On the gauge theory. Geometry correspondence (Q2782334)

The authors propose a new duality: they show that the large \(N\) limit of \(\text{SU}(N)\) Chern-Simons theory on the 3-sphere \(S^3\) is exactly the same as an \(N=2\) topological closed string theory blow up of the conifold geometry. The \(\text{SU}(N)\) Chern-Simons theory on \(S^3\) arises from the A-model open string theory on the Calabi-Yau manifold \(T^*S^3\) with Dirichlet boundary conditions on \(S^3\). The authors compare the partition functions of the Chern-Simons and the closed string theories and find a strikingly exact match for all values of the 't Hooft coupling constant \(\lambda\) and to all orders of \(1/N\). They discuss a possibility to derive the duality from the 2-d linear sigma model, considered by E. Witten, that is an \(N=2\) supersymmetric \(U(1)\) gauge theory, whose low energy dynamics description reduces to the usual nonlinear sigma model on the \(S^2\) blown up version of the conifold. The authors believe that the linear sigma model approach can be also useful in deriving the AdS/CFT correspondence.NEWLINENEWLINEFor the entire collection see [Zbl 0980.00027].