### Abstract

Three-dimensional conformal field theories (CFTs) of deconfined gauge fields coupled to gapless flavors of fermionic and bosonic matter describe quantum critical points of condensed matter systems in two spatial dimensions. An important characteristic of these CFTs is the finite part of the entanglement entropy across a circle. The negative of this quantity is equal to the finite part of the free energy of the Euclidean CFT on the three-sphere, and it has been proposed to satisfy the so called F-theorem, which states that it decreases under RG flow and is stationary at RG fixed points. We calculate the three-sphere free energy of non-supersymmetric gauge theory with a large number N_{F} of bosonic and/or fermionic flavors to the first subleading order in 1/N_{F}. We also calculate the exact free energies of the analogous chiral and non-chiral N = 2 supersymmetric theories using localization, and find agreement with the 1/N_{F} expansion. We analyze some RG flows of supersymmetric theories, providing further evidence for the F-theorem.

Original language | English (US) |
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Article number | 36 |

Journal | Journal of High Energy Physics |

Volume | 2012 |

Issue number | 5 |

DOIs | |

State | Published - Jan 1 2012 |

Externally published | Yes |

### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Keywords

- 1/N expansion
- Chern-simons theories
- Field theories in lower dimensions
- Renormalization group

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## Cite this

*Journal of High Energy Physics*,

*2012*(5), [36]. https://doi.org/10.1007/JHEP05(2012)036