Bonus symmetry and the operator product expansion of N=4 SuperYang-Mills

May, 1999
23 pages
Published in:
  • Nucl.Phys.B 559 (1999) 165-183
e-Print:
Report number:
  • UCSD-PTH-99-06,
  • IASSNS-HEP-99-45

Citations per year

19992005201120172023051015
Abstract:
The superconformal group of N=4 super-Yang-Mills has two types of operator representations: short and long. We conjecture that operator product expansions for which at least two of the three operators are short exactly respect a bonus U(1)_Y R-symmetry, which acts as an automorphism of the superconformal group. This conjecture is for arbitrary gauge group G and gauge coupling g_{YM}. A consequence is that n\leq 4-point functions involving only short operators exactly respect the U(1)_Y symmetry, as has been previously conjectured based on AdS duality. This, in turn, would imply that all n\leq 3 -point functions involving only short operators are not renormalized, as has also been previously conjectured and subjected to perturbative checks. It is argued that instantons are compatible with our conjecture. Some perturbative checks of the conjecture are presented and SL(2,Z) modular transformation properties are discussed.
Note:
  • 22 pages, 2 figures, harvmac
  • gauge field theory: Yang-Mills
  • supersymmetry
  • operator product expansion
  • group: conformal
  • instanton
  • transformation: modular
  • symmetry: SL(2,Z)
  • correlation function
  • charge: U(1)
  • fermion: zero mode