Algebraic structures on the moduli spaces in gauge theories

International audienceThe partition function of a four-dimensional supersymmetric gauge theory on a four-sphere is factorizable in holomorphic and antiholomorphic blocks similar to the correlation functions of the two-dimensional supersymmetric gauge theory on a four-sphere is factorizable in holomorphic and antiholomorphic blocks similar to the correlation functions of the two-dimensional conformal field theories. The holomorphic blocks are controlled by the geometry of the moduli spaces of vacua in 4d supersymmetric gauge theory, and this reveals a deep connection with algebraic structures of quantum integrable systems, two-dimensional conformal field theories and their q-deformations