期刊
JOURNAL OF HIGH ENERGY PHYSICS
卷 -, 期 8, 页码 -出版社
SPRINGER
DOI: 10.1007/JHEP08(2020)064
关键词
Conformal and W Symmetry; Conformal Field Theory; Discrete Symmetries; Global Symmetries
资金
- US Department of Energy (DOE) [DESC0009919]
- Simons Foundation [568420]
- Ambrose Monell Foundation
- DOE [DE-SC0009988]
We derive Cardy-like formulas for the growth of operators in different sectors of unitary 2 dimensional CFT in the presence of topological defect lines by putting an upper and lower bound on the number of states with scaling dimension in the interval [Delta - delta, Delta + delta] for large Delta at fixed delta. Consequently we prove that given any unitary modular invariant 2D CFT symmetric under finite global symmetry G(acting faithfully), all the irreducible representations of G appear in the spectra of the untwisted sector; the growth of states is Cardy like and proportional to the square of the dimension of the irrep. In the Schwarzian limit, the result matches onto that of JT gravity with a bulk gauge theory. If the symmetry is non-anomalous, the result applies to any sector twisted by a group element. For c > 1, the statements are true for Virasoro primaries. Furthermore, the results are applicable to large c CFTs. We also extend our results for the continuous U(1) group.
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