Bootstrapping the minimal N $$ \mathcal{N} $$ = 1 superconformal field theory in three dimensions

Junchen Rong (DESY Hamburg, Theory Group, Notkestraße 85, Hamburg, D-22607, Germany) ; Ning Su (Department of Physics, University of Pisa, Largo Bruno Pontecorvo 3, Pisa, I-56127, Italy)

We develop the numerical bootstrap technique to study the 2 + 1 dimensional N $$ \mathcal{N} $$ = 1 superconformal field theories (SCFTs). When applied to the minimal N $$ \mathcal{N} $$ = 1 SCFT, it allows us to determine its critical exponents to high precision. This model was argued in [1] to describe a quantum critical point (QCP) at the boundary of a 3 + 1D topological superconductor. More interestingly, this QCP can be reached by tuning a single parameter, where supersymmetry (SUSY) is realized as an emergent symmetry. We show that the emergent SUSY condition also plays an essential role in bootstrapping this SCFT. But performing a “two-sided” Padé re-summation of the large N expansion series, we calculate the critical exponents for Gross-Neveu-Yukawa models at N =4 and N =8.

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      "source": "Springer", 
      "value": "We develop the numerical bootstrap technique to study the 2 + 1 dimensional   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 1 superconformal field theories (SCFTs). When applied to the minimal   <math> <mi>N</mi> </math>  $$ \\mathcal{N} $$  = 1 SCFT, it allows us to determine its critical exponents to high precision. This model was argued in [1] to describe a quantum critical point (QCP) at the boundary of a 3 + 1D topological superconductor. More interestingly, this QCP can be reached by tuning a single parameter, where supersymmetry (SUSY) is realized as an emergent symmetry. We show that the emergent SUSY condition also plays an essential role in bootstrapping this SCFT. But performing a \u201ctwo-sided\u201d Pad\u00e9 re-summation of the large N expansion series, we calculate the critical exponents for Gross-Neveu-Yukawa models at N =4 and N =8."
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Published on:
25 June 2021
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2021 (2021)
Issue 6
Pages 1-15
DOI:
https://doi.org/10.1007/JHEP06(2021)154
arXiv:
1807.04434
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: