期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 3, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP03(2015)167
关键词
Field Theories in Lower Dimensions; Nonperturbative Effects
资金
- US DOE [DE-SC0010010]
- Marie Curie Intra-European Fellowship of the European Community's 7th Framework Programme [PIEF-GA-2013-623606]
- US Department of Energy [DE-SC0010010]
- Galkin fellowship
We consider the conformal bootstrap for spacetime dimension 1 < d < 2. We determine bounds on operator dimensions and compare our results with various theoretical and numerical models, in particular with resummed epsilon-expansion and Monte Carlo simulations of the Ising model on fractal lattices. The bounds clearly rule out that these models correspond to unitary conformal field theories. We also clarify the d -> 1 limit of the conformal bootstrap, showing that bounds can be - and indeed are - discontinuous in this limit. This discontinuity implies that for small epsilon = d - 1 the expected critical exponents for the Ising model are disallowed, and in particular those of the d - 1 expansion. Altogether these results strongly suggest that the Ising model universality class cannot be described by a unitary CFT below d = 2. We argue this also from a bootstrap perspective, by showing that the 2 <= d < 4 Ising kink splits into two features which grow apart below d = 2.
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