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Marginal boundary deformations in a two dimensional conformal field theory correspond to a family of classical solutions of the equations of motion of open string field theory. In this paper we develop a systematic method for relating the…
Partition of unities appear in many places in analysis. Typically they are generated by compactly supported functions with a certain regularity. In this paper we consider partition of unities obtained as integer-translates of entire…
In previous studies, we have examined a resonant excitation of disk oscillations in deformed disks. In these studies, however, mathematical treatment around the resonant points was not rigorous. In this paper the inadequate point is…
We give a Pfaffian formula to compute the partition function of the Ising model on any graph $G$ embedded in a closed, possibly non-orientable surface. This formula, which is suitable for computational purposes, is based on the relation…
In string percolation model, the study of colliding systems at high energies is based on a continuum percolation theory in two dimensions where the number of strings distributed in the surface of interest is strongly determined by the size…
Using the boundary string field theory (BSFT) techniques we study the boundary state and partition function for a dynamical (rotating-moving) D$p$-brane coupled to the electromagnetic and tachyonic background fields in superstring theory.…
Using previous work by Merca, we show the partition function involving parts of k different magnitudes, shifted by the triangular numbers, equals the self convolution of the unrestricted partition function. We also provide a combinatorial…
We compute correlation functions of closed strings in Misner space, a big crunch big bang universe. We develop a general method for correlators with twist fields, which are relevant for the investigation on the condensation of winding…
We use open string field theory to study the dynamics of unstable branes in the bosonic string theory, in the background of a generic linear dilaton. We find a simple exact solution describing a dynamical interpolation between the…
The purpose of this paper is to present a collection of interesting generating functions for partitions which have connections to positive definite binary quadratic forms. In establishing our results we obtain some new Bailey pairs.
Distribution functions (DFs) for dynamically warm thin stellar disks residing in arbitrary axisymmetric potentials are presented which approximately reproduce pre-described surface-density and velocity-dispersion profiles. The functional…
For a dissipative system with Ohmic friction, we obtain a simple and exact solution for the wave function of the system plus the bath. It is described by the direct product in two independent Hilbert space. One of them is described by an…
This review summarizes the recent developments in topological string theory from the author's perspective, mostly focused on aspects of research in which the author is involved. After a brief overview of the theory, we discuss two aspects…
We revisit non-interacting string partition functions in Rindler space by summing over fields in the spectrum. In field theory, the total partition function splits in a natural way in a piece that does not contain surface terms and a piece…
Open topological string partition function gives rise to open Gromov-Witten invariants, open Donaldson-Thomas invariants and 3D-5D BPS indices. Utilizing the remodelling conjecture which connects topological recursion and topological string…
We derive the partition function of 5d ${\cal N}=1$ gauge theories on the manifold $S^3_b \times \Sigma_{\frak g}$ with a partial topological twist along the Riemann surface, $\Sigma_{\frak g}$. This setup is a higher dimensional uplift of…
The boundary state associated with the rolling tachyon solution on an unstable D-brane contains a part that decays exponentially in the asymptotic past and the asymptotic future, but it also contains other parts which either remain constant…
We demonstrate the presence of modular properties in partition functions of $T\bar{T}$ deformed conformal field theories. These properties are verified explicitly for the deformed free boson. The modular features facilitate a derivation of…
We construct the $Z_{N}$ symmetry extended fusion ring of bulk and chiral theories and the corresponding modular partition functions with nonanomalous subgroup $Z_{n}(\subset Z_{N})$. The chiral fusion ring provides fundamental data for…
We reduce the computation of three point function of three spinning operators with arbitrary polarizations to a statistical mechanics problem via the hexagon formalism. The central building block of these correlation functions is the…