arXiv subjects

Satoshi Iso

Publications and source records attributed to Satoshi Iso.

At least 91 records · Page 5Linked to original sources

arXiv2005

Dynamical generation of a nontrivial index on the fuzzy 2-sphere

In the previous paper hep-th/0312199 we studied the 't Hooft-Polyakov (TP) monopole configuration in the U(2) gauge theory on the fuzzy 2-sphere and showed that it has a nonzero topological charge in the formalism based on the Ginsparg-Wilson relation. In this paper, by showing that the TP monopole configuration is stabler than the U(2) gauge theory without any condensation in the Yang-Mills-Chern-Simons matrix model, we will present a mechanism for dynamical generation of a nontrivial index. We further analyze the instability and decay processes of the U(2) gauge theory and the TP monopole configuration.

hep-th↗

arXiv2004

Wilson Loops and Vertex Operators in Matrix Model

We systematically construct wave functions and vertex operators in the type IIB (IKKT) matrix model by expanding a supersymmetric Wilson loop operator. They form a massless multiplet of the N=2 type IIB supergravity and automatically satisfy conservation laws.

hep-th↗

arXiv2004

Ginsparg-Wilson Relation and 't Hooft-Polyakov Monopole on Fuzzy 2-Sphere

We investigate several properties of Ginsparg-Wilson fermion on fuzzy 2-sphere. We first examine chiral anomaly up to the second order of the gauge field and show that it is indeed reduced to the correct form of the Chern character in the commutative limit. Next we study topologically non-trivial gauge configurations and their topological charges. We investigate 't Hooft-Polyakov monopole type configuration on fuzzy 2-sphere and show that it has the correct commutative limit. We also consider more general configurations in our formulation.

hep-th↗

arXiv2004

Gauge Theory on Noncommutative Supersphere from Supermatrix Model

We construct a supermatrix model which has a classical solution representing the noncommutative (fuzzy) two-supersphere. Expanding supermatrices around the classical background, we obtain a gauge theory on a noncommutative superspace on sphere. This theory has $osp(1|2)$ supersymmetry and $u(2L+1|2L)$ gauge symmetry. We also discuss a commutative limit of the model keeping radius of the supersphere fixed.

hep-th↗

arXiv2003

Note on Gauge Theory on Fuzzy Supersphere

We construct a supermatrix model whose classical background gives two-dimensional noncommutative supersphere. Quantum fluctuations around it give the supersymmetric gauge theories on the fuzzy supersphere constructed by Klimcik. This model has a parameter $β$ which can tune masses of the particles in the model and interpolate various supersymmetric gauge theories on sphere.

hep-th↗

arXiv2003

Noncommutative Superspace, Supermatrix and Lowest Landau Level

By using graded (super) Lie algebras, we can construct noncommutative superspace on curved homogeneous manifolds. In this paper, we take a flat limit to obtain flat noncommutative superspace. We particularly consider $d=2$ and $d=4$ superspaces based on the graded Lie algebras $osp(1|2)$, $su(2|1)$ and $psu(2|2)$. Jacobi identities of supersymmetry algebras and associativities of star products are automatically satisfied. Covariant derivatives which commute with supersymmetry generators are obtained and chiral constraints can be imposed. We also discuss that these noncommutative superspaces can be understood as constrained systems analogous to the lowest Landau level system.

hep-th↗

arXiv2003

Chiral Anomaly and Ginsparg-Wilson Relation on the Noncommutative Torus

We evaluate chiral anomaly on the noncommutative torus with the overlap Dirac operator satisfying the Ginsparg-Wilson relation in arbitrary even dimensions. Utilizing a topological argument we show that the chiral anomaly is combined into a form of the Chern character with star products.

hep-th↗

arXiv2003

Chiral Anomaly on Fuzzy 2-Sphere

We investigate chiral anomaly for fermions in fundamental representation on noncommutative (fuzzy) 2-sphere. In spite that this system is realized by finite dimensional matrices and no regularization is necessary for either UV or IR, we can reproduce the correct chiral anomaly which is consistent with the calculations done in flat noncommutative space. Like the flat case, there are ambiguities to define chiral currents. We define chiral currents in a gauge-invariant way and a gauge-covariant way, and show that the corresponding anomalous chiral Ward-Takahashi identities take different forms. The Ward-Takahashi identity for the gauge-invariant current contains explicit nonlocality while that for the covariant one is given by a local expression.

hep-th↗

arXiv2003

Ginsparg-Wilson Relation, Topological Invariants and Finite Noncommutative Geometry

We show that the Ginsparg-Wilson (GW) relation can play an important role to define chiral structures in {\it finite} noncommutative geometries. Employing GW relation, we can prove the index theorem and construct topological invariants even if the system has only finite degrees of freedom. As an example, we consider a gauge theory on a fuzzy two-sphere and give an explicit construction of a noncommutative analog of the GW relation, chirality operator and the index theorem. The topological invariant is shown to coincide with the 1st Chern class in the commutative limit.

