Super-Yang-MillsN=4theory in light-cone gauge and the “bridge” identities

Abstract

The light-cone gauge allows to single out a set of "transverse" fields (TF), whose Green functions are free from UV divergences in SYM N =4. Green functions with external lines involving the remaining fields do instead exhibit divergences: indeed those fields can be expressed, by solving their equations of motion, as composite operators in terms of "transverse" fields. A set of exact identities (bridge identities) automatically realize their insertions in a path-integral formulation.DFPD/TH 07-07

Supersymmetric Wilson loops at two loops

“…The tree-level correlation function A a λ (p 1 )A b µ (p 2 )A c ν (p 3 ) is given in ref. [63]. We get where ǫ(t 1 , t 2 , t 3 ) is the same function defined in sec.…”

“…In ref. [63] the self-energy corrections to the gluon and scalar propagators at O(g 2 ) for SUSY N = 4 have been computed. Since the Wilson loop we are considering lies on the plane orthogonal to the gauge vectors n and n, it is easy to convince oneself that only "transverse" Green functions contribute, which, in turn, get only f inite O(g 2 ) corrections in this gauge [60], at variance with the more familiar Feynman gauge [26].…”

“…The tree-level correlation function A a λ (p 1 )A b µ (p 2 )A c ν (p 3 ) is given in ref. [63]. We get e ip 2 •(x 2 −x 1 )+ip…”

N=8supergravity on the light cone

“…Supergraph light-cone Feynman rules were also used in [49] to compute some diagrams in an N =4 SYM theory deformed to N =1. The extensive set of light-cone computations was performed in N =4 SYM theory in components, not manifestly supersymmetric, see [50] and references therein. So far, however, in existing literature there are no explicit supergraph computations of the on shell amplitudes in which we are interested.…”

“…(4.10) of Brink, Lindgren, Nilsson paper in [18]. In SYM the loop computations were performed in components, see for example the papers of Bassetto et al [50] and references therein. What they call "transverse" fields are exactly the components of the light-cone superfield for which they find all Z-factors are equal to 1.…”