An Update on AdS/CFT: Sasaki-Einstein Metrics, Toric Quivers and Z-Minimisation

          @misc{ pirsa_PIRSA:05040054,
            doi = {10.48660/05040054},
            url = {https://pirsa.org/05040054},
            author = {},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {An Update on AdS/CFT: Sasaki-Einstein Metrics, Toric Quivers and Z-Minimisation},
            publisher = {Perimeter Institute},
            year = {2005},
            month = {apr},
            note = {PIRSA:05040054 see, \url{https://pirsa.org}}
          }
          

Abstract

In this talk I will summarise the recent progress in AdS/CFT due to the construction of the new infinite family of Sasaki-Einstein metrics Y^{p,q}, and their dual superconformal gauge theories. I will review some aspects of Sasaki-Einstein geometry and the main features of the Y^{p,q} metrics. I will then discuss the use of toric geometry to obtain a description of the corresponding Y^{p,q} Calabi-Yau singularities. I will explain how the AdS/CFT dual N=1 supersymmetric gauge theories were constructed using the combined information obtained from the metrics and the toric singularities. A crucial check on the consistency of the construction is provided by the field theory technique of a-maximisation. In the last part of the talk I will briefly discuss the recently formulated geometric dual of this, i.e. "Z-minimisation".