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  A Question about Abelian Dualities in 2+1 Dimensions

+ 2 like - 0 dislike

I have a question from the paper "More Abelian Dualities in 2+1 Dimensions".


On  page 3, it says that we flow towards IR by sending $\alpha\rightarrow\infty$ and tuning the mass to zero.

$$S[\phi ;A]=\int d^{3}x |(\partial_{\mu}-iA_{\mu})\phi|^{2}-\alpha|\phi|^{4}.$$

My question is that why this limit takes the theory to IR.

asked Feb 20, 2018 in Theoretical Physics by New Student (270 points) [ revision history ]
recategorized Feb 21, 2018 by Dilaton

1 Answer

+ 1 like - 0 dislike

$\alpha \to \infty$ in the IR because the $|\phi|^4$ term has dimension 1. Then there is a comma missing, the mass is tuned to zero to achieve criticality. The mass term is relevant like always though. It has to be tuned by hand.

answered Feb 21, 2018 by Ryan Thorngren (1,895 points) [ no revision ]

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