arXiv subjects
Publications and source records attributed to Takeshi Oota.
We study spacetimes with a closed conformal Killing-Yano tensor. It is shown that the D-dimensional Kerr-NUT-de Sitter spacetime constructed by Chen-Lu-Pope is the only spacetime admitting a rank-2 closed conformal Killing-Yano tensor with a certain symmetry.
Assuming the existence of a single rank-2 closed conformal Killing-Yano tensor with a certain symmetry we show that there exist mutually commuting rank-2 Killing tensors and Killing vectors. We also discuss the condition of separation of variables for the geodesic Hamilton-Jacobi equations.
We explicitly calculate the Riemannian curvature of D-dimensional metrics recently discussed by Chen, Lu and Pope. We find that they can be concisely written by using a single function. The Einstein condition which corresponds to the Kerr-NUT-de Sitter metric is clarified for all dimensions. It is shown that the metrics are of type D.
We construct a new infinite family of quiver gauge theories which blow down to the X^{p,q} quiver gauge theories found by Hanany, Kazakopoulos and Wecht. This family includes a quiver gauge theory for the third del Pezzo surface. We show, using Z-minimaization, that these theories generically have irrational R-charges. The AdS/CFT correspondence implies that the dual geometries are irregular toric Sasaki-Einstein manifolds, although we do not know the explicit metrics.
We present an explicit non-singular complete toric Calabi-Yau metric using the local solution recently found by Chen, Lu and Pope. This metric gives a new supergravity solution representing D3-branes.
Symplectic potentials are presented for a wide class of five dimensional toric Sasaki-Einstein manifolds, including L^{a,b,c} which was recently constructed by Cvetic et al. The spectrum of the scalar Laplacian on L^{a,b,c} is also studied. The eigenvalue problem leads to two Heun's differential equations and the exponents at regular singularities are directly related to toric data. By combining knowledge of the explicit symplectic potential and the exponents, we show that the ground states, or equivalently holomorphic functions, have one-to-one correspondence with integral lattice points in the convex polyhedral cone. The scaling dimensions of the holomorphic functions are simply given by scalar products of the Reeb vector and the integral vectors, which are consistent with R-charges of BPS states in the dual quiver gauge theories.
A Berkovits type action for pure spinors in even dimensions is considered. The equations of motion for pure spinors are investigated by using explicit parameterizations which solve the pure spinor constraints. For general interactions, the equations of motions are shown to be modified from the naive ones. The extra terms contain a particular projector. If the interactions are restricted to the ``ghost number'' u(1) and the Lorentz so(p,q) current couplings, the action has a large ``gauge symmetry''. In this case, in some ``gauges'', the extra terms vanish and the equations of motion for the pure spinors retain the naive form even if the pure spinor constraints are taken into account.
In the framework of the quantum inverse scattering method, we consider a problem of constructing local operators for two-dimensional quantum integrable models, especially for the lattice versions of the nonlinear Schrodinger and sine-Gordon models. We show that a certain class of local operators can be constructed from the matrix elements of the monodromy matrix in a simple way. They are closely related to the quantum projectors and have nice commutation relations with the half of the matrix elements of the elementary monodromy matrix. The form factors of these operators can be calculated by using the standard algebraic Bethe ansatz techniques.
The system of D1 and D5 branes with a Kaluza-Klein momentum is re-investigated using the five-dimensional U-duality group E_{6(+6)}(Z). We show that the residual U-duality symmetry that keeps this D1-D5-KK system intact is generically given by a lift of the Weyl group of F_{4(+4)}, embedded as a finite subgroup in E_{6(+6)}(Z). We also show that the residual U-duality group is enhanced to F_{4(+4)}(Z) when all the three charges coincide. We then apply the analysis to the AdS(3)/CFT(2) correspondence, and discuss that among 28 marginal operators of CFT(2) which couple to massless scalars of AdS(3) gravity at boundary, 16 would behave as exactly marginal operators for generic D1-D5-KK systems. This is shown by analyzing possible three-point couplings among 42 Kaluza-Klein scalars with the use of their transformation properties under the residual U-duality group.
The type IIA/IIB effective actions compactified on T^d are known to be invariant under the T-duality group SO(d, d; Z) although the invariance of the R-R sector is not so direct to see. Inspired by a work of Brace, Morariu and Zumino,we introduce new potentials which are mixture of R-R potentials and the NS-NS 2-form in order to make the invariant structure of R-R sector more transparent. We give a simple proof that if these new potentials transform as a Majorana-Weyl spinor of SO(d, d; Z), the effective actions are indeed invariant under the T-duality group. The argument is made in such a way that it can apply to Kaluza-Klein forms of arbitrary degree. We also demonstrate that these new fields simplify all the expressions including the Chern-Simons term.
Two point correlation functions of the off-critical primary fields ϕ_{1, 1+s} are considered in the perturbed minimal models M_{2, 2N+3} + ϕ_{1,3}. They are given as infinite series of form factor contributions. The form factors of ϕ_{1, 1+s} are conjectured from the known results for those of ϕ_{1,2} and ϕ_{1,3}. The conjectured form factors are rewritten in the form which is convenient for summing up. The final expression of the two point functions is written as a determinant of an integral operator.
We consider the scaling Lee-Yang model. It corresponds to the unique perturbation of the minimal CFT model M(2,5). This is not a unitary model. We used known expression for form factors in order to obtain a closed expression for a correlation function of a trace of energy-momentum tensor. This expression is a determinant of an integral operator. Similar determinant representation were proven to be useful not only for quantum correlation functions but also in matrix models.
The Lie algebraic structures of the S-matrices for the affine Toda field theories based on the dual pairs (X_N^{(1)}, Y_M^{(l)}) are discussed. For the non-simply-laced horizontal subalgebra X_N and the simply-laced horizontal subalgebra Y_M, we introduce a ``q-deformation'' of a Coxeter element and a ``p-deformation'' of a twisted Coxeter element respectively. Using these deformed objects, expressions for the generating function of the multiplicities of the building block of the S-matrices are obtained. The relation between the deformed version of Dorey's rule and generalized Dorey's rule due to Chari and Pressley are discussed.
Form factor bootstrap approach is applied for diagonal scattering theories. We consider the ADE theories and determine the functional equations satisfied by the minimal two-particle form factors. We also determine the parameterization of the singularities in two particle form factors. For $A^{(1)}_{2}$ Affine Toda field theory which is the simplest non-self conjugate theory, form factors are derived up to four-body and identification of operator is done. Generalizing this identification to the $A^{(1)}_N$ Affine Toda cases, we fix the two particle form factors. We also determine the additional pole structure of form factors which comes from the double pole of the $S$-matrices of the $A^{(1)}_N$ theory. For $A_N$ theories, existence of the conserved ${\bf Z}_{N+1}$ charge leads to the division of the set of form factors into $N+1$ decoupled sectors.