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講演者：野坂 朋生 氏（SISSA）
タイトル：M2-branes and discrete Painleve systems
It is known that the generating function of the partition function of the ABJM theory, the 3d Chern-Simons matter theory on N M2-branes probing C^4/Z_k orbifold background, enjoys a non-linear difference relation called the q-deformed Painleve III equation. We found that a similar relation holds also when the theory is deformed by the mass terms of the matter fields. The mass deformed ABJM theory is conjectured to exhibit a large N phase transition where the standard large N expansion formula for the massless case breaks down. The q-difference relation we found might be a useful tool to approach the phase transition in the future research.
Based on the idea of Painleve/gauge correspondence and the conjectured relation between the five dimensional Yang-Mills theories and the quantization of algebraic curves, it is further suggested that the same non-linear relation is also enjoyed by the theories of M2-branes placed on more general backgrounds. As an example I will also comment on the relation between the four node circular quiver Chern-Simons matter theory and the q-deformed Painleve VI equations.