Mingling of the infrared and ultraviolet and the “cosmological constant” for interacting QFT in 2d

We propose a proper definition of the vacuum expectation value stress energy tensor $\langle 0 | T_{\mu\nu} |0 \rangle$ for integrable quantum field theories in two spacetime dimensions, which is analog cosmological constant 4d. For wide variety models, massive or massless, we show $\rho_{\rm vac} = - m^2/2 \mathfrak{g} $ exactly, where $\mathfrak{g} generalized coupling compute and $m$ basic mass scale. The kinds models consider are sinh-Gordon sine-Gordon perturbations Yang-Lee 3-state Potts pure $T\bar{T}$ infra-red QFT's, UV completions latter massless flows between IR fixed points. In case lightest particle related to parameters 2-body S-matrix. some examples =0$ due an unbroken fractional supersymmetry. cases, can be scale spontaneous symmetry breaking. "cosmological problem" generically arises free limit \to 0$, thus interactions potentially resolve problem at least most cases considered this paper. speculate on extensions these results 4 dimensions =- m^4/2 \mathfrak{g}$,however without integrability cannot yet precise manner calculate $\mathfrak{g}$. Nevertheless, based data $, if \approx 1$ then order experimental values proposed neutrino masses.