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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeJul 13th 2013
   • PermaLink
   Author: Urs
   Format: MarkdownItexcreated _[[worldline formalism]]_ to go with [this Physics.SE answer](http://physics.stackexchange.com/questions/70836/what-is-the-relationship-between-string-theory-and-quantum-field-theory/70987#70987)

   created worldline formalism to go with this Physics.SE answer

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeFeb 10th 2018
   • (edited Feb 10th 2018)
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   Author: Urs
   Format: MarkdownItexadded a little more to _[[worldline formalism]]_. In particular I added mentioning of this old but curious fact, which I only just learned of from looking again at the review [Schubert 96](https://arxiv.org/abs/hep-th/9610108): > In ([Metsaev-Tseytlin 88](https://ncatlab.org/nlab/show/worldline+formalism#MetsaevTseytlin88)) the [[1-loop]] [[beta function]] for pure [[Yang-Mills theory]] was obtained as the point-particle limit of the [[partition function]] of a [[bosonic string|bosonic]] [[open string]] in a Yang-Mills [[background field]]. This provided a theoretical explanation for the observation, made earlier in ([Nepomechie 83](https://ncatlab.org/nlab/show/worldline+formalism#Nepomechie83)) that when computed via [[dimensional regularization]] then this [[beta function]] coefficient of [[Yang-Mills theory]] vanishes in [[spacetime]] [[dimension]] 26. This of course is the critical dimension of the [[bosonic string]].

   added a little more to worldline formalism.

   In particular I added mentioning of this old but curious fact, which I only just learned of from looking again at the review Schubert 96:

   In (Metsaev-Tseytlin 88) the 1-loop beta function for pure Yang-Mills theory was obtained as the point-particle limit of the partition function of a bosonic open string in a Yang-Mills background field. This provided a theoretical explanation for the observation, made earlier in (Nepomechie 83) that when computed via dimensional regularization then this beta function coefficient of Yang-Mills theory vanishes in spacetime dimension 26. This of course is the critical dimension of the bosonic string.