arXiv subjects

Katsushi Ito

Publications and source records attributed to Katsushi Ito.

At least 73 records · Page 4Linked to original sources

arXiv2004

N=2 Supersymmetric U(1) Gauge Theory in Noncommutative Harmonic Superspace

We study N=2 supersymmetric U(1) gauge theory in the noncommutative harmonic superspace with nonanticommutative fermionic coordinates. We examine the gauge transformation which preserves the Wess-Zumino gauge by harmonic expansions of component fields. The gauge transformation is shown to depend on the deformation parameters and the anti-holomorphic scalar field. We compute the action explicitly up to the third order in component fields and discuss the field redefinitions so that the component fields transform canonically.

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arXiv2003

Supersymmetric Gauge Theories on Noncommutative Superspace

We study four dimensional supersymmetric gauge theory on the noncommutative superspace, recently proposed by Seiberg. We construct the gauge-invariant action of N=1 super Yang-Mills theory with chiral and antichiral superfields, which has N=1/2 supersymmetry on the noncommutative superspace. We also construct the action of N=2 super Yang-Mills theory. It is shown that this theory has only N=1/2 supersymmetry.

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arXiv2003

Penrose Limit and Enhancon Geometry

We study superstring theories on the Penrose limit of the enhancon geometry realized by the D(p+4)-branes wrapped on a K3 surface. We first examine the null geodesics with fixed radius in general brane backgrounds, which give solvable superstring theories with constant masses. In most cases, the superstring theories contain negative mass-squared. We clarify a condition that the world-sheet free fields have positive mass-squared. We then apply this condition to the enhancon geometry and find that the null geodesics with fixed radius exist only for p=0 case. They define the superstring theories with positive mass-squared. For p>0 case, we show that there is no null geodesic with fixed radius. We also discuss the decoupling limit which gives the dual geometry of super Yang-Mills theory with 8 supercharges. We discuss the K3-volume dependence of the superstring spectrum.

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arXiv2002

Penrose Limit and String Theories on Various Brane Backgrounds

We investigate the Penrose limit of various brane solutions including Dp-branes, NS5-branes, fundamental strings, (p,q) fivebranes and (p,q) strings. We obtain special null geodesics with the fixed radial coordinate (critical radius), along which the Penrose limit gives string theories with constant mass. We also study string theories with time-dependent mass, which arise from the Penrose limit of the brane backgrounds. We examine equations of motion of the strings in the asymptotic flat region and around the critical radius. In particular, for (p,q) fivebranes, we find that the string equations of motion in the directions with the B field are explicitly solved by the spheroidal wave functions.

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arXiv2002

On the Moduli Space of Noncommutative Multi-solitons at Finite Theta

We study the finite theta correction to the metric of the moduli space of noncommutative multi-solitons in scalar field theory in (2+1) dimensions. By solving the equation of motion up to order O(theta^{-2}) explicitly, we show that the multi-soliton solution must have the same center for a generic potential term. We examine the condition that the multi-centered configurations are allowed. Under this condition, we calculate the finite theta correction to the metric of the moduli space of multi-solitons and argue the possibility of the non right-angle scattering of two solitons. We also obtain the potential between two solitons.

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arXiv2002

Hybrid Superstrings on Singular Calabi-Yau Fourfolds

Two-dimensional hybrid superstring on singular Calabi-Yau manifolds is studied by the field redefinition of the NSR formalism. The compactification on singular Calabi-Yau fourfold is described by N=2 super-Liouville theory and N=2 Landau-Ginzburg models. We examine the world-sheet topological N=4 superconformal algebra, which is useful to identify physical states of the theory. It is shown that the space-time superconformal symmetry is not compatible with this original topological algebra. A new model is proposed by modifying the topological superconformal generators, which is consistent with space-time N=2 superconformal symmetry.

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arXiv2001

Scattering of Noncommutative (n,1) Solitons

We study scattering of noncommutative solitons in 2+1 dimensional scalar field theory. In particular, we investigate a system of two solitons with level n and n' (the (n,n')-system) in the large noncommutativity limit. We show that the scattering of a general (n,n')-system occurs at right angles in the case of zero impact parameter. We also derive an exact Kahler potential and the metric of the moduli space of the (n,1)-system. We examine numerically the (n,1) scattering and find that the closest distance for a fixed scattering angle is well approximated by a function a+b*sqrt{n} where a and b are some numerical constants.

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arXiv1999

Green-Schwarz Superstrings on AdS_3 and the Boundary N=4 Superconformal Algebra

We study the hybrid formulation of Green-Schwarz superstrings on AdS_3 with NS flux and the boundary N=4 superconformal algebra. We show the equivalence between the NSR and GS superstrings by a field redefinition. The boundary N=4 superconformal algebra is realized by the free fields of the affine Lie superalgebra A(1|1)^{(1)}. We also consider the light-cone gauge and obtain the N=4 super-Liouville theory which describes the effective theory of the single long string near the singularities of the D1-D5 system.

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arXiv1999

A-D-E Singularity and the Seiberg-Witten Theory

We study the low-energy effective theory of N=2 supersymmetric Yang-Mills theory with ADE gauge groups in view of the spectral curves of the periodic Toda lattice and the A-D-E singularity theory. We examine the exact solutions by using the Picard-Fuchs equations for the period integrals of the Seiberg-Witten differential. In particular, we find that the superconformal fixed point in the strong coupling region of the Coulomb branch is characterized by the ADE superpotential. We compute the scaling exponents, which agree with the previous results.

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arXiv1998

Extended Superconformal Algebras on AdS_{3}

We study a supersymmetric extension of the Virasoro algebra on the boundary of the anti-de Sitter space-time AdS_{3}. Using the free field realization of the currents, we show that the world-sheet affine Lie superalgebras osp(1|2)^{(1)}, sl(1|2)^{(1)} and sl(2|2)^{(1)} provide the boundary N=1,2 and 4 extended superconformal algebras, respectively.

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arXiv1998

Seiberg-Witten Theory as d<1 Topological Strings

In view of two-dimensional topological gravity coupled to matter, we study the Seiberg-Witten theory for the low-energy behavior of N=2 supersymmetric Yang-Mills theory with ADE gauge groups. We construct a new solution of the Picard-Fuchs equations obeyed by the Seiberg-Witten periods. Our solution is expressed as the linear sum over the infinite set of one-point functions of gravitational descendants in $d<1$ topological strings. It turns out that our solution provides the power series expansion around the origin of the quantum moduli space of the Coulomb branch. For SU(N) gauge group we show how the Seiberg-Witten periods are reconstructed from the present solution.

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arXiv1998

The WDVV Equations in N=2 Supersymmetric Yang-Mills Theory

We present a simple proof of the WDVV equations for the prepotential of four-dimensional N=2 supersymmetric Yang-Mills theory with all ADE gauge groups. According to our proof it is clearly seen that the WDVV equations in four dimensions have their origin in the associativity of the chiral ring in two-dimensional topological Landau-Ginzburg models. The WDVV equations for the BC gauge groups are also studied in the Landau-Ginzburg framework. We speculate about the topological field theoretic interpretation of the Seiberg-Witten solution of N=2 Yang-Mills theory.

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arXiv1998

A-D-E Singularity and Prepotentials in N=2 Supersymmetric Yang-Mills Theory

We calculate the instanton corrections in the effective prepotential for N=2 supersymmetric Yang-Mills theory with all A-D-E gauge groups from the Seiberg-Witten geometry constructed out of the spectral curves of the affine Toda lattice. The one-instanton contribution is determined explicitly by solving the Gauss-Manin system associated with the A-D-E singularity. Our results are in complete agreement with the ones obtained from the microscopic instanton calculations.

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arXiv1997

Flat Coordinates, Topological Landau-Ginzburg Models and the Seiberg-Witten Period Integrals

We study the Picard-Fuchs differential equations for the Seiberg-Witten period integrals in N=2 supersymmetric Yang-Mills theory. For A-D-E gauge groups we derive the Picard-Fuchs equations by using the flat coordinates in the A-D-E singularity theory. We then find that these are equivalent to the Gauss-Manin system for two-dimensional A-D-E topological Landau-Ginzburg models and the scaling relation for the Seiberg-Witten differential. This suggests an interesting relationship between four-dimensional N=2 gauge theories in the Coulomb branch and two-dimensional topological field theories.

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arXiv1997

Picard-Fuchs Equations and Prepotential in N=2 Supersymmetric G_{2} Yang-Mills Theory

We study the low-energy effective theory of N=2 supersymmetric Yang-Mills theory with the exceptional gauge group $G_{2}$. We obtain the Picard-Fuchs equations for the $G_{2}$ spectral curve and compute multi-instanton contribution to the prepotential. We find that the spectral curve is consistent with the microscopic supersymmetric instanton calculus. It is also shown that $G_{2}$ hyperelliptic curve does not reproduce the microscopic result.

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arXiv1997

One-instanton calculations in N=2 SU(Nc) Supersymmetric QCD

We study the low-energy effective theory in N=2 SU(Nc) supersymmetric QCD with Nf =< 2Nc fundamental hypermultiplets in the Coulomb branch by microscopic and exact approaches. We calculate the one-instanton correction to the modulus u=< 1/2 Tr A^2 > from microscopic instanton calculation. We also study the one-instanton corrections from the exact solutions for Nc=3 with massless hypermultiplets. They agree with each other except for Nf=2Nc-2 and 2Nc cases. These differences come from possible ambiguities in the constructions of the exact solutions or the definitions of the operators in the microscopic theories.

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arXiv1996

Exact and microscopic one-instanton calculations in N=2 supersymmetric Yang-Mills theories

We study the low-energy effective theory in N=2 super Yang-Mills theories by microscopic and exact approaches. We calculate the one-instanton correction to the prepotential for any simple Lie group from the microscopic approach. We also study the Picard-Fuchs equations and their solutions in the semi- classical regime for classical gauge groups with rank r \leq 3. We find that for gauge groups G=A_r, B_r, C_r (r \leq 3) the microscopic results agree with those from the exact solutions.

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arXiv1996

One-Instanton Calculations in $N=2$ Supersymmetric $SU(N_c)$ Yang-Mills Theory

We calculate the one-instanton contribution to the prepotential in $N=2$ supersymmetric $SU(N_c)$ Yang-Mills theory from the microscopic viewpoint. We find that the holomorphy argument simplifies the group integrations of the instanton configurations. For $N_{c}=3$, the result agrees with the exact solution.

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