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Multi-Instantons and Maldacena ’ s Conjecture
| Content Provider | Semantic Scholar |
|---|---|
| Author | Dorey, Nicholas Hollowood, Timothy J. Khoze, Valentin V. Mattis, Michael P. Vandoren, Stefan |
| Copyright Year | 1999 |
| Abstract | We examine certain n-point functions Gn in N = 4 supersymmetric SU(N) gauge theory at the conformal point. In the large-N limit, we are able to sum all leading-order multiinstanton contributions exactly. We find compelling evidence for Maldacena’s conjecture: (1) The large-N k-instanton collective coordinate space has the geometry of AdS5 × S . (2) In exact agreement with type IIB superstring calculations, at the k-instanton level, Gn = √ N g ke k/g ∑ d|k d −2 · Fn(x1, . . . , xn), where Fn is identical to a convolution of n bulk-to-boundary SUGRA propagators. A remarkable conjecture by Maldacena [1] (see also [2] and references therein) relates the large-N limit of 4-dimensional N = 4 supersymmetric Yang-Mills theory (SYM) at the conformal point of vanishing VEVs, to the low-energy behavior of type IIB superstrings on AdS5 × S. In this conjectured correspondence, the SYM theory is defined on the boundary of the AdS5; the generating functionals of SYM correlation functions are then equated to partition functions in the bulk with specific boundary conditions. When the string coupling is small and the radii of both the AdS5 and S 5 are large (namely small g but large gN , where g is the gauge theory coupling) the string calculation can be approximated by classical supergravity, whereas when gN is small the SYM model is amenable to standard perturbative and semiclassical analysis. An important consequence of Maldacena’s conjecture is that Yang-Mills instantons should be related in a specific way to the D-instantons of the IIB string theory on AdS5 × S. In particular, Banks and Green [3] showed that the AdS5×S background solves the field equations of the same SL(2, Z) invariant effective action which describes D-instanton corrections to the IIB theory in flat space. The proposed AdS/CFT correspondence then yields predictions for an infinite series of multi-instanton contributions in the N = 4 theory. This relation was studied, at the 1-instanton level, in Ref. [4] for gauge group SU(2), and in Ref. [5] for general SU(N). In this Letter, we extend the 1-instanton results of [5] to arbitrary YangMills multi-instantons. For any finite N , the jump from singleto multi-instantons is always accompanied by an enormous increase in calculational complexity, endemic to the ADHM formalism. But in the large-N limit there are compensating simplifications, namely: (i) The integration over the k-instanton collective coordinate space (“ADHM moduli space”) becomes dominated by k single instantons living in k mutually commuting SU(2) subgroups of SU(N). (In this one respect only, the problem becomes dilute-gas-like.) This intuitively obvious remark, which we derive below from a large-N saddle-point treatment of the ADHM formalism, follows from statistical considerations alone, and is independent of supersymmetry. Additionally in the large-N limit, other less intuitive but equally remarkable features appear, which depend crucially on the N = 4 supersymmetry: (ii) To leading order in the large-N saddle-point expansion, the geometry of the k-instanton moduli space is described by (AdS5 × S). Here the AdS5 factors are coordinatized by the positions and sizes (xn, ρi) of the k instantons, as has been noted previously [4, 6]. But the emergence of the S factors is a newly observed feature of large N even at the 1-instanton level; the (S) coordinates are the auxiliary antisymmetric-tensor variables χAB, 1 ≤ i ≤ k, 1 ≤ A, B ≤ 4, used to bilinearize a certain fermion quadrilinear term in the N = 4 instanton action. One can check that the SO(6)R non-singlet operators which correspond to the Kaluza-Klein modes of the IIB dilaton on S couple to these angular degrees of freedom in the correct way [7]. (iii) Integrations in the vicinity of the large-N saddle-point generate an attractive singular |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-th/9810243v1.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-th/9810243v2.pdf |
| Alternate Webpage(s) | http://arxiv.org/pdf/hep-th/9810243v3.pdf |
| Language | English |
| Access Restriction | Open |
| Subject Keyword | AngularJS Approximation algorithm Bank (environment) Bibliographic Reference Calcifying Fibrous Pseudotumor Convolution Emergence Formal system IBM Integration Bus Numerous Perturbation theory (quantum mechanics) Propagator Semiclassical physics Singlet state Singular Yang Deficiency |
| Content Type | Text |
| Resource Type | Article |
