3-Branes on Eguchi-Hanson 6D Instantons.pdf

a r X i v : h e p - t h / 0 7 0 1 1 4 0 v 2 2 7 A p r 2 0 0 7 hep-th/yymmnnn SINP/TNP/07-01 3-Branes on Eguchi-Hanson 6D Instantons Harvendra Singh Saha Institute of Nuclear Physics 1/AF Bidhannagar, Kolkata 700064, India E-mail: h.singh[AT]saha.ac.in Abstract We use the approach used by Eguchi-Hanson in constructing four-dimensional instan- ton metrics and construct a class of regular six-dimensional instantons which are nothing but S2 × S2 resolved conifolds. We then also obtain D3-brane solutions on these EH- resolved conifolds. 1 1 Introduction The AdS/CFT conjecture [1, 2, 3] relates string theory on anti-de Sitter bulk spacetime to a four-dimensional conformal gauge theory on the boundary. It serves as being one of the concrete realisation of the holographic idea [4]. In this picture the SU(N) super- Yang-Mills theory lives on the boundary of the bulk AdS5 × S5 space. Since then this gauge-gravity duality has been extensively tested and has provided a fruitful alternative in understanding of various aspects of gauge theories, both qualitatively and quantitatively. The large body of work is cited in some reviews, for example [5]. It has been rather interesting to study AdS/CFT for the class of manifolds AdS5×T 1,1 which have less supersymmetry, where T 1,1 is an Einstein space. This requires constructing D3-brane solutions over M4 × Y p,q spaces where Y p,q is the six-dimensional Calabi-Yau cone. These cone-like geometries are singular at the tip of the cone, but deformations on these conifold geometries can be performed [6] so that they become regular Calabi-Yau geometries. Several new resolved solutions have recently appeared in literature [7, 8]. In this short note we first construct a regular Calabi-Yau cone solution which we obtain by adopting standard method of constructing Eguchi-Hanson 4D instantons. We call them EH-resolved cone as they share some unique properties with Eguchi-Hanson instantons. But there are standard techniques to resolve these c