MS Seminar (Mathematics - String Theory)

Speaker: Rak-Kyeong Seong (KIAS)
Title: Hilbert Series and Mass-deformed Brane Tilings
Date: Tue, Oct 14, 2014, 13:15 - 14:45
Place: Seminar Room A
Abstract: We present renormalisation group flows among N=1 superconformal fields theories which are represented by a bipartite graph on the torus - also known as a Brane Tiling. These new flows are triggered by masses for adjoint or vector-like pairs of bifundamentals and are identified as generalisations of the Klebanov-Witten construction for the N=1 conifold theory. We give a geometrical interpretation of the flows as complex deformations of the Calabi-Yau singularity. Moreover, we present that in agreement with the holographic a-theorem, the volume of the Sasaki-Einstein 5-base of the Calabi-Yau cone increases along the flow. In fact, we discover that the ratio of the volumes at the beginning and at the end of the flow is a universal constant for large classes of theories.

Generating functions counting gauge invariant operators known as Hilbert series play a crucial role in our analysis. In the first part of my talk, I will give a brief introduction to Hilbert series and their applications for studying moduli spaces of various supersymmetric gauge theories. In the second part of my talk, I will illustrate our observations on mass-deformed Brane Tilings and apply Hilbert series techniques in this context. The talk is based on arXiv:1408.1957.