Alladi Ramakrishnan Hall

Integrable lattice models from four dimensional field theory

Zodinmawia

IMSc

Kevin Costello (arXiv:1303.2632) had constructed a four dimensional field theory by deforming and
twisting a 4d pure N=1 supersymmetric gauge theory. He had proved that this field theory is related to
integrable lattice models whose R-matrices are the same as R-matrices with spectral parameter constructed
by Drinfeld using quantum groups. We are currently trying to gain new insight into this relation and
attempt to find a simpler proof. Since this is a work in progress, the talk will be mostly a
review of Costello's work (arXiv:1303.2632).
I will also talk about another work in progress where we are trying to test the quantum volume
conjecture put forward by Sergei Gukov (arXiv:hep-th/0306165) using the exact partition function of BTZ
black hole obtained by T.R Govindarajan, Romesh Kaul and V. Suneeta (arXiv:gr-qc/0104010).