Perturbative Critical Behavior from Spacetime Dependent Couplings
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{sup {kappa}}{mu}{sup {kappa}}, with a small parameter {kappa} playing a role analogous to {epsilon}. We show, in {phi}{sup 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}{sub *}(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}{sup 6} theories and two-dimensional sigma models with curved target spaces. We also describe strongly coupled examples using conformal perturbation theory.
- Research Organization:
- SLAC National Accelerator Lab., Menlo Park, CA (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC)
- DOE Contract Number:
- AC02-76SF00515
- OSTI ID:
- 1047549
- Report Number(s):
- SLAC-PUB-15201; arXiv:1207.6663; TRN: US1203954
- Journal Information:
- ArXiv, Journal Name: ArXiv
- Country of Publication:
- United States
- Language:
- English
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