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

Abstract

Abstract We study the expectation value of the $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ operator in maximally symmetric spacetimes. We define an diffeomorphism invariant biscalar whose coinciding limit gives the expectation value of the $$ \mathrm{T}\overline{\mathrm{T}} $$ T 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 $$ \mathrm{T}\overline{\mathrm{T}} $$ T T ¯ operator depends on both the one- and two-point functions of the stress-energy tensor.