Related papers: Hyperbolic Geometry and Closed Bosonic String Fiel…
We construct Witten-type string field theory vertices for a fermionic first order system with conformal weights (0,1) in the operator formulation using delta-function overlap conditions as well as the Neumann function method. The identity,…
We study the Batalin-Vilkovisky master equation for both open and closed string field theory with special attention to anomalies. Open string field theory is anomaly free once the minimal coupling to closed strings induced by loop…
The determination of the string vertices of closed string field theory is shown to be a conformal field theory problem solvable by combining insights from Liouville theory, hyperbolic geometry, and conformal bootstrap. We first demonstrate…
While the fundamental object in Riemannian geometry is a metric, closed string theories call for us to put a two-form gauge field and a scalar dilaton on an equal footing with the metric. Here we propose a novel differential geometry which…
We outline the construction of type II superstring field theory leading to a geometric and algebraic BV master equation, analogous to Zwiebach's construction for the bosonic string. The construction uses the small Hilbert space. Elementary…
We begin developing tools to compute off-shell string amplitudes with the recently proposed hyperbolic string vertices of Costello and Zwiebach. Exploiting the relation between a boundary value problem for Liouville's equation and a…
We define string geometry: spaces of superstrings including the interactions, their topologies, charts, and metrics. Trajectories in asymptotic processes on a space of strings reproduce the right moduli space of the super Riemann surfaces…
We present a variety of geometrical and combinatorial tools that are used in the study of geometric structures on surfaces: volume, contact, symplectic, complex and almost complex structures. We start with a series of local rigidity results…
This thesis is almost entirely devoted to studying string theory backgrounds characterized by simple geometrical and integrability properties. The archetype of this type of system is given by Wess-Zumino-Witten models, describing string…
In this article, we study geometric aspects of semi-arithmetic Riemann surfaces by means of number theory and hyperbolic geometry. First, we show the existence of infinitely many semi-arithmetic Riemann surfaces of various shapes and prove…
The main limitations of string field theory arise because its present formulation requires a background representing a classical solution, a background defined by a strictly conformally invariant theory. Here we sketch a construction for a…
Generalizing previous work, we give a new analytic solution in Witten's open bosonic string field theory which can describe any open string background. The central idea is to use Riemann surface degenerations as a mechanism for taming OPE…
The $\mathbf{O}(D,D)$ covariant generalized metric, postulated as a truly fundamental variable, can describe novel geometries where the notion of Riemannian metric ceases to exist. Here we quantize a closed string upon such backgrounds and…
In the framework of simplicial models, we construct and we fully characterize a scalar boundary conformal field theory on a triangulated Riemann surface. The results are analysed from a string theory perspective as tools to deal with…
We introduce a two parameter family of string field theory vertices, which we refer to as hyperbolic Kaku vertices. It is defined in terms of hyperbolic metrics on the Riemann surface, but the geometry is allowed to depend on inputs of the…
We study covariant open bosonic string field theory in lightcone gauge. When lightcone gauge is well-defined, we find two results. First, the vertices of the gauge-fixed action consist of Mandelstam diagrams with stubs covering specific…
The connection between Riemann surfaces with boundaries and the theory of vertex operator algebras is discussed in the framework of conformal field theories defined by Kontsevich and Segal and in the framework of their generalizations in…
We study classical dynamics of cylindrical membranes wrapped around the extra compact dimension of a $(D+1)$-dimensional Riemann-Cartan spacetime. The world-sheet equations and boundary conditions are obtained from the universally valid…
We explore the hyperbolic structure of the RNS formulation of perturbative superstring theory. The aim is to provide a systematic method to explicitly compute on-shell and off-shell closed superstring amplitudes with an arbitrary number of…
This thesis presents several new insights on the interface between mathematics and theoretical physics, with a central role for fermions on Riemann surfaces. First of all, the duality between Vafa-Witten theory and WZW models is embedded…