Related papers: Open intersection numbers and free fields
GSO projected Superconformal field theory (Spin Model) with boundary is considered. There were written the boundary states. For this model were derived one-point structure constants and "bootstrap" equations for boundary-bulk structure…
We analyse boundary conformal field theories on random surfaces using the conformal gauge approach of David, Distler and Kawai. The crucial point is the choice of boundary conditions on the Liouville field. We discuss the Weyl anomaly…
We give a complete numerical description of the geometry of the four-point contact interaction of closed bosonic string field theory. Namely, we compute the boundary of the relevant region of the moduli space of the four-punctured spheres,…
How can Transformers model and learn enumerative geometry? What is a robust procedure for using Transformers in abductive knowledge discovery within a mathematician-machine collaboration? In this work, we introduce a Transformer-based…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
In this note we study curves (arrangements) in the complex projective plane which can be considered as generalizations of free curves. We construct families of arrangements which are nearly free and possess interesting geometric properties.…
By employing polynomial-reduced KP integrability, combined with the string equation, this work establishes explicit relationships between the generalized Kontsevich model, the topological recursion of the spectral curve, and the geometry of…
The correlation functions of a two-dimensional rational conformal field theory, for an arbitrary number of bulk and boundary fields and arbitrary world sheets can be expressed in terms of Wilson graphs in appropriate three-manifolds. We…
We present a method for classifying conformal field theories based on Coulomb gases (bosonic free-field construction). Given a particular geometric configuration of the screening charges, we give necessary conditions for the existence of…
We describe examples of drastic truncations of conformal bootstrap equations encoding much more information than that obtained by a direct numerical approach. A three-term truncation of the four point function of a free scalar in any space…
The purpose of this work is to present some basic concepts about the non-linear sigma model in a simple and direct way. We start with showing the bosonic model and the Wess