hep-th↗

arXiv2001

Supermatrix Models

We investigate several matrix models based on super Lie algebras, osp(1|32,R), u(1|16,16) and gl(1|32,R). They are natural generalizations of IIB matrix model and were first proposed by Smolin. In particular, we study the supersymmetry structures of these models and discuss possible reductions to IIB matrix model. We also point out that diffeomorphism invariance is hidden in gauge theories on noncommutative space which are derived from matrix models. This symmetry is independent of the global SO(9,1) invariance in IIB matrix model and we report our trial to extend the global Lorentz invariance to local symmetry by introducing u(1|16,16) or gl(1|32,R) super Lie algebras.

hep-th↗

arXiv2000

Bi-local Fields in Noncommutative Field Theory

We propose a bi-local representation in noncommutative field theory. It provides a simple description for high momentum degrees of freedom. It also shows that the low momentum modes can be well approximated by ordinary local fields. Long range interactions are generated in the effective action for the lower momentum modes after integrating out the high momentum bi-local fields. The low momentum modes can be represented by diagonal blocks in the matrix model picture and the high momentum bi-local fields correspond to off-diagonal blocks. This block-block interaction picture simply reproduces the infrared singular behaviors of nonplanar diagrams in noncommutative field theory.

hep-th↗

arXiv1999

Scaling Behaviors of Branched Polymers

We study the thermodynamic behavior of branched polymers. We first study random walks in order to clarify the thermodynamic relation between the canonical ensemble and the grand canonical ensemble. We then show that correlation functions for branched polymers are given by those for $ϕ^3$ theory with a single mass insertion, not those for the $ϕ^3$ theory themselves. In particular, the two-point function behaves as $1/p^4$, not as $1/p^2$, in the scaling region. This behavior is consistent with the fact that the Hausdorff dimension of the branched polymer is four.

hep-th↗

arXiv1999

Wilson Loops in Noncommutative Yang Mills

We study the correlation functions of the Wilson loops in noncommutative Yang-Mills theory based upon its equivalence to twisted reduced models. We point out that there is a crossover at the noncommutativity scale. At large momentum scale, the Wilson loops in noncommmutative Yang-Mills represent extended objects. They coincide with those in ordinary Yang-Mills theory in low energy limit. The correlation functions on D-branes in IIB matrix model exhibit the identical crossover behavior. It is observed to be consistent with the supergravity description with running string coupling. We also explain that the results of Seiberg and Witten can be simply understood in our formalism.

hep-th↗

arXiv1999

Branched Polymer Revisited

We show that correlation functions for branched polymers correspond to those for $ϕ^3$ theory with a single mass insertion, not those for the $ϕ^3$ theory themselves, as has been widely believed. In particular, the two-point function behaves as 1/p^4, not as 1/p^2. This behavior is consistent with the fact that the Hausdorff dimension of the branched polymer is four.

hep-th↗

arXiv1997

Breakdown of Universality in Random Matrix Models

We calculate smoothed correlators for a large random matrix model with a potential containing products of two traces $\tr W_1(M) \cdot \tr W_2(M)$ in addition to a single trace $\tr V(M)$. Connected correlation function of density eigenvalues receives corrections besides the universal part derived by Brezin and Zee and it is no longer universal in a strong sense.

cond-mat.dis-nn↗

arXiv1994

Anyon Basis of c=1 Conformal Field Theory

We study the $c=1$ conformal field theory of a free compactified boson with radius $r=\sqrtβ$ ($β$ is an integer). The Fock space of this boson is constructed in terms of anyon vertex operators and each state is labeled by an infinite set of pseudo-momenta of filled particles in pseudo-Dirac sea. Wave function of multi anyon state is described by an eigenfunction of the Calogero-Sutherland (CS) model. The $c=1$ conformal field theory at $r=\sqrtβ$ gives a field theory of CS model. This is a natural generalization of the boson-fermion correspondence in one dimension to boson-anyon correspondence. There is also an interesting duality between anyon with statistics $θ=π/β$ and particle with statistics $θ=βπ$.

hep-th↗

arXiv1994

Long-Distance Universality of Laughlin State and Calogero-Sutherland Model

We study the universal long-distance behaviour of the Laughlin state for the fractional quantum Hall effect and the ground state of the Calogero-Sutherland model (one dimensional $1/r^2$ interaction model). In particular, it is shown that these two wave functions coincide exactly when Laughlin state is confined in a narrow cylinder geometry. The seeming difference of dimensionality is merely a difference of representation of wave functions. We also give a recipe to interpret operators acting on states in the lowest Landau level in terms of the usual one dimensional Fermion operators, which is important for extracting the Tomonaga-Luttinger liquid behaviour of the edge states.

cond-mat↗

arXiv1993

Explicit Relation of Quantum Hall Effect and Calogero-Sutherland Model

Explicit relation between Laughlin state of the quantum Hall effect and one-dimensional(1D) model with long-ranged interaction ($1/r^2$) is discussed. By rewriting lowest Landau level wave functions in terms of 1D representation, Laughlin state can be written as a deformation of the ground state of Calogero-Sutherland model. Corresponding to Laughlin state on different geometries, different types of 1D $1/r^2$ interaction models are derived.

hep-th↗