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      Questions tagged [quantum-field-theory]

      For questions about mathematical problems arising from quantum field theory, the branch of physics which describes subatomic particles and their interactions in terms of perturbations of the corresponding scalar, vector or tensor fields.

      2
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      46 views

      Dimension of the skein module of a closed manifold?

      I'm looking for a reference to Witten's conjecture that the free part of the (Kauffman bracket) skein module of a closed 3-manifold is finitely generated, i.e. the dimension of $K(M)$, where $M$ is a ...
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      votes
      0answers
      77 views

      Conformal group and cobordism

      In this post, I am exploring my thoughts on the implementation of conformal symmetry group structure and cobordism relations. Namely, I like to know what has been done and explored in the past? on ...
      6
      votes
      0answers
      66 views

      Relate two different mod 2 indices: $\eta$ invariant and the number of zero modes of Dirac operator, associated to SU(2)

      My major question in this post here is that: How can we relate the following two mod 2 indices: $\eta$ invariant, the number of the zero modes of the Dirac operator $N_0'$ mod 2, associated to ...
      8
      votes
      0answers
      145 views

      Lagrangian subgroups/submanifolds, 2d topological boundary and 3d “non-abelian” Chern–Simons theory

      This post is meant to ask for proper references to fill a gap in the literature. My short question is that are there known and precise ways to formulate 2d topological boundary conditions" for ...
      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/...
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      votes
      0answers
      78 views

      $T\bar{T}$ deformation: Stress-energy momentum tensor deformed in CFT and in QFT for various $d$-dimensions

      The $T\bar{T}$ deformation is based on the original work of Zamolochikov [1] explored deformations of two-dimensional conformal field theories (CFT) by an operator that is quadratic in the stress-...
      14
      votes
      0answers
      267 views

      How does quotienting by a finite subgroup act on the framed-cobordism class of a group manifold?

      Let $G$ be a connected simple connected compact Lie group, and $\Gamma \subset G$ a finite subgroup. Then (the underlying manifold of) $G$ can be framed by right-invariant vector fields, and this ...
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      votes
      1answer
      219 views

      One particle irreducible Feynman diagrams

      In quantum field theory Feynman has invented a diagrammatic method to encode various terms in the Taylor decomposition of integrals of the following form below which I will write in a baby version as ...
      10
      votes
      1answer
      594 views

      References on dualities on quantum field theory for mathematicians

      Dualities on QFT–also called Quantum Field Theory dynamics–is a huge and fundamental research area. However, despite underpinning major mathematical breakthroughs such as the work of Kapustin and ...
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      votes
      0answers
      149 views

      Yang-Mills theory v.s. Kaluza–Klein theory: Classical actions

      In general Yang-Mills theory [1] seems to be different from the dimensional reduced Kaluza–Klein theory. However, the historical account was that people tried to trace back the origin of non-Abelian ...
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      votes
      0answers
      242 views

      Yang-Mills theory with non-compact gauge groups G

      Physicists are familiar working with Yang-Mills theory with compact and semi-simple gauge groups $G$ (Lie groups). However, it is not entirely clear the formulation of Yang-Mills theory with non-...
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      votes
      0answers
      112 views

      Geometry of Affine Kac-Moody Algebras

      I recently asked this question on phys.SE and it was suggested to me to ask it here. One can reconstruct the unitary irreducible representations of compact Lie groups very beautifully in geometric ...
      4
      votes
      0answers
      178 views

      Chern-Simons theory with non-compact gauge groups G

      This is related to a previous question, where a nonlinear σ model (NLSM) describes a scalar field Σ which takes on values in a nonlinear manifold called the target manifold T. There we ask the general ...
      7
      votes
      0answers
      290 views

      Witten zeta function v.s. Riemann zeta function

      From a talk, we learned that The symplectic volume of the space $M$ of gauge equivalence classes of flat G connections is given by the “Witten zeta function”: where we sum over irreducible ...
      4
      votes
      1answer
      136 views

      Nonlinear sigma models with non-compact groups / target spaces

      A nonlinear σ model (NLSM) describes a scalar field Σ which takes on values in a nonlinear manifold called the target manifold T. The target manifold T is equipped with a Riemannian metric g. Σ is ...

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