Multi-instanton calculus and the AdS / CFT correspondence in N=4 superconformal field theory

Jan, 1999
87 pages
Published in:
  • Nucl.Phys.B 552 (1999) 88-168
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Abstract:
We present a self-contained study of ADHM multi-instantons in SU(N) gauge theory, especially the novel interplay with supersymmetry and the large-N limit. We give both field- and string-theoretic derivations of the N=4 supersymmetric multi-instanton action and collective coordinate integration measure. As a central application, we focus on certain n-point functions G_n, n=16, 8 or 4, in N=4 SU(N) gauge theory at the conformal point (as well as on related higher-partial-wave correlators); these are correlators in which the 16 exact supersymmetric and superconformal fermion zero modes are saturated. In the large-N limit, for the first time in any 4-dimensional theory, we are able to evaluate all leading-order multi-instanton contributions exactly. We find compelling evidence for Maldacena's conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of a single copy of AdS_5 x S^5. (2) The integration measure on this space includes the partition function of 10-dimensional N=1 SU(k) gauge theory dimensionally reduced to 0 dimensions, matching the description of D-instantons in Type IIB string theory. (3) In exact agreement with Type IIB string calculations, at the k-instanton level, G_n = \sqrt{N} g^8 k^{n-7/2} e^{2\pi ik\tau} \sum_{d|k} d^{-2} F_n(x_1,...,x_n), where F_n is identical to a convolution of n bulk-to-boundary supergravity propagators.
Note:
  • 87 pages, uses an avant-garde version of Latex. Version 3 has an improved discussion of the expansion around the saddle-point solution Journal-ref: Nucl.Phys. B552 (1999) 88-168
  • field theory: conformal
  • supersymmetry
  • space-time: anti-de Sitter
  • instanton
  • gauge field theory: SU(N)
  • expansion 1/N
  • n-point function
  • string model
  • saddle-point approximation
  • supergravity