Katsushi Ito

Study of N = 2 superconformal field theories in 4 dimensions

Making use of the exact solutions of the N = 2 supersymmetric gauge theories, we construct new classes of superconformal field theories (SCFTs) by fine-tuning the moduli parameters and bringing the theories to critical points. SCFTs we have constructed represent universality classes of the 4-dimensional N = 2 SCFTs.

Prepotentials in N = 2 SU(2) supersymmetric Yang-Mills theory with massless hypermultiplets

Abstract We calculate the prepotential of the low-energy effective action for N = 2 SU(2) supersymmetric Yang-Mills theory with Nf massless hypermultiplets (Nf = 1, 2, 3). The precise evaluation of the instanton corrections is performed by making use of the Picard-Fuchs equations associated with elliptic curves. The flavor dependence of the instanton effect is determined explicitly both in the weak- and strong-coupling regimes.

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

Abstract 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 ⩽ 3. We find that for gauge groups G = Ar, Br, Cr (r ⩽ 3) the microscopic results agree with those from the exact solutions.

The WDVV equations in N=2 supersymmetric Yang-Mills theory

Abstract 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.

Picard-Fuchs equations and prepotential in N = 2 supersymmetric G2 Yang-Mills theory☆

We study the low-energy effective theory of N = 2 supersymmetric Yang-Mills theory with the exceptional gauge group G2. We obtain the Picard-Fuchs equations for the G2 spectral curve and compute the 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 the G2 hyperelliptic curve does not reproduce the microscopic result.

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

Abstract 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.

One-Instanton Calculations in N = 2 SU(Nc) Supersymmetric QCD

We study the low-energy effective theory in N=2SU(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

Free field realization of N = 2 super-W3 algebra

u\equiv \langle \frac{1}{2} {\rm Tr} A^2 \rangle

ADE SINGULARITY AND PREPOTENTIALS IN N=2 SUPERSYMMETRIC YANG–MILLS THEORY

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.

Extended superconformal algebras and free field realizations from Hamiltonian reduction

Abstract We study the quantum N = 2 super-W3 algebra using the free field realization, which is obtained from the supersymmetric Miura transformation associated with the Lie superalgebra A ( 2 1 ) . We compute the full operator product expansions of the algebra explicitly. It is found that the results agree with those obtained by the OPE method.