摘要
We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory(CFT). The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by ?. For the case of two short intervals on a complex plane, we expand the R′enyi mutual information by the cross ratio x to order x^(2△+2). For the case of one interval on a torus with low temperature, we expand the R′enyi entropy by q = exp(-2πβ/L), with β being the inverse temperature and L being the spatial period, to order q^(△+2). To make the result meaningful, we require that the scaling dimension ? cannot be too small. For two intervals on a complex plane we need △ 〉 1, and for one interval on a torus we need △ 〉 2.We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side,and find matches of gravity and CFT results.
We calculate the contributions of a general non-vacuum conformal family to R′enyi entropy in twodimensional conformal field theory(CFT). The primary operator of the conformal family can be either non-chiral or chiral, and we denote its scaling dimension by ?. For the case of two short intervals on a complex plane, we expand the R′enyi mutual information by the cross ratio x to order x^(2△+2). For the case of one interval on a torus with low temperature, we expand the R′enyi entropy by q = exp(-2πβ/L), with β being the inverse temperature and L being the spatial period, to order q^(△+2). To make the result meaningful, we require that the scaling dimension ? cannot be too small. For two intervals on a complex plane we need △ 〉 1, and for one interval on a torus we need △ 〉 2.We work in the small Newton constant limit on the gravity side and so a large central charge limit on the CFT side,and find matches of gravity and CFT results.
基金
Supported by ERC Starting Grant 637844-HBQFTNCER