Related papers: On tabulating virtual strings
Isotropic Quot schemes parameterize rank $r$ isotropic subsheaves of a vector bundle equipped with symplectic or symmetric quadratic form. We define a virtual fundamental class for isotropic Quot schemes over smooth projective curves. Using…
We extend an earlier proposal for a gauge invariant description of off-shell open strings (at tree level), using loop variables, to off-shell closed strings (at tree level). The basic idea is to describe the closed string amplitudes as a…
We study the stable pair theory on toric surfaces and determine the virtual tangent space over the fixed point loci. Further, we present a program to compute the virtual Euler characteristic, illustrated by the case of the projective plane.…
We construct a virtual fundamental class on the Quot scheme parametrizing quotients of a trivial bundle on a curve. We use the virtual localization formula to calculate virtual intersection numbers on Quot. As a consequence, we reprove the…
These notes on string theory are based on a series of talks I gave during my graduate studies. As the talks, this introductory essay is intended for young students and non-string theory physicists.
The role of integrable systems in string theory is discussed. We remind old examples of the correspondence between stringy partition functions or effective actions and integrable equations, based on effective application of the matrix model…
A covariant calculus for the construction of effective string theories is developed. Effective string theory, describing quantum string-like excitations in arbitrary dimension, has in the past been constructed using the principles of…
We introduce the concept of associativity for string functions, where a string function is a unary operation on the set of strings over a given alphabet. We discuss this new property and describe certain classes of associative string…
The evaluation of graphs on 2-spheres is a central ingredient of the Turaev-Viro construction of three-dimensional topological field theories. In this article, we introduce a class of graphs, called extruded graphs, that is relevant for the…
We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a…
We relate the computational complexity of finite strings to universal representations of their underlying symmetries. First, Boolean functions are classified using the universal covering topologies of the circuits which enumerate them. A…
The closed topological vertex is the simplest ``off-strip'' case of non-compact toric Calabi-Yau threefolds with acyclic web diagrams. By the diagrammatic method of topological vertex, open string amplitudes of topological string theory…
This note is intended to be a friendly introduction to virtual classes. We review virtual classes and we give a number of properties and applications. We also include a new virtual push-forward theorem and many computations of virtual…
In critical as well as in non-critical string theory the partition function reduces to an integral over moduli space after integration over matter fields. For non-critical string theory this moduli integrand is known for genus one surfaces.…
We present a complete classification of spherical knotoids with up to six crossings and conjecture that our classification up to seven crossings is complete. Our work extends the tradition of knot tabulation to the setting of knotoids…
As of today there exist consistent, gauge-invariant string field theories describing all string theories: bosonic open and closed strings, open superstrings, heterotic strings and type II strings. The construction of these theories require…
Two natural generalizations of knot theory are the study of spatial graphs and virtual knots. Our goal is to unify these two approaches into the study of virtual spatial graphs. This paper is a survey, and does not contain any new results.…
String theory requires two kinds of loop expansion: classical $(\alpha')$ worldsheet loops with expansion parameter $<T>$ where $T$ is a modulus field, and quantum $(\hbar)$ spacetime loops with expansion parameter $<S>$ where $S$ is the…
We over-approximate reachability sets in string rewriting by languages defined by admissible factors, called tiles. A sparse set of tiles contains only those that are reachable in derivations, and is constructed by completing an automaton.…
Although reasoning about equations over strings has been extensively studied for several decades, little research has been done for equational reasoning on general clauses over strings. This paper introduces a new superposition calculus…