# Questions tagged [topological-field-theory]

Use this tag for topological field theory (Tft) and topological string theory (tst) questions.

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### Why is the correlation function of local operators in topological field theory independent of the position they are inserted?

I am reading "A mini course on topological strings"(hep-th/0504147). In the last paragraph of section 3.1, author mentioned that if a topological field theory have general coordinate ...
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### Sigma models as topological quantum field theories

I'm wondering how sigma models are supposed to define TQFTs. Suppose I want to consider a 2D TQFT with target $X$ (see page 15 of https://www.ams.org/bookstore/pspdf/ulect-72-intro.pdf)*. According ...
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### Is it actually true that Chern-Simons theory is topological?

Chern-Simons theory has action $$\tag{1} S = \frac{k}{4\pi}\int_X tr(A\wedge dA + \frac{2}{3}A\wedge A\wedge A).$$ Here, $X$ is some compact 3-manifold, perhaps with boundary, and $A$ is a connection ...
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### How do you calculate the partition function on a manifold-with-corners in extended TQFT?

In Atiyah's formulation, a Topological Quantum Field Theory (TQFT), is a functor $Z:d\text{Bord}\to\text{Hilb}$. That is, $Z$ assigns: \begin{align} \text{Closed compact $(d-1)$-manifolds} &\to \...
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### 1+1D simple vacuum EFE solution

Can there be any solutions for simple vacuum Einstein Field Equations in 1+1D (1 space and 1 time dimension) i.e $R_{\mu\nu} = 0$ except for flat space? I tried different combinations of random ...
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### Why does additional term to electromagnetic Lagrangian leave Maxwell's equations unchanged?

The addition of $$\mathcal{L}' = \epsilon_{\mu\nu\rho\sigma}F^{\mu\nu}F^{\rho\sigma} \propto \vec{E}\cdot\vec{B}$$ to the electromagnetic Lagrangian density leaves Maxwell's equations unchanged (shown ...
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### What are non-propagating fields?

I have read at different places that in 3 spacetime dimensions, there are NO propagating gravitational degrees of freedom. This seems to imply that we have only "non-propagating" degrees of ...
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### Can we expect some nice "conservation laws" to be hold at each vertex of any Feynman diagram?

I'm reading two textbooks: A. Zee's QFT book and Bruce Bartlett's TQFT book. In Zee's book, chapter 1 & 2 introduces Feynman diagram smoothly. Although notations are slightly different, I'll ...
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### Can any useful physical theories other than TQFTs be formulated on a smooth manifold without a metric structure?

The vast majority of physical theories are formulated on a spacetime that is mathematically represented by a pseudo-Riemannian manifold, i.e. a smooth manifold with a metric tensor structure. The ...
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### Topological and non-topological defects?

The meaning of topological defect is only known intuitively to me. One explanation is it is some discontinuity in a system that cannot be removed. But I would like to know the precise mathematical ...
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