Deformation of Super Virasoro Algebra in Noncommutative Quantum Superspace
We present a twisted commutator deformation for $N=1,2$ super Virasoro algebras based on $GL_q(1,1)$ covariant noncommutative superspace.
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arXiv subjects
Haru-Tada Sato
Publications and source records attributed to Haru-Tada Sato.
Multiloop $Φ^3$ Amplitudes from Bosonic String Theory
We show how the multiloop amplitudes of $Φ^3$ theory (in the worldline formulation of Schmidt and Schubert) are recovered from the N-tachyon $(h+1)$-loop amplitude in bosonic string theory in the $α' \to 0$ limit, if one keeps the tachyon coupling constant fixed. In this limit the integral over string moduli space receives contributions only from those corners where the world-sheet resembles a $Φ^3$ particle diagram. Technical issues involved are a proper choice of local world-sheet coordinates, needed to take the string amplitudes off-shell, and a formal procedure for introducing a free mass parameter $M^2$ instead of the tachyonic value $-4/α'$.
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Multiloop World-Line Green Functions from String Theory
We show how the multiloop bosonic Green function of closed string theory reduces to the world-line Green function as defined by Schmidt and Schubert in the limit where the string world-sheet degenerates into a $Φ^3$ particle diagram. To obtain this correspondence we have to make an appropriate choice of the local coordinates defined on the degenerate string world sheet. We also present a set of simple rules that specify, in the explicit setting of the Schottky parametrization, which is the corner of moduli space corresponding to a given multiloop $Φ^3$ diagram.
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Notes on Curtright-Zachos Deformations of osp(1,2) and Super Virasoro Algebras
Based on the quantum superspace construction of $q$-deformed algebra, we discuss a supersymmetric extension of the deformed Virasoro algebra, which is a subset of the $q$-$W_{\infty}$ algebra recently appeared in the context of two-dimensional string theory. We analyze two types of deformed super-Virasoro algebra as well as their $osp(1,2)$ subalgebras. Applying our quantum superspace structure to conformal field theory, we find the same type of deformation of affine $sl(2)$ algebra.
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$q$-Virasoro Operators from $q$-Noether Currents
We discuss the $q$-Virasoro algebra based on the arguments of the Noether currents in a two-dimensional massless fermion theory as well as in a three-dimensional nonrelativistic one. Some notes on the $q$-differential operator realization and the central extension are also included.
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OPE formulae for deformed super-Virasoro algebras
We show the OPE formulae for three types of deformed super-Virasoro algebras: Chaichian-Presnajder's deformation, Belov-Chaltikhian's one and its modified version. Fundamental (anti-)commutation relations toward a ghost realization of deformed super-Virasoro algebra are also discussed.
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On Bogoliubov Transformation of Scalar Wave Functions in De Sitter Space
We discuss the Bogoliubov transformation of the scalar wave functions caused by the change of coordinates in 4 dimensional de Sitter space. It is shown that the exact Bogoliubov coefficients can be obtained from the global coordinates to the static coordinates where there exist manifest horizon. We consider two type of global coordinates. In one global coordinates, it is shown that the Bogoliubov transformation to the static coordinates can be expressed by the discontinuous integral of Weber and Schafheitlin. The positive and negative energy states in the global coordinates degenerate in the static coordinates. In the other global coordinates, we obtain the Bogoliubov coefficients by using the analytic continuation of the hypergeometric functions in two variables.
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