Expectation value of $$ \mathrm{T}\overline{\mathrm{T}} $$ operator in curved spacetimes
Yunfeng Jiang
Abstract
A bstract We study the expectation value of the $$ \mathrm{T}\overline{\mathrm{T}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> operator in maximally symmetric spacetimes. We define an diffeomorphism invariant biscalar whose coinciding limit gives the expectation value of the $$ \mathrm{T}\overline{\mathrm{T}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> 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 $$ \mathrm{T}\overline{\mathrm{T}} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> <mml:mover> <mml:mi>T</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> </mml:math> operator depends on both the one- and two-point functions of the stress-energy tensor.