Can 3D String Theory Overcome UV Divergences Found in 1D String Theory?

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SUMMARY

The discussion centers on the feasibility of formulating a 3D string theory as an alternative to traditional 1D string theory. It is established that while a 3D string can be conceptualized as a small 3-brane, this formulation introduces ultraviolet (UV) divergences that cannot be eliminated perturbatively. In contrast, 1D string theories allow for the perturbative elimination of UV divergences due to the unique properties of the conformal group in two dimensions. The insights draw from Zwiebach's work on string theory and highlight the complexities involved in higher-dimensional string formulations.

PREREQUISITES
  • Understanding of string theory concepts, particularly 1D and 3D strings.
  • Familiarity with branes, specifically 1-branes and 3-branes.
  • Knowledge of ultraviolet (UV) divergences in quantum field theory.
  • Basic grasp of conformal groups and their dimensional properties.
NEXT STEPS
  • Research the implications of UV divergences in quantum field theories.
  • Study the properties and applications of 3-branes in string theory.
  • Explore the conformal group in two dimensions and its significance in string theory.
  • Read Zwiebach's "A First Course in String Theory" for foundational concepts.
USEFUL FOR

The discussion is beneficial for theoretical physicists, string theorists, and researchers interested in advanced quantum field theories and the implications of dimensionality in string formulations.

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I was wondering if anyone has ever tried to formulate a string theory with a 3D string rather than a 1D string. Has this been done? Is this much more complicated?
 
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I guess you've never noticed all this talk of branes or membranes.
 
Well...
Branes are not what I'm thinking about unless a 3D string is equivalent to a 3 brane. I've read the first half of Zwiebach, but I might have forgot about the part where he said a 1 D brane was a string.

Anyway, I'm thinking kind of a real string with width, height and length but just exceedingly small.
 
What you are talking about is a small 3-brane. One can formulate such a theory, but unlike the string theory (1-brane), the quantum theory contains UV divergences that cannot be eliminated, at least not perturbatively. In fact, UV divergences can be (perturbatively) eliminated only for objects extended in 1 dimension (not 0, not 2, ...), which is related to the fact that the conformal group in 2 dimensions (the other dimension is due to the extension in time) is much reacher than in other numbers of dimensions.
 

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