We study the expectation value of the $\mathrm{ T}\overline{ \mathrm{ T}}$ operator in spacetimes with constant curvature. We define an diffeomorphism invariant biscalar whose coinciding limit gives the expectation value of the $\mathrm{ T}\overline{ \mathrm{ T}}$ 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 $\mathrm{ T}\overline{ \mathrm{ T}}$ operator depends on both the one-point and two-point functions of the stress-energy tensor.
Categories: hep-th