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      Questions tagged [tqft]

      Topological quantum field theory.

      8
      votes
      1answer
      257 views

      Does there exist a discrete gauge theory as a TQFT detecting the figure-8 knot?

      My question: Does there exist a discrete gauge theory as TQFT detecting the figure-8 knot? By detecting, I mean that computing the path integral (partition function with insertions of the knot/...
      5
      votes
      0answers
      93 views

      Equivariant L-infinity structure associated to a DGBV algebra

      Let $V$ be a differential graded Batalin-Vilkovisky (DGBV) algebra over say $\mathbb{C}$. This means that $V$ is a commutative differential graded algebra (CDGA), with differential $\partial$ of ...
      4
      votes
      0answers
      107 views

      Chern-Simons and framing dependence$.$

      I posted this question to physics.SE last week (cf. here), but it got not attention. I hope it is not too trivial to post it here. According to ref.1, the correlation functions of a Chern-Simons ...
      17
      votes
      1answer
      484 views

      How is Chern-Simons theory related to Floer homology?

      Chern-Simons theory (say, with gauge group $G$) is the quantum theory of the Chern-Simons functional $$CS(A)=\frac{k}{8\pi^2}\int_M \text{Tr}\left(A\wedge dA + \frac{2}{3}A\wedge A \wedge A\right)$$ ...
      5
      votes
      0answers
      173 views

      Projecting GxG onto subspace with tied irreducible representations

      Suppose I have a finite group $G$. With this group, I can associate an ortho-normal Hilbert space spanned by elements of the group $$\mathcal{H} = \{|g\rangle: g \in G \}$$. I could alternatively ...
      5
      votes
      1answer
      110 views

      How do I calculate the modular fusion category from a given Lie algebra and level in Chern-Simons theory?

      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 ...
      9
      votes
      3answers
      211 views

      Generalization of Drinfeld double to comodule algebras

      Let $ \mathcal C $ be a monoidal category. Then $ \mathcal C $ is both a left and right module category over itself. Moreover, the Drinfeld centre of $ \mathcal C $ can be defined as the category of ...
      16
      votes
      2answers
      437 views

      What are some mathematical consequences of the study of 6D $\mathcal N = (2,0)$ SCFT?

      Arguments made in physics apparently predict the existence of a family of six-dimensional $\mathcal N = (2,0)$ superconformal field theories (Wikipedia, nLab, PhysicsOverflow) sometimes called Theory $...
      6
      votes
      1answer
      316 views

      Physical consequences of cobordism hypothesis?

      Let $C$ be a symmetric monoidal $n$-category. An extended framed $C$-valued TQFT is a symmetric monoidal functor from the framed bordism category $\mathrm{Cob}^{fr}_n(n)$ to $C$. The cobordism ...
      9
      votes
      0answers
      139 views

      What is the “classical limit” of Khovanov homology?

      Let me first explain what I mean by the "classical limit". For quantum group invariants of links and webs (such as colored Jones polynomials), the "classical limit" means the limit $k\rightarrow +\...
      3
      votes
      1answer
      198 views

      Framing dependence of HOMFLY polynomial

      I want to understand the framing dependence of the Khovanov-Rozansky homology, and as its first step, I am trying to understand the framing dependence of the HOMFLY polynomial (i.e. quantum $sl(n)$ ...
      9
      votes
      0answers
      196 views

      Twisted Chern-Simons, and Twisted Wess-Zumino Term

      I am asking this question about Chern-Simons theory from the paper "Quantum Field Theory and Jones Polynomial" by Edward Witten. Let $M$ be a closed three dimensional manifold, and $P\rightarrow M$ ...
      7
      votes
      0answers
      163 views

      What is the mathematical structure of 2d TQFT from the 2d foam category (instead of 2d cobordism category)?

      It is well-known that the category of 2d TQFTs is equivalent to the category of commutative Frobenius algebras. What about functors from the 2d foam category (instead of 2d cobordism category) to ...
      4
      votes
      1answer
      115 views

      2-morphisms for Bord(n)

      I am currently reading in Boundary Conditions for Topological Quantum Field Theories, Anomalies and Projective Modular Functors, and have a (I guess) pretty basic question for my understanding of the (...
      10
      votes
      0answers
      175 views

      Define the 3d Chern-Simons TQFT on a discrete simplicial complex

      Question: What is the challenge and the current status to define the 3d Chern-Simons(-Witten) (CSW) theory on a simplicial complex or on a discrete lattice? (Or is there a no-go or an obstruction ...

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