KEK Theory Workshop 2022

Exact solution of the finite Grosse-Wulkenhaar model

8 Dec 2022, 16:00

20m

Online (Zoom)

Parallel session A

Speaker

Mr Naoyuki Kanomata (Tokyo University of Science)

Description

We find the exact solutions of the ${\mathrm{\Phi }}_2^3$ finite matrix model (Grosse-Wulkenhaar model). In the ${\mathrm{\Phi }}_2^3$ finite matrix model, multipoint correlation functions are expressed as $G_{|a_1^1\dots a_{N_1}^1|\dots |a_1^B\dots a_{N_B}^B|}$. The $\sum _{i=1}^B{N}_i$-point function denoted by $G_{|a_1^1\dots a_{N_1}^1|\dots |a_1^B\dots a_{N_B}^B|}$ is given by the sum over all Feynman diagrams (ribbon graphs) on Riemann surfaces with $B$-boundaries, and each $|a_1^i\cdots a_{N_i}^i|$ corresponds to the Feynman diagrams having $N_i$-external lines from the $i$-th boundary. It is known that any $G_{|a_1^1\dots a_{N_1}^1|\dots |a_1^B\dots a_{N_B}^B|}$ can be expressed using $G_{|a^1|\dots |a^n|}$ type $n$-point functions. Thus we focus on rigorous calculations of $G_{|a^1|\dots |a^n|}$. The formula for $G_{|a^1|\dots |a^n|}$ is obtained, and it is achieved by using the partition function $\mathcal{Z}[J]$ calculated by the Harish-Chandra-Itzykson-Zuber integral.

Presentation materials

KEK-TH2022_Kanomata.pdf