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Bubble-resummation and critical-point methods for ß-functions at large N

MPS-Authors
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Alanne,  Tommi
Florian Goertz - Max Planck Research Group, Junior Research Groups, MPI for Nuclear Physics, Max Planck Society;

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Blasi,  Simone
Division Prof. Dr. Manfred Lindner, MPI for Nuclear Physics, Max Planck Society;

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1904.05751.pdf
(Preprint), 549KB

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Citation

Alanne, T., Blasi, S., & Dondi, N. A. (2019). Bubble-resummation and critical-point methods for ß-functions at large N. The European Physical Journal C: Particles and Fields, 79(8): 689. doi:10.1140/epjc/s10052-019-7190-9.


Cite as: http://hdl.handle.net/21.11116/0000-0005-42B2-7
Abstract
We investigate the connection between the bubble-resummation and critical-point methods for computing the $\beta$-functions in the limit of large number of flavours, $N$, and show that these can provide complementary information. While the methods are equivalent for single-coupling theories, for multi-coupling case the standard critical exponents are only sensitive to a combination of the independent pieces entering the $\beta$-functions, so that additional input or direct computation are needed to decipher this missing information. In particular, we evaluate the $\beta$-function for the quartic coupling in the Gross-Neveu-Yukawa model, thereby completing the full system at $\mathcal{O}(1/N)$. The corresponding critical exponents would imply a shrinking radius of convergence when $\mathcal{O}(1/N^2)$ terms are included, but our present result shows that the new singularity is actually present already at $\mathcal{O}(1/N)$, when the full system of $\beta$-functions is known.