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

Abstract

AbstractWe propose a proper definition of the vacuum expectation value of the stress energy tensor 〈0| Tμν| 0〉 for integrable quantum field theories in two spacetime dimensions, which is the analog of the cosmological constant in 4d. For a wide variety of models, massive or massless, we show$$ {\rho}_{\textrm{vac}}=-{m}^2/2\mathfrak{g} $$ρvac=−m2/2gexactly, where$$ \mathfrak{g} $$gis a generalized coupling which we compute andmis a basic mass scale. The kinds of models we consider are the massive sinh-Gordon and sine-Gordon theories and perturbations of the Yang-Lee and 3-state Potts models, pure$$ T\overline{T} $$TT¯perturbations of infra-red QFT’s, and UV completions of the latter which are massless flows between UV and IR fixed points. In the massive casemis the physical mass of thelightestparticle and$$ \mathfrak{g} $$gis related to parameters in the 2-body S-matrix. In some examplesρvac= 0 due to a fractional supersymmetry. For massless cases,mcan be a scale of spontaneous symmetry breaking. The “cosmological constant problem” generically arises in the free field limit$$ \mathfrak{g} $$g→ 0, thus interactions can potentially resolve the problem at least for most cases considered in this paper. We speculate on extensions of these results to 4 spacetime dimensions and propose$$ {\rho}_{\textrm{vac}}={m}^4/2\mathfrak{g} $$ρvac=m4/2g, however without integrability we cannot yet propose a precise manner in which to calculate$$ \mathfrak{g} $$g. Nevertheless, based on cosmological data onρvac, if$$ \mathfrak{g} $$g~ 1 then it is worth pointing out that the lightest mass particle is on the order of experimental values of proposed neutrino masses.