Instantons and Emergent AdS_3 x S^3 Geometry.pdfVIP

a r X i v : h e p - t h / 0 6 0 4 0 9 0 v 2 2 7 A p r 2 0 0 6 Preprint typeset in JHEP style - PAPER VERSION Instantons and Emergent AdS3×S3 Geometry Heng-Yu Chen and David Tong Department of Applied Mathematics and Theoretical Physics, University of Cambridge, UK h.y.chen, d.tong@damtp.cam.ac.uk Abstract: Two dimensional N = (4, 4) gauge theories flow to interacting supercon- formal field theories on their Higgs branch. We examine worldsheet instantons in these theories through the eyes of a D-brane construction. The effective instanton partition function is shown to reveal an emergent background AdS3 × S3 geometry. Dedicated to the memory of John Brodie and Andrew Chamblin and the roadtrip to Roswell. 1. Introduction The notion of gravity as an emergent force holds a certain appeal. The no-go theorem of Weinberg and Witten [1] presents a hurdle that any attempt to dynamically generate a generally covariant theory of gravity must negotiate, and several examples which evade the assumptions of the theorem are now known. The most compelling of these is the celebrated AdS/CFT correspondence [2] in which both gravity and the bulk of spacetime appear dynamically. The emergence of a bulk geometry from field theoretic origins is a strong coupling phenomenon that is not easy to see. Indeed, it is hard to determine from first principles which field theories have a string dual. A window is provided by BPS solitons. Within the framework of the AdS5/CFT4 correspondence, it is Yang-Mills instantons which provide a natural probe of the emergent geometry where they are represented by D- instantons which may roam the higher dimensional space [3, 4]. It was shown by Dorey et. al. [5] that the partition function of instantons in SU(N) N = 4 super Yang-Mills coincides with that of the D-instanton. Most notably, the effective large N moduli space of Yang-Mills instantons in this theory is AdS5 × S5. The radial direction of AdS5 arises from the scaling mode of the instanton while t