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# Entanglement entropy of 3-d conformal gauge theories with many flavors

## Author(s): Klebanov, Igor R; Pufu, Silviu S; Sachdev, Subir; Safdi, Benjamin R

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 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. Publication Date: May-2012 Electronic Publication Date: 10-May-2012 Citation: Klebanov, Igor R, Pufu, Silviu S, Sachdev, Subir, Safdi, Benjamin R. (2012). Entanglement entropy of 3-d conformal gauge theories with many flavors. JOURNAL OF HIGH ENERGY PHYSICS, 10.1007/JHEP05(2012)036 DOI: doi:10.1007/JHEP05(2012)036 ISSN: 1029-8479 Type of Material: Journal Article Journal/Proceeding Title: JOURNAL OF HIGH ENERGY PHYSICS Version: Author's manuscript

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