# Math-Phys Joint Seminar by Dr. Naotaka Kubo on December 14, 2020

His talk was on the test of non-perturbative dynamics of three-dimensional gauge theories from the perspective of brane dynamics in string theory.

In the first half of his talk, he explained important ideas in quantum field theory at an elementary level, such as renormalization group (RG) flow, supersymmetry (SUSY), and world-volume theory on branes in string/M-theory. Combining these fundamental ideas, he moved on to the discussion of duality cascades in quantum gauge theories in four and three dimensions. Using branes in string theory, he demonstrated that the duality cascades in M2-brane world-volume theories can be understood from the brane dynamics in type IIB string theory, which is the so-called Hanany-Witten move/transition. In particular, he mentioned that after the sequence of the Hanany-Witten transitions, one may predict if the original gauge theories have SUSY breaking under the RG flow. Then he concluded that all the world-volume theories related by the Hanany-Witten transitions would flow to the same IR theory, and SUSY will be broken if anti-D3-branes are created.

In the latter part of the talk, he argued the non-perturbative tests of duality cascades in three-dimensional supersymmetric gauge theories using partition functions of the theories. He first introduced the notion of partition functions of quantum field theories on S^3 and rephrased the conclusion given in the first part in the language of partition function. He then illustrated the general idea to exactly compute the partition function of supersymmetric gauge theories, which is an analogue of Duistermaat-Heckman formula and is called supersymmetric localization. He gave a dictionary between the viewpoint of brane configuration and the partition function of supersymmetric gauge theories. With such a dictionary, the Hanany-Witten transition of branes was rewritten by an equality between the partition functions. Moreover, one can directly check the duality cascades and SUSY breaking by calculating the partition functions. Finally, he showed the duality cascades and SUSY breaking in supersymmetric gauge theories by an explicit evaluation of partition functions, with comments on Fermi gas formalism and residue computation.