Perturbative Critical Behavior from Spacetime Dependent Couplings

XI DONG; BART HORN; EVA SILVERSTEIN; GONZALO TORROBA

PHYSICAL REVIEW D

AMER PHYSICAL SOC

Lugar: New York; Año: 2012 vol. 86 p. 1 - 10

1550-7998

We find novel perturbative fixed points by introducing mildly spacetime-dependent couplings into otherwise marginal terms. In four-dimensional QFT, these are physical analogues of the small-$epsilon$ Wilson-Fisher fixed point. Rather than considering 4-epsilon dimensions, we stay in four dimensions but introduce couplings whose leading spacetime dependence is of the form $lambda x^kappa mu^kappa$, with a small parameter $kappa$ playing a role analogous to $epsilon$. We show, in $phi^4$ theory and in QED and QCD with massless flavors, that this leads to a critical theory under perturbative control over an exponentially wide window of spacetime positions $x$. The exact fixed point coupling $lambda_*(x)$ in our theory is identical to the running coupling of the translationally invariant theory, with the scale replaced by $1/x$. Similar statements hold for three-dimensional $phi^6$ theories and two-dimensional sigma models with curved target spaces. We also describe strongly coupled examples using conformal perturbation theory.