Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the \${\textbackslash}varepsilon\$ Expansion. Osborn, H. & Stergiou, A. arXiv:2010.15915 [cond-mat, physics:hep-th], October, 2020. arXiv: 2010.15915
Heavy Handed Quest for Fixed Points in Multiple Coupling Scalar Theories in the \${\textbackslash}varepsilon\$ Expansion [link]Paper  abstract   bibtex   
The tensorial equations for non trivial fully interacting fixed points at lowest order in the \${\textbackslash}varepsilon\$ expansion in \$4-{\textbackslash}varepsilon\$ and \$3-{\textbackslash}varepsilon\$ dimensions are analysed for \$N\$-component fields and corresponding multi-index couplings \${\textbackslash}lambda\$ which are symmetric tensors with four or six indices. Both analytic and numerical methods are used. For \$N=5,6,7\$ in the four-index case large numbers of irrational fixed points are found numerically where \${\textbar}{\textbar}{\textbackslash}lambda {\textbar}{\textbar}{\textasciicircum}2\$ is close to the bound found by Rychkov and Stergiou in arXiv:1810.10541. No solutions, other than those already known, are found which saturate the bound. These examples in general do not have unique quadratic invariants in the fields. For \$N {\textbackslash}geqslant 6\$ the stability matrix in the full space of couplings always has negative eigenvalues. In the six index case the numerical search generates a very large number of solutions for \$N=5\$.
@article{osborn_heavy_2020,
	title = {Heavy {Handed} {Quest} for {Fixed} {Points} in {Multiple} {Coupling} {Scalar} {Theories} in the \${\textbackslash}varepsilon\$ {Expansion}},
	url = {http://arxiv.org/abs/2010.15915},
	abstract = {The tensorial equations for non trivial fully interacting fixed points at lowest order in the \${\textbackslash}varepsilon\$ expansion in \$4-{\textbackslash}varepsilon\$ and \$3-{\textbackslash}varepsilon\$ dimensions are analysed for \$N\$-component fields and corresponding multi-index couplings \${\textbackslash}lambda\$ which are symmetric tensors with four or six indices. Both analytic and numerical methods are used. For \$N=5,6,7\$ in the four-index case large numbers of irrational fixed points are found numerically where \${\textbar}{\textbar}{\textbackslash}lambda {\textbar}{\textbar}{\textasciicircum}2\$ is close to the bound found by Rychkov and Stergiou in arXiv:1810.10541. No solutions, other than those already known, are found which saturate the bound. These examples in general do not have unique quadratic invariants in the fields. For \$N {\textbackslash}geqslant 6\$ the stability matrix in the full space of couplings always has negative eigenvalues. In the six index case the numerical search generates a very large number of solutions for \$N=5\$.},
	urldate = {2020-11-09},
	journal = {arXiv:2010.15915 [cond-mat, physics:hep-th]},
	author = {Osborn, Hugh and Stergiou, Andreas},
	month = oct,
	year = {2020},
	note = {arXiv: 2010.15915},
	keywords = {condensed matter, high energy physics, mentions sympy},
}
Downloads: 0