Is Phi^3 Theory in Five Dimensions Supposed to Be Finite?

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Discussion Overview

The discussion revolves around the finiteness of phi^3 theory in five dimensions, specifically examining the implications of regularization techniques and the behavior of loop contributions to the propagator. The scope includes theoretical considerations and mathematical reasoning related to quantum field theory.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested, Mathematical reasoning

Main Points Raised

  • One participant expresses confusion regarding the divergence of the 1-loop contribution to the propagator in six dimensions, as shown in Srednicki's work, and questions why a similar analysis in five dimensions yields a finite result.
  • Another participant requests clarification on the specific content of equation 14.3 to better address the initial question.
  • A third participant suggests referring to a different thread for additional context or information.
  • A fourth participant questions the relevance of equation 14.3 in resolving the issues raised about equation 14.30.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as the initial question remains unresolved and further clarification is sought regarding the equations mentioned.

Contextual Notes

There is a lack of detail regarding the specific content of the equations referenced, which may limit the ability to fully address the concerns raised. The discussion also highlights the complexity of regularization in different dimensions.

electroweak
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OK, I think I am missing something very basic...

When regularizing phi^3 theory in six dimensions, Srednicki comes to eq 14.30, which shows that the 1-loop contribution to the propagator diverges (the gamma function has a pole). This is good.

OK. Now let d=5 (or epsilon=1). Actually, go ahead and let d=1001 or any odd number. Then 14.30 is finite, which definitely seems wrong. "Superficially," the diagram should diverge...

What am I screwing up?
 
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Your question would be easier to answer if you actually told us what's in equation 14.3.
 
@dauto, how is 14.3 going to help resolve equation 14.30?
 

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