Twist Quantization of String and Hopf Algebraic Symmetry

We describe the twist quantization of string worldsheet theory, which unifies the description of quantization and the target space symmetry, based on the twisting of Hopf and module algebras. We formulate a method of decomposing a twist into successive twists to analyze the twisted Hopf and module algebra structure, and apply it to several examples, including finite twisted diffeomorphism and extra treatment for zero modes

Comments on Gauge Equivalence in Noncommutative Geometry

We investigate the transformation from ordinary gauge field to noncommutative one which was introduced by N.Seiberg and E.Witten (hep-th/9908142). It is shown that the general transformation which is determined only by gauge equivalence has a path dependence in `\theta-space'. This ambiguity is negligible when we compare the ordinary Dirac-Born-Infeld action with the noncommutative one in the U(1) case, because of the U(1) nature and slowly varying field approximation. However, in general, in the higher derivative approximation or in the U(N) case, the ambiguity cannot be neglected due to its noncommutative structure. This ambiguity corresponds to the degrees of freedom of field redefinition.Comment: 10 pages, LaTeX2e, note adde

On the Generalized Gluing and Resmoothing Theorem

The generalized gluing and resmoothing theorem originally proved by LeClair, Peskin and Preitschopf, gives a powerful formula for the fused vertex obtained by contracting any two vertices in string field theories. Although the theorem is naturally expected to hold for the vertices at any loop level, the original proof was restricted to the vertices at tree level. Here we present a simplified proof for the tree level theorem and then prove explicitly the extended version at one-loop level. We also find that a non-trivial sign factor, which depends on the string states to be contracted, appears in the theorem. This sign factor turns out to be essential for reproducing correctly the conformal field theory correlation function on the torus.Comment: 19 pages, LaTeX with PTPTeX.sty, 3 eps figure

BRS Invariance of Unoriented Open-Closed String Field Theory

We present the full action for the unoriented open-closed string field theory which is based on the \alpha=p^+ HIKKO type vertices. The BRS invariance of the action is proved up to the terms which are expected to cancel the anomalous one-loop contributions. This implies that the system is invariant under the gauge transformations with open and closed string field parameters up to the anomalies.Comment: 53 pages, LaTeX with PTPTeX.sty, 23 eps figures, style file replace

Boundary state analysis on the equivalence of T-duality and Nahm transformation in superstring theory

We investigated the equivalence of the T-duality for a bound state of D2 and D0-branes with the Nahm transformation of the corresponding gauge theory on a 2-dimensional torus, using the boundary state analysis in superstring theory. In contrast to the case of a 4-dimensional torus, it changes a sign in a topological charge, which seems puzzling when regarded as a D-brane charge. Nevertheless, it is shown that it agrees with the T-duality of the boundary state, including a minus sign. We reformulated boundary states in the RR-sector using a new representation of zeromodes, and show that the RR-coupling is invariant under the T-duality. Finally, the T-duality invariance at the level of the Chern-Simon coupling is shown by deriving the Buscher rule for the RR-potentials, known as the 'Hori formula', including the correct sign.Comment: 31 pages. v2: references added, typos correcte

Hopf Algebra Symmetry and String Theory

We investigate the Hopf algebra structure in string worldsheet theory and give a unified formulation of the quantization of string and the space-time symmetry. We reformulate the path integral quantization of string as a Drinfeld twist at the worldsheet level. The coboundary relation shows that the Drinfeld twist defines a module algebra which is equivalent to operators with normal ordering. Upon applying the twist, the space-time diffeomorphism is deformed into a twisted Hopf algebra, while the Poincar\'e symmetry is unchanged. This suggests a characterization of the symmetry: unbroken symmetries are twist invariant Hopf subalgebras, while broken symmetries are realized as twisted ones. We provide arguments that relate this twisted Hopf algebra to symmetries in path integral quantization.Comment: 35 pages, no figure, v2: references and comments added, typos corrected, v3: requires PTP style, title changed, final version published in PT

Excited D-branes and Supergravity Solutions

We investigate the general solution with the symmetry ISO(1,p)xSO(9-p) of Type II supergravity (the three-parameter solution) from the viewpoint of the superstring theory. We find that one of the three parameters (c_1) is closely related to the ``dilaton charge'' and the appearance of the dilaton charge is a consequence of deformations of the boundary condition from that of the boundary state for BPS D-branes. We give three examples of the deformed D-branes by considering the tachyon condensation from systems of D-\bar{D}p-branes, unstable D9-branes and unstable D-instantons to the BPS saturated Dp-branes, respectively. We argue that the deformed systems are generally regarded as tachyonic and/or massive excitations of the open strings on Dp-\bar{D}p-brane systems.Comment: 29 pages, 6 figures, LaTeX2e, typos corrected, references adde