Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
  
  
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeMay 16th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have considerably expanded the entry [[sigma-model]] and will probably continue to do so in small steps in the nearer future (with interruptions). This goes in parallel with a discussion we are having on the $n$Café [here](http://golem.ph.utexas.edu/category/2011/05/dijkgraafwitten_theory.html).

   I have considerably expanded the entry sigma-model and will probably continue to do so in small steps in the nearer future (with interruptions). This goes in parallel with a discussion we are having on the Café here.

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeMay 26th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexI have now filled content into the section _Chern-Simons theory as a $\sigma$-model_ at [[sigma-model]] . As with the previous sections, I am posting this to the $n$Café [here](http://golem.ph.utexas.edu/category/2011/05/dijkgraafwitten_theory.html#c038205).

   I have now filled content into the section Chern-Simons theory as a -model at sigma-model . As with the previous sections, I am posting this to the Café here.

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMay 28th 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a section <a href="http://www.ncatlab.org/nlab/show/sigma-model#SecondQuantization">Exposition of second quantization of sigma-models</a>

   added a section Exposition of second quantization of sigma-models

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeJun 6th 2011
   • (edited Jun 6th 2011)
   • PermaLink
   Author: Urs
   Format: MarkdownItexwrote a section <a href="http://ncatlab.org/nlab/show/sigma-model#StringTopology">string topology as a sigma-model</a> -- also posted this to the Caf&eacute; [here](http://golem.ph.utexas.edu/category/2011/06/string_topology_as_a_sigmamode.html)

   wrote a section string topology as a sigma-model – also posted this to the Café here

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeAug 3rd 2011
   • PermaLink
   Author: Urs
   Format: MarkdownItexSince the entry [[sigma-model]] would not save any more (too long) I have splitt off the Exposition-subsections as separate entries * [[sigma-model -- exposition of classical sigma-models]] * [[sigma-model -- exposition of higher gauge theories as sigma-models]] * [[sigma-model -- exposition of quantum sigma-models]] * [[sigma-model -- exposition of a general abstract formulation]] * [[sigma-model -- exposition of second quantization of sigma-models]] Then I expanded a little the second one of these, adding remarks on AKSZ theory.

   Since the entry sigma-model would not save any more (too long) I have splitt off the Exposition-subsections as separate entries

   • sigma-model – exposition of classical sigma-models

   • sigma-model – exposition of higher gauge theories as sigma-models

   • sigma-model – exposition of quantum sigma-models

   • sigma-model – exposition of a general abstract formulation

   • sigma-model – exposition of second quantization of sigma-models

   Then I expanded a little the second one of these, adding remarks on AKSZ theory.

6. • CommentRowNumber6.
   • CommentAuthorUrs
   • CommentTimeJul 1st 2014
   • (edited Jul 1st 2014)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded a pointer to [Witten 08 here](http://ncatlab.org/nlab/show/sigma-model#Witten08), where in section 6 is something that is meant as an explanation of the stack of G-connections for physicists.

   added a pointer to Witten 08 here, where in section 6 is something that is meant as an explanation of the stack of G-connections for physicists.

7. • CommentRowNumber7.
   • CommentAuthorDmitri Pavlov
   • CommentTimeJun 22nd 2022
   • PermaLink
   Author: Dmitri Pavlov
   Format: MarkdownItexCorrected the redirect “∞-model” to “σ-model”. <a href="https://ncatlab.org/nlab/revision/diff/sigma-model/74">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-model/74">v74</a>, <a href="https://ncatlab.org/nlab/show/sigma-model">current</a>

   Corrected the redirect “∞-model” to “σ-model”.

   diff, v74, current

8. • CommentRowNumber8.
   • CommentAuthorperezl.alonso
   • CommentTimeOct 30th 2023
   • PermaLink
   Author: perezl.alonso
   Format: MarkdownItexpointers to Friedan's original 2d renormalization articles. <a href="https://ncatlab.org/nlab/revision/diff/sigma-model/76">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-model/76">v76</a>, <a href="https://ncatlab.org/nlab/show/sigma-model">current</a>

   pointers to Friedan’s original 2d renormalization articles.

   diff, v76, current

9. • CommentRowNumber9.
   • CommentAuthorperezl.alonso
   • CommentTimeOct 30th 2023
   • PermaLink
   Author: perezl.alonso
   Format: MarkdownItexGeneral exposition of $n$-dimensional $\sigma$-models, including the fact that these are [[renormalization|non-renormalizable]] for $n\geq 3$: * [[Christopher Hull]]. "Lectures on Non-Linear Sigma-Models and Strings". In *Super field theories*, pp. 77-168. Boston, MA: Springer US, 1987. <a href="https://ncatlab.org/nlab/revision/diff/sigma-model/76">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-model/76">v76</a>, <a href="https://ncatlab.org/nlab/show/sigma-model">current</a>

   General exposition of -dimensional -models, including the fact that these are non-renormalizable for :

   • Christopher Hull. “Lectures on Non-Linear Sigma-Models and Strings”. In Super field theories, pp. 77-168. Boston, MA: Springer US, 1987.

   diff, v76, current

10. • CommentRowNumber10.
    • CommentAuthorUrs
    • CommentTimeOct 30th 2023
    • PermaLink
    Author: Urs
    Format: MarkdownItexadded [doi:10.1007/978-1-4613-0913-0_4](https://doi.org/10.1007/978-1-4613-0913-0_4) <a href="https://ncatlab.org/nlab/revision/diff/sigma-model/77">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-model/77">v77</a>, <a href="https://ncatlab.org/nlab/show/sigma-model">current</a>

    added doi:10.1007/978-1-4613-0913-0_4

    diff, v77, current

11. • CommentRowNumber11.
    • CommentAuthorperezl.alonso
    • CommentTimeNov 10th 2023
    • PermaLink
    Author: perezl.alonso
    Format: MarkdownItexAdded reference: * Rafał R. Suszek. *Towards higher super-$\sigma$-model categories*. (2023). ([arXiv:2311.01768](https://arxiv.org/abs/2311.01768)). (as a sidenote, since this is a paper about super-$\sigma$-models on gerbes, WZW models, and mentions prequantization a couple of times, it's missing some obvious references...) <a href="https://ncatlab.org/nlab/revision/diff/sigma-model/78">diff</a>, <a href="https://ncatlab.org/nlab/revision/sigma-model/78">v78</a>, <a href="https://ncatlab.org/nlab/show/sigma-model">current</a>

    Added reference:

    • Rafał R. Suszek. Towards higher super--model categories. (2023). (arXiv:2311.01768).

    (as a sidenote, since this is a paper about super--models on gerbes, WZW models, and mentions prequantization a couple of times, it’s missing some obvious references…)

    diff, v78, current