期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 4, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP04(2012)074
关键词
Field Theories in Higher Dimensions; Statistical Methods
资金
- US NSF [PHY-0756966]
- IBM Einstein Fellowship at the Institute for Advanced Study
- John Simon Guggenheim Memorial Fellowship
- Pappalardo Fellowship
- U.S. Department of Energy [DE-FG02-05ER41360]
- National Science Foundation [DMR-1103860]
- MURI
- AFOSR
- NSF Graduate Research Fellowship Program
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1103860] Funding Source: National Science Foundation
Renyi entropies S-q are useful measures of quantum entanglement; they can be calculated from traces of the reduced density matrix raised to power q, with q >= 0. For (d + 1)-dimensional conformal field theories, the Renyi entropies across Sd-1 may be extracted from the thermal partition functions of these theories on either (d+1)-dimensional de Sitter space or R x H-d, where H-d is the d-dimensional hyperbolic space. These thermal partition functions can in turn be expressed as path integrals on branched coverings of the (d+1)-dimensional sphere and S-1 x H-d, respectively. We calculate the Renyi entropies of free massless scalars and fermions in d = 2, and show how using zeta-function regularization one finds agreement between the calculations on the branched coverings of,S-3 and on S-1 x H-2. Analogous calculations for massive free fields provide monotonic interpolating functions between the Renyi entropies at the Gaussian and the trivial fixed points. Finally, we discuss similar Renyi entropy calculations in d > 2.
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