Related papers: Hyperbolic Geometry and Closed Bosonic String Fiel…
This paper continues a geometric study of Harvey's Complex of Curves, whose ultimate goal is to apply the theory of hyperbolic spaces and groups to algorithmic questions for the Mapping Class Group and geometric properties of Kleinian…
This paper gives a construction, using heat kernels, of differential forms on the moduli space of metrised ribbon graphs, or equivalently on the moduli space of Riemann surfaces with boundary. The construction depends on a manifold with a…
The equation of motion for Berkovits' WZW-like open (super)string field theory is shown to be integrable in the sense that it can be written as the compatibility condition ("zero-curvature condition") of some linear equations. Employing a…
A classical theorem in the theory of minimal surfaces establishes a correspondence between minimal surfaces in $\mathbb{R}^n$ and null holomorphic curves in $\mathbb{C}^n$. A hyperbolic version of this correspondence is due to Bryant: null…
In typical examples of the AdS/CFT correspondence, the world-sheet theory with holes in the presence of D-branes is assumed to be equivalent in a low-energy limit to a world-sheet theory without holes for a different background such as…
Topological field theories of Schwarz-type generally admit symmetries whose algebra does not close off-shell, e.g. the basic symmetries of BF models or vector supersymmetry of the gauge-fixed action for Chern-Simons theory (this symmetry…
I consider a three-dimensional string theory whose action, besides the standard area term, contains one of the form $\int_{\Sigma} \epsilon_{\mu\nu\sigma} X^{\mu} d X^{\nu} \wedge d X^{\sigma}$. In the case of closed strings this extra term…
Using the generalized hamiltonian method of Batalin, Fradkin and Vilkovisky, we investigate the algebraic structure of anomalies in the Polyakov string theory that appear as the Schwinger terms in super-commutation relations between BRST…
We complete the set of string vertices of non-negative dimension by introducing in a consistent manner those moduli spaces which had previously been excluded. As a consequence we obtain a `geometrised' string action taking the simple form…
In these lecture notes, we take a closer look at the calculation of scattering amplitudes for the bosonic string. It is believed that string theories form the UV completions of (super)gravity theories. Support for this claim can be found in…
Nonrelativistic string theory is a unitary, ultraviolet finite quantum gravity theory with a nonrelativistic string spectrum. The vertex operators of the worldsheet theory determine the spacetime geometry of nonrelativistic string theory,…
We investigate classical bosonic open-string field theory from the perspective of the Wilson renormalization group of world-sheet theory. The microscopic action is identified with Witten's covariant cubic action and the short-distance…
We explore the hyperbolic band theory under a magnetic field for the first time. Our theory is a general extension of the conventional band theory defined on a Euclidean lattice into the band theory on a general hyperbolic lattice/Riemann…
This is the author Master's Thesis and its main purpose is to demonstrate that it is possible to formulate Einstein's field equations as an initial value problem. The first chapter concerns the hyperbolic equations theory. The definition of…
We study a cosmic string solution of an N=1-supersymmetric version of the Cremmer-Scherk-Kalb-Ramond (CSKR) Lagrangian coupled to a vector superfield by means of a topological mass term. The 2-form gauge potential is proposed to couple…
The tachyon-free nonsupersymmetric string theories in ten dimensions have dilaton tadpoles which forbid a Minkowski vacuum. We determine the maximally symmetric backgrounds for the $USp(32)$ Type I string and the $SO(16)\times SO(16)$…
The correspondence between Matrix String Theory in the strong coupling limit and IIA superstring theory can be shown by means of the instanton solutions of the former. We construct the general instanton solutions of Matrix String Theory…
We present an open-closed topological quantum field theory for inverse monoids which generalizes the theory of principle fiber bundles with finite gauge group over Riemann surfaces with boundary. The theory is constructed using the…
We fully characterize the set of finite shapes with minimal perimeter on hyperbolic lattices given by regular tilings of the hyperbolic plane whose tiles are regular $p$-gons meeting at vertices of degree $q$, with $1/p+1/q<\frac{1}{2}$. In…
We construct the $\mathrm{SL}(2, \mathbb C)$ quartic vertex with a generic stub parameter for the bosonic closed string field theory by characterizing the vertex region in the moduli space of 4-punctured sphere, and providing the necessary…