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We consider certain elliptic modular graph functions that arise in the asymptotic expansion around the non--separating node of genus two string invariants that appear in the integrand of the $D^8 R^4$ interaction in the low momentum…
We study difference equations which are obtained from the asymptotic expansion of topological string theory on the deformed and the resolved conifold geometries as well as for topological string theory on arbitrary families of Calabi-Yau…
The low-energy expansion of one-loop amplitudes in type II string theory generates a series of world-sheet integrals whose integrands can be represented by world-sheet Feynman diagrams. These integrands are modular invariant and…
Noncommutative \phi^3 field theory in six dimensions exhibits the logarithmic UV/IR mixing at the two-loop order. We show that open string theory in the presence of constant background NS-NS two-form field yields the same amplitude upon…
We extend the model of string as a polymer of string bits to the case of superstring. We mainly concentrate on type II-B superstring, with some discussion of the obstacles presented by not II-B superstring, together with possible strategies…
We generalize Gopakumar's microscopic derivation of Witten diagrams in large N free quantum field theory [1] to interacting theories in perturbative expansion. For simplicity we consider a matrix scalar field with $\Phi^h$ interaction in d…
The three string vertex for Type IIB superstrings in a maximally supersymmetric plane-wave background can be constructed in a light-cone gauge string field theory formalism. The detailed formula contains certain Neumann coefficients, which…
We propose a new general BRST approach to string and string-like theories which have a wider range of applicability than e g the conventional conformal field theory method. The method involves a simple general regularization of all basic…
A matrix model on a D-dimensional Euclidean space is introduced as a generalization of random matrix models and as a non-perturbative definition of discretized closed string theory. The free energy of the matrix model is formally derived to…
In this paper we investigate a result of Ueno on the modularity of generating series associated to the zeta functions of binary Hermitian forms previously studied by Elstrodt et al. We improve his result by showing that the generating…
In the previous paper, the authors pointed out correspondence between a supersymmetric double-well matrix model and two-dimensional type IIA superstring theory on a Ramond-Ramond background from the viewpoint of symmetry and spectrum. This…
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…
We relate one-loop scattering amplitudes of massless open- and closed-string states at the level of their low-energy expansion. The modular graph functions resulting from integration over closed-string punctures are observed to follow from…
We consider special Lambert series as generating functions of divisor sums and determine their complete transseries expansion near rational roots of unity. Our methods also yield new insights into the Laurent expansions and modularity…
In presence of a static pair of sources, the spectrum of low-lying states of any confining gauge theory in D space-time dimensions is described, at large source separations, by an effective string theory. Recently two important advances…
The use of supersymmetric localisation has recently led to modular covariant expressions for certain integrated correlators of half-BPS operators in $\mathcal{N} = 4$ supersymmetric Yang-Mills theory with a general classical gauge group…
We define and study 'non-abelian' Poincar\'e series for the group $G=\mathrm{SU} (2,1)$, i.e. Poincar\'e series attached to a Stone-Von Neumann representation of the unipotent subgroup $N$ of $G$. Such Poincar\'e series have in general…
The genus-dependence of multi-loop superstring amplitudes is bounded at large orders in perturbation theory using the super-Schottky group parametrization of supermoduli space. Partial estimates of supermoduli space integrals suggest an…
Closed string amplitudes at genus $h\leq 3$ are given by integrals of Siegel modular functions on a fundamental domain of the Siegel upper half-plane. When the integrand is of rapid decay near the cusps, the integral can be computed by the…
Upon treating the whole closed string massless sector as stringy graviton fields, Double Field Theory may evolve into Stringy Gravity, i.e. the stringy augmentation of General Relativity. Equipped with an $\mathrm{O}(D,D)$ covariant…