Expectation value of T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ operator in curved spacetimes

• Main Author: Yunfeng Jiang
• Format: Article
• Language: English
• Published: SpringerOpen 2020-02-01
• Series: Journal of High Energy Physics
• Subjects: Effective Field Theories; Field Theories in Lower Dimensions; Renormalization Group
• Online Access: http://link.springer.com/article/10.1007/JHEP02(2020)094

Abstract We study the expectation value of the T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ operator in maximally symmetric spacetimes. We define an diffeomorphism invariant biscalar whose coinciding limit gives the expectation value of the T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ operator. We show that this biscalar is a constant in flat spacetime, which reproduces Zamolodchikov’s result in 2004. For spacetimes with non-zero curvature, we show that this is no longer true and the expectation value of the T T ¯ $$ \mathrm{T}\overline{\mathrm{T}} $$ operator depends on both the one- and two-point functions of the stress-energy tensor.