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Toshiya Suzuki

Publications and source records attributed to Toshiya Suzuki.

12 recordsLinked to original sources
arXiv2015

Gauge theories on noncommutative ${\mathbb C}P^N$ and BPS-like equations

We give the Fock representation of a noncommutative $\mathbb{C}P^N$ and gauge theories on it. The Fock representation is constructed based on star products given by deformation quantization with separation of variables and operators which act on states in the Fock space are explicitly described by functions of inhomogeneous coordinates on ${\mathbb C}P^N$. Using the Fock representation, we are able to discuss the positivity of Yang-Mills type actions and the minimal action principle. Other types of actions including the Chern-Simons term are also investigated. BPS-like equations on noncommutative $\mathbb{C}P^1$ and $\mathbb{C}P^2$ are derived from these actions. There are analogies between BPS-like equations on $\mathbb{C}P^1$ and monopole equations on ${\mathbb R}^3$, and BPS-like equations on $\mathbb{C}P^2$ and instanton equations on ${\mathbb R}^8$. We discuss solutions of these BPS-like equations.

hep-th↗
arXiv2014

Gauge Theories in Noncommutative Homogeneous Kähler Manifolds

We construct a gauge theory on a noncommutative homogeneous Kähler manifold, where we employ the deformation quantization with separation of variables for Kähler manifolds formulated by Karabegov. A key point in this construction is to obtaining vector fields which act as inner derivations for the deformation quantization. We show that these vector fields are the only Killing vector fields. We give an explicit construction of this gauge theory on noncommutative ${\mathbb C}P^N$ and noncommutative ${\mathbb C}H^N$.

hep-th↗
arXiv2012

Explicit Formulae for Noncommutative Deformations of CP^N and CH^N

We give explicit expressions of a deformation quantization with separation of variables for CP^N and CH^N. This quantization method is one of the ways to perform a deformation quantization of Kahler manifolds, which is introduced by Karabegov. Star products are obtained as explicit formulae in all order in the noncommutative parameter. We also give the Fock representations of the noncommutative CP^N and CH^N.

math-ph↗
arXiv2006

Dimensional Reduction of Seiberg-Witten Monopole Equations, N=2 Noncommutative Supersymmetric Field Theories and Young Diagrams

We investigate the Seiberg-Witten monopole equations on noncommutative(N.C.) R^4 at the large N.C. parameter limit, in terms of the equivariant cohomology. In other words, N}=2 supersymmetric U(1) gauge theories with hypermultiplet on N.C. R}^4 are studied. It is known that after topological twisting partition functions of N}>1 supersymmetric theories on N.C. R^2D are invariant under N.C.parameter shift, then the partition functions can be calculated by its dimensional reduction. At the large N.C. parameter limit, the Seiberg-Witten monopole equations are reduced to ADHM equations with the Dirac equation reduced to 0 dimension. The equations are equivalent to the dimensional reduction of non-Abelian U(N) Seiberg-Witten monopole equations in N -> \infty. The solutions of the equations are also interpreted as a configuration of brane anti-brane system. The theory has global symmetries under torus actions originated in space rotations and gauge symmetries. We investigate the Seiberg-Witten monopole equations reduced to 0 dimension and the fixed point equations of the torus actions. We show that the Dirac equation reduced to 0 dimension is trivial when the fixed point equations and the ADHM equations are satisfied. For finite N, it is known that the fixed points of the ADHM data are isolated and are classified by the Young diagrams. We give a new proof of this statement by solving the ADHM equations and the fixed point equations concretely and by giving graphical interpretations of the field components and these equations.

hep-th↗
arXiv2005

Partition functions of Supersymmetric Gauge Theories in Noncommutative R^{2D} and their Unified Perspective

We investigate cohomological gauge theories in noncommutative R^{2D}. We show that vacuum expectation values of the theories do not depend on noncommutative parameters, and the large noncommutative parameter limit is equivalent to the dimensional reduction. As a result of these facts, we show that a partition function of a cohomological theory defined in noncommutative R^{2D} and a partition function of a cohomological field theory in R^{2D+2} are equivalent if they are connected through dimensional reduction. Therefore, we find several partition functions of supersymmetric gauge theories in various dimensions are equivalent. Using this technique, we determine the partition function of the N=4 U(1) gauge theory in noncommutative R^4, where its action does not include a topological term. The result is common among (8-dim, N=2), (6-dim, N=2), (2-dim, N=8) and the IKKT matrix model given by their dimensional reduction to 0-dim.

hep-th↗
arXiv2004

Recovery of Full N=1 Supersymmetry in Non(anti-)commutative Superspace

We investigate SUSY of Wess-Zumino models in non(anti-)commutative Euclidean superspaces. Non(anti-)commutative deformations break 1/2 SUSY, then non(anti-)commutative Wess-Zumino models do not have full SUSY in general. However, we can recover full SUSY at specific coupling constants satisfying some relations. We give a general way to construct full SUSY non(anti-)commutative Wess-Zumino models. For a some example, we investigate quantum corrections and $β$-functions behavior.

hep-th↗
arXiv2004

PST-type SL(2;R)-covariant Super D3-brane Action in Flat Spacetime

We give an explicit form of the PST-type SL(2;R)-covariant super D3-brane action for the flat Minkowski background. To this end, we follow the prescription developed by Hatsuda and Kamimura. As an application of the action, we obtain the supercharge of the action by using the standard Noether's method and calculate the Poisson bracket algebra of the supercharge. The central charge of the supersymmetry algebra is given in a manifestly SL(2;R)-covariant way.

hep-th↗
arXiv2003

Ring Structure of SUSY * Product and 1/2 SUSY Wess-Zumino Model

There are two types of non(anti-)commutative deformation of D=4, N=1 supersymmetric field theories and D=2, N=2 theories. One is based on the non-supersymmetric star product and the other is based on the supersymmetric star product . These deformations cause partial breaking of supersymmetry in general. In case of supersymmetric star product, the chirality is broken by the effect of the supersymmetric star product, then it is not clear that lagrangian or observables including F-terms preserve part of supersymmetry. In this article, we investigate the ring structure whose product is defined by the supersymmetric star product. We find the ring whose elements correspond to 1/2 SUSY F-terms. Using this, the 1/2 SUSY invariance of the Wess-Zumino model is shown easily and directly.

hep-th↗
arXiv1996

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.

hep-th↗
arXiv1995

Integrability of Schwinger-Dyson Equations in 2D Quantum Gravity and c < 1 Non-critical String Field Theory

We investigate the integrability of the Schwinger-Dyson equations in $c = 1 - \frac{6}{m(m+1)}$ string field theory which were proposed by Ikehara et al as the continuum limit of the Schwinger-Dyson equations of the matrix chain model. We show the continuum Schwinger-Dyson equations generate a closed algebra. This algebra contains Virasoro algebra but does not coincide with $W_{\infty}$ algebra. We include in the Schwinger-Dyson equations a new process of removing from the loop boundaries the operator ${\cal H}(σ)$ which locally changes the spin configuration. We also derive the string field Hamiltonian from the continuum Schwinger-Dyson equations. Its form is universal for all $c = 1 - \frac{6}{m(m+1)}$ string theories.

hep-th↗