Shogo Aoyama

Topological Landau-Ginzburg theory with a rational potential and the dispersionless KP hierarchy

Based on the dispersionless KP (dKP) theory, we study a topological Landau-Ginzburg (LG) theory characterized by a rational potential. Writing the dKP hierarchy in a general form treating all the primaries in an equal basis, we find that the hierarchy naturally includes the dispersionless (continuous) limit of Toda hierarchy and its generalizations having a finite number of primaries. Several flat solutions of the topological LG theory are obtained in this formulation, and are identified with those discussed by Dubrovin. We explicitly construct gravitational descendants for all the primary fields. Giving a residue formulae for the 3-point functions of the fields, we show that these 3-point functions satisfy the topological recursion relation. The string equation is obtained as the generalized hodograph solutions of the dKP hierarchy, which show that all the gravitational effects to the constitutive equations (2-point functions) can be renormalized into the coupling constants in the small phase space.

Classical exchange algebra of the superstring on S5 with AdS-time

A classical exchange algebra of the superstring on S5 with AdS-time is shown on the light-like plane. To this end, we use the geometrical method of which consistency is guaranteed by the classical Yang–Baxter equation. The Dirac method does not work, since there are constraints in which first-class and second-class constraints are mixed and one can hardly disentangle with each other keeping the isometry.

The Whitham deformation of the Dijkgraaf-Vafa theory

We discuss the Whitham deformation of the effective superpotential in the Dijkgraaf-Vafa (DV) theory. It amounts to discussing the Whitham deformation of an underlying (hyper)elliptic curve. Taking the elliptic case for simplicity we derive the Whitham equation for the period, which governs flowings of branch points on the Riemann surface. By studying the hodograph solution to the Whitham equation it is shown that the effective superpotential in the DV theory is realized by many different meromorphic differentials. Depending on which meromorphic differential to take, the effective superpotential undergoes different deformations. This aspect of the DV theory is discussed in detail by taking the N = 1* theory. We give a physical interpretation of the deformation parameters.

The disc amplitude of the Dijkgraaf-Vafa theory: 1/N expansion vs. complex curve analysis

According to Dijkgraaf and Vafa the effective glueball superpotential of the = 1 supersymmetric QCD coupled with an adjoint chiral multiplet is given by the planar amplitude in the 1/N expansion of a matrix model. It was shown that, when the = 1 supersymmetric QCD is coupled with fundamental chiral multiplets as well, the effective glueball superpotential is modified by the disc amplitude of the generalized matrix model. The diagramatic computation of this disc amplitude is fairly involved for the multi-cut solution. Instead we compute it with recourse to the complex analysis of the hyperelliptic curve. The result is given in series of the gluino condensation Si. The explicit computation for the generic multi-cut solution is done up to order S3. It is systematic so that it can be extended to higher orders.

The fuzzy Kähler coset space with the Darboux coordinates

Abstract The Fedosov deformation quantization of the symplectic manifold is determined by a 1-form differential r . We identify a class of r for which the ★-product becomes the Moyal product by taking appropriate Darboux coordinates, but invariant by canonically transforming the coordinates. This respect of the ★-product is explained by studying the fuzzy algebrae of the Kahler coset space.

Consistently constrained SL(N) WZWN models and classical exchange algebra

A bstractCurrents of the SL(N) WZWN model are constrained so that the remaining symmetry is a symmetry of constrained currents as well. Such consistency enables us to study the Poisson structure of constrained SL(N) WZWN models properly. We establish the Poisson brackets which satisfy the Jacobi identities owing to the classical Yang-Baxter equation. The Virasoro algebra is shown by using them. An SL(N) conformal primary is constructed. It satisfies a quadratic algebra, which might become an exchange algebra by its quantum deformation.

More on the triplet Killing potentials of quaternionic Kähler manifolds

Abstract We show the properties of the triplet Killing potentials of quaternionic Kahler manifolds which have been missing in the literature. It is done by means of the metric formula of the manifolds. We compute the triplet Killing potentials for the quaternionic Kahler manifold Sp ( n + 1 ) / ( ( Sp ( n ) ⊗ Sp ( 1 ) ) ) as an illustration.

The fuzzy S4 by quantum deformation

The fuzzy algebra of S4 is discussed by quantum deformation. To this end we embed the classical S4 in the Kahler coset space SO(5)/U(2). The harmonic functions of S4 are constructed in terms of the complex coordinates of SO(5)/U(2). Being endowed with the symplectic structure they can be deformed by the Fedosov formalism. We show that they generate the fuzzy algebra A∞(S4) under the ★ product defined therein, by using the Darboux coordinate system. The fuzzy spheres of higher even dimensions can be discussed similarly. We give basic arguments for the generalization as well.

The fuzzy Kähler coset space by the Fedosov formalism

Abstract We discuss deformation quantization of the Kahler coset space by using the Fedosov formalism. We show that the Killing potentials of the Kahler coset space satisfy the fuzzy algebrae, when the coset space is irreducible.

N = 4 super-Schwarzian theory on the coadjoint orbit and PSU(1,1|2)

A bstractAn N = 4 super-Schwarzian theory is formulated by the coadjoint orbit method. It is discovered that the action has symmetry under PSU(1,1|2).