Questions tagged [topological-field-theory]
Use this tag for topological field theory (Tft) and topological string theory (tst) questions.
536 questions
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What is the link between the vector field generating the group action and the covariant derivative
I am currently working through Witten's "Two Dimensional Gauge Theories revisited". He defines an operator (p.28, but the redefinition is for p.32)
\begin{equation}
D = \sum_i \psi^i \frac{\...
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Do TQFTs have a notion of symmetry?
I've recently started learning about topological quantum field theories (via the Atiyah–Segal axioms), and noticed that I haven't seen any mention of symmetries present. Considering how important ...
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D-branes, string field theory, and Chern-Simons
Reading the book$^{\dagger}$ Chern-Simons Theory, Matrix Models, and Topological Strings by Marcos Marino, I'm trying to understand the argument in 7.3.2: here are my main questions which can also be ...
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Do topological operators for higher form Symmetries have to be embeddable in a single time slice?
I have a question about higher form symmetries. I can't find anything about this in the literature. The story you usually hear is: higher form symmetries are always abelian because the topological ...
- 1,015
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Relationship between the Quantum Tetrahedron, V4 geometry in topological photonics, and The Cobordism Hypothesis?
Looking for someone with a background in TQFT/related to answer a question over a posited relationship on a few concepts that tie in together.
First - John Baez's early research into LQG via the ...
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Physical Quantities as Fully Dualizable Objects
In answering the recent question, Scalars, Vectors, Tensors: are they all?, I arrived at this broader insight. The objects of discussion often live in $\operatorname{Vect}_k^\otimes$, the symmetric ...
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The boundary condition of symTFT construction for 1+1D $\mathbb{Z}_2\times\mathbb{Z}_2$ SPT with two copies of toric code
I am reading a lecture note on topological holography: https://xiechen.caltech.edu/documents/28637/UQM2024_XC.pdf
In section 2 of the note, a transverse Ising model is obtained by sandwiching a toric ...
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How the topology induces degeneracy of anyons?
I'm a graduate student in physics, i'm studying about anyons. I have a good knowledge on the traditional quantum physics like J.J. Sakurais book lectures. I also have a base knowledge in differential ...
- 183
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Equations of motion from (TQFT) actions with discrete-valued cochains
I was wondering how the equations of motion (EOM) for a TQFT defined with discrete cochains actually follow from the action.
Consider for example a four dimensional space $X$ and $\mathbb{Z}_2$-valued ...
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Curl of singular phase using Dirac's delta function
I am investigating topological defects using a complex-valued order parameter of the form
$A=|A|e^{i\theta}$.
A defect is located wherever the phase $\theta$ is not defined and can be spatially ...
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Supersymmetric localisation - Mathematically rigorous proof
My aim is to understand the derivation of the Kapustin-Witten equations (3.29) in this paper. They are a direct result of the path integral localising on (an infinitesimal neighbourhood) of the field ...
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Tenfold classification and its applicability
I am learning on how to use tenfold classification of insulators and superconductors in my research. I am confused about when I can use this table and for what kind of Hamiltonians. I have heard ...
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Microscopic vs. Macroscopic description of topological order: a precise relation
In condensed matter physics, a widely adoped definition of topological order is the following: "A topological order is a gapped phase of matter whose properties at low energy are described by a ...
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Topological theory in four dimensions
Is there a four-dimensional theory (topological or otherwise) that can induce chern-simons theory on its three-dimensional boundary? In the same way, for example, that chern-simons on three-...
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Topological Degeneracy for superconductors
It has been claimed that Superconductors are topologically ordered. In the linked paper, they show the low energy TQFT description of vortices and quasiparticles in traditional superconductors is ...
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