Perturbative Critical Behavior from Spacetime Dependent Couplings

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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 ... continued below

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21 pages

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Dong, Xi; Horn, Bart; Silverstein, Eva & Torroba, Gonzalo August 3, 2012.

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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.

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21 pages

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  • Journal Name: ArXiv

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  • Report No.: SLAC-PUB-15201
  • Grant Number: AC02-76SF00515
  • Office of Scientific & Technical Information Report Number: 1047549
  • Archival Resource Key: ark:/67531/metadc831947

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  • August 3, 2012

Added to The UNT Digital Library

  • May 19, 2016, 9:45 a.m.

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  • June 20, 2016, 9:11 p.m.

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Dong, Xi; Horn, Bart; Silverstein, Eva & Torroba, Gonzalo. Perturbative Critical Behavior from Spacetime Dependent Couplings, article, August 3, 2012; United States. (digital.library.unt.edu/ark:/67531/metadc831947/: accessed July 23, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.