Compact analytical form for non-zeta terms in critical exponents at order 1/N3

  title={Compact analytical form for non-zeta terms in critical exponents at order 1/N3},
  author={David John Broadhurst and Anatoly V. Kotikov},
  journal={Physics Letters B},
Abstract We simplify, to a single integral of dilogarithms, the least tractable O(1/ N 3 ) contribution to the large- N critical exponent η of the non-linear σ -model, and hence φ 4 -theory, for any spacetime dimensionality, D . It is the sole generator of irreducible multiple zeta values in e -expansions with D =2−2 e , for the σ -model, and D =4−2 e , for φ 4 -theory. In both cases we confirm results of Broadhurst, Gracey and Kreimer (BGK) that relate knots to counterterms. The new compact… Expand
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