Related papers: A Symplectic Structure for String Theory on Integr…
This paper determines the symplectic leaves for a remarkable Poisson structure on $\mathbb{C}\mathbb{P}^{n-1}$ discovered by Feigin and Odesskii, and, independently, by Polishchuk. The Poisson bracket is determined by a holomorphic line…
In this paper, which is a revised version of the author's PhD thesis, we analyze two different applications of string theory. In the first part, we focus on four dimensional compactifications of Type II string theories preserving N=1…
Nonassociative structures have appeared in the study of D-branes in curved backgrounds. In recent work, string theory backgrounds involving three-form fluxes, where such structures show up, have been studied in more detail. We point out…
Recently Sekino and Yoneya proposed a way to regularize the world volume theory of membranes wrapped around $S^1$ by matrices and showed that one obtains matrix string theory as a regularization of such a theory. We show that this…
To every Poisson algebraic variety X over an algebraically closed field of characteristic zero, we canonically attach a right D-module M(X) on X. If X is affine, solutions of M(X) in the space of algebraic distributions on X are Poisson…
We introduce non-smooth symplectic forms on manifolds and describe corresponding Poisson structures on the algebra of Colombeau generalized functions. This is achieved by establishing an extension of the classical map of smooth functions to…
Generalized complex geometry was classically formulated by the language of differential geometry. In this paper, we reformulated a generalized complex manifold as a holomorphic symplectic differentiable formal stack in a homotopical sense.…
We apply stochastic quantization method to real symmetric matrix-vector models for the second quantization of non-orientable strings, including both open and closed strings. The Fokker-Planck hamiltonian deduces a well-defined…
It is argued that the complete S-matrix of string theory at tree level in a flat background can be obtained from a small set of target space properties, without recourse to the worldsheet description. The main non-standard inputs are…
Recent work in signal processing and statistics have focused on defining new regularization functions, which not only induce sparsity of the solution, but also take into account the structure of the problem. We present in this paper a class…
Two dimensional string theory is known to have an infinite dimensional symmetry, both in the continuum formalism as well as in the matrix model formalism. We develop a systematic procedure for computing the conserved charges associated with…
We show that the symplectic contraction map of Hilgert-Manon-Martens -- a symplectic version of Popov's horospherical contraction -- is simply the quotient of a Hamiltonian manifold $M$ by a "stratified null foliation" that is determined by…
We introduce scattering-symplectic manifolds, manifolds with a type of minimally degenerate Poisson structure that is not too restrictive so as to have a large class of examples, yet restrictive enough for standard Poisson invariants to be…
Let $G$ be a Lie group with a biinvariant metric, not necessarily positive definite. It is shown that a certain construction carried out in an earlier paper for the fundamental group of a closed surface may be extended to an arbitrary…
The bracket operation on mutually local BRST classes may be combined with Lorentz invariance and analyticity to write an infinite set of finite difference relations on string scattering amplitudes. When combined with some simple physical…
An algebra isomorphism between algebras of matrices and difference operators is used to investigate the discrete integrable hierarchy. We find local and non-local families of R-matrix solutions to the modified Yang-Baxter equation. The…
Let $\mathfrak g$ be a finite-dimensional Lie algebra. The symmetric algebra $\mathcal S(\mathfrak g)$ is equipped with the standard Lie-Poisson bracket. In this paper, we elaborate on a surprising observation that one naturally associates…
The R-matrix formalism for the construction of integrable systems with infinitely many degrees of freedom is reviewed. Its application to Poisson, noncommutative and loop algebras as well as central extension procedure are presented. The…
It is known that classical string dynamics in pure AdS_5\times S^5 is integrable and plays an important role in solvability. This is a deep and central issue in holography. Here we investigate similar classical integrability for a more…
We revisit semiclassical strings, in particular we focus on rigidly rotating strings, in the near horizon geometry of two orthogonal stacks of NS5-branes (I-branes) using the string sigma model. We determine the conserved charges for the…