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Equations of GR with a cosmological constant $\Lambda$ read

$R_{{\mu}{

u}}-\dfrac{1}{2}Rg_{{\mu}{

u}} + \Lambda g_{{\mu}{

u}} =8\pi T_{{\mu}{

u}}$

Therefore,

$R-\dfrac{D}{2}R+D\Lambda=8\pi T$

($D$ is the number of spacetime dimensions.)

Or,

$\Lambda = \dfrac{8\pi T}{D} + \bigg(\dfrac{D-2}{2D}\bigg)R$

Therefore,

$\Lambda = \bigg(\dfrac{D-2}{2D}\bigg)R_0$ where $R_0 := R_{vacuum}$

Therefore, for $D=2$, $\Lambda=0$.

So, a universe with $1+1$ dimensions can't have a non-zero cosmological constant. Now, would the quantum fields in such a universe have a positive zero-point energy? If yes then the cosmological constant should be expected to be positive. If so then the cosmological constant problem appears to be extraordinarily sharp and of the form of a theoretical paradox--because we have got the value of the cosmological constant to be positive from a theoretical argument (the one related to the zero-point energy of quantum fields) and we have also got a vanishing cosmological constant from the theory (GR) in a straightforward manner. Whereas in the 3+1 universe, the problem is about a disagreement between the theoretical prediction and the experiment--in particular, GR in itself predicts no value of the cosmological constant in $3+1$ but it seems to do so in $1+1$.

The only crucial assumption (as far as I can see) in my argument is that the quantum fields would give positive zero-point energy in a 1+1 universe--this, sadly, I can't verify owing to my limited knowledge of QFT. I am posting this question, of course, to find out if my argument really poses a paradox.