arXiv subjects

Shinji Shimasaki

Publications and source records attributed to Shinji Shimasaki.

41 records · Page 3Linked to original sources

arXiv2008

Fiber Bundles and Matrix Models

We investigate relationship between a gauge theory on a principal bundle and that on its base space. In the case where the principal bundle is itself a group manifold, we also study relations of those gauge theories with a matrix model obtained by dimensionally reducing them to zero dimensions. First, we develop the dimensional reduction of Yang-Mills (YM) on the total space to YM-higgs on the base space for a general principal bundle. Second, we show a relationship that YM on an SU(2) bundle is equivalent to the theory around a certain background of YM-higgs on its base space. This is an extension of our previous work (hep-th/0703021), in which the same relationship concerning a U(1) bundle is shown. We apply these results to the case of $SU(n+1)$ as the total space. By dimensionally reducing YM on $SU(n+1)$, we obtain YM-higgs on $SU(n+1)/SU(n)\simeq S^{2n+1}$ and on $SU(n+1)/(SU(n)\times U(1))\simeq CP^n$ and a matrix model. We show that the theory around each monopole vacuum of YM-higgs on $CP^n$ is equivalent to the theory around a certain vacuum of the matrix model in the commutative limit. By combing this with the relationship concerning a U(1) bundle, we realize YM-higgs on $SU(n+1)/SU(n)\simeq S^{2n+1}$ in the matrix model. We see that the relationship concerning a U(1) bundle can be interpreted as Buscher's T-duality.

hep-th↗

arXiv2008

N=4 Super Yang-Mills from the Plane Wave Matrix Model

We propose a nonperturbative definition of N=4 super Yang-Mills (SYM). We realize N=4 SYM on RxS^3 as the theory around a vacuum of the plane wave matrix model. Our regularization preserves sixteen supersymmetries and the gauge symmetry. We perform the 1-loop calculation to give evidences that the superconformal symmetry is restored in the continuum limit.

hep-th↗

arXiv2008

On relationships among Chern-Simons theory, BF theory and matrix model

Chern-Simons theory on a U(1) bundle over a Riemann surface Σ_g of genus g is dimensionally reduced to BF theory with a mass term, which is equivalent to the two-dimensional Yang-Mills on Σ_g. We show that the former is inversely obtained from the latter by the extended matrix T-duality developed in hep-th/0703021. For the case of g=0 (i.e. S^2), the U(1) bundle represents the lens space S^3/Z_p. We find that in this case both the Chern-Simons theory and the BF theory with the mass term are realized in a matrix model. We also construct Wilson loops in the matrix model that correspond to those in the Chern-Simons theory on S^3.

hep-th↗

arXiv2007

Embedding of theories with SU(2|4) symmetry into the plane wave matrix model

We study theories with SU(2|4) symmetry, which include the plane wave matrix model, 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k. All these theories possess many vacua. From Lin-Maldacena's method which gives the gravity dual of each vacuum, it is predicted that the theory around each vacuum of 2+1 SYM on RxS^2 and N=4 SYM on RxS^3/Z_k is embedded in the plane wave matrix model. We show this directly on the gauge theory side. We clearly reveal relationships among the spherical harmonics on S^3, the monopole harmonics and the harmonics on fuzzy spheres. We extend the compactification (the T-duality) in matrix models a la Taylor to that on spheres.

hep-th↗

arXiv2007

T-duality, Fiber Bundles and Matrices

We extend the T-duality for gauge theory to that on curved space described as a nontrivial fiber bundle. We also present a new viewpoint concerning the consistent truncation and the T-duality for gauge theory and discuss the relation between the vacua on the total space and on the base space. As examples, we consider S^3(/Z_k), S^5(/Z_k) and the Heisenberg nilmanifold.

hep-th↗