All Questions
Tagged with tqft or topological-quantum-field-theory
85 questions
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55
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Difficulties in explicitly constructing the "cap" bordism
EDIT: I made a mistake and I cross-posted this question also on MathOverflow, where it already has an answer. Please refer to the MathOverflow post and ignore this one.
Freed's notes give the ...
- 1,015
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39
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Defining a 2D TQFT that maps $S^1$ to the vector space of of all $n×n$ matrices over $\Bbbk$.
Searching for some simple examples of TQFTs I found the following among the Exercises of Kock's "Frobenius algebras and 2D Topological Quantum Field Theories".
There Kock considers a TQFT $ ...
- 11
2
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85
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The role of strictness in the equivalence between $ 2 $-dimensional topological quantum field theories and Frobenius algebras
Monoidal categories and monoidal functors come in many flavors. The former can be weak or strict, while the latter can be lax, strong or even strict themself.
In it's Frobenius Algebras and 2D ...
- 1,015
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45
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A module which eliminates torsion "A little at a time" by tensoring
For concreteness, let $R = \mathbb Z[x]$, but I'm interested in what could be said for other $R$ as well. For an $R$-module $M$, let Free$(M)$ be the torsion-free part of $M$. Let $M^{\otimes k}$ be ...
- 123
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77
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"Maximum cuppability" of uncappable element of Temperley-Lieb algebra?
I'll mostly use the notation at this Wikipedia page in discussing the Temperley-Lieb algebra $TL_m(\delta)$ on $m$ nodes over a pointed commutative ground ring $(R,\delta)$.
However, unlike the ...
- 3,191
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49
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Indexed monoidal categories with lax monoidal structure?
As defined in nLab, an indexed monoidal category consists of a base category $S$ and a pseudofunctor $S^{op} \rightarrow \text{MonCat}$ to the 2-category of monoidal categories and strong monoidal ...
- 463
2
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95
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A question about Dijkgraaf Witten theory on a triangulated manifold
In the paper "Topological gauge theories and group cohomology" by Dijkgraaf and Witten (https://link.springer.com/article/10.1007/BF02096988), a TQFT is constructed on a triangulated ...
3
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1
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92
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Order of the images of Dehn twists in the quantum representation of Reshetikhin-Turaev TQFT and relation to Vafa's theorem
Short version
Let $\mathcal T$ be the modular functor of a Reshetikhin-Turaev TQFT defined over a modular (semisimple) category $\mathcal C$ and a ring $K$, and $\Sigma$ be some compact (closed) ...
- 73
3
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1
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80
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Compact group with a finite fundamental group "built" from a connected, simply connected group and a finite group
I am reading the Dijkgraaf-Witten paper on the classification of TQFT. In the first part, the authors considered two opposite types of gauge group. The first type is a connected and simply-connected ...
- 133
4
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2
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197
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Cobordism Hypothesis in dimension 1
I am trying to understand consequences of the Cobordism Hypothesis in dimension 1, following section 4.2 of Lurie's "On the Classification of Topological Field Theories". Especially, I want ...
- 711
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62
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calculation of partition function: choice of a cross-section
Given a TFT $Z$, I aim to calculate the partition function $Z(\mathbb{S}^2)$ as discussed by Lurie on page-7, Example 1.2.1 in:
https://arxiv.org/abs/0905.0465
If I am not wrong I do need to show that ...
1
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0
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200
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Partition function of a QFT.
There is a YouTube lecture by Robert Dijkgraaf titled:"Introduction to Topological and Conformal Field Theory (1 of 2)."
https://www.youtube.com/watch?v=jEEQO-tcyHc&t=2977s
At one point ...
2
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1
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542
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TQFT vs CQFT vs QFT intro
What is a vague motivational intro to the relationship between topological quantum field theory, cohomological quantum field theory, and quantum field theory?
I am a beginner.
Here are the vague basic ...
- 459
1
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0
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58
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Clarification on a paper
I have a question about the following excerpt from p.93-94 in a paper of Donaldson:
Suppose $U_0, U_1$ are finite-dimensional vector spaces and $\Gamma$ is a linear subspace of $U_0 \oplus U_1$. Then,...
- 180
1
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1
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90
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Could the word "symmetry" represent different things in different contexts? (naive question)
I just wanted to bring up some discussion about an apparently essential concept for some fields in mathematics as so as for some in physics, as already mentioned in the title, I'm referring to the ...
