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A novel large-<i>N</i> reduction on <sup>S3</sup>: Demonstration in Chern–Simons theory
Ishiki, Goro,Shimasaki, Shinji,Tsuchiya, Asato Elsevier 2010 Nuclear Physics, Section B Vol.834 No.3
<P><B>Abstract</B></P><P>We show that the planar Chern–Simons (CS) theory on <SUP>S3</SUP> can be described by its dimensionally reduced model. This description of CS theory can be regarded as a novel large-<I>N</I> reduction for gauge theories on <SUP>S3</SUP>. We find that if one expands the reduced model around a particular background consisting of multiple fuzzy spheres, the reduced model becomes equivalent to CS theory on <SUP>S3</SUP> in the planar limit. In fact, we show that the free energy and the vacuum expectation value of unknot Wilson loop in CS theory are reproduced by the reduced model in the large-<I>N</I> limit.</P>
Boundary correlation numbers in one matrix model
Ishiki, G.,Rim, C. North-Holland Pub. Co 2010 Physics letters: B Vol.694 No.3
We introduce one matrix model coupled to multi-flavor vectors. The two-flavor vector model is demonstrated to reproduce the two-point correlation numbers of boundary primary fields of two dimensional (2,2p+1) minimal Liouville gravity on disk, generalizing the loop operator (resolvent) description. The model can properly describe non-trivial boundary conditions for the matter Cardy state as well as for the Liouville field. From this we propose that the n-flavor vector model will be suited for producing the boundary correlation numbers with n different boundary conditions on disk.
Ishiki, Goro,Kim, Sang-Woo,Nishimura, Jun,Tsuchiya, Asato American Physical Society 2009 Physical review letters Vol.102 No.11
<P>We test the recent claim that supersymmetric matrix quantum mechanics with mass deformation preserving maximal supersymmetry can be used to study N=4 super Yang-Mills theory on R x S{3} in the planar limit. When the mass parameter is large, we can integrate out all of the massive fluctuations around a particular classical solution, which corresponds to R x S{3}. The resulting effective theory for the gauge field moduli at finite temperature reproduces the deconfinement phase transition in N=4 super Yang-Mills theory on R x S{3} at weak coupling. This transition was speculated to be a continuation of the conjectured phase transition at strong coupling, which corresponds to the Hawking-Page transition based on the gauge-gravity duality. At strong coupling, one can study the target theory by the new simulation method for supersymmetric matrix quantum mechanics.</P>