said to be non- …
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7
votes
0
answers
110
views
Are there attempts to numerically finding algebraic structures over finite-dimensional vecto...
By "algebraic structure" I mean a finite set of linear operators between tensor products of copies of one (or more) finite-dimensional (complex or real) vector spaces, fulfilling a set of axioms with …
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21
votes
1
answer
1k
views
Fully extended TQFT and lattice models
I often read that fully extended TQFTs are supposed to classify topological phases of matter. So I would like to understand the formal nature of fully extended TQFTs on a more direct physical level (w …
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4
votes
0
answers
169
views
CFT as an axiomatic field theory
I'm trying to understand CFT from a purely axiomatic-field-theoretical perspective. That is, there is a vector space $V$ associated to the circle, and an element of $V^{\otimes n}$ associated to every …
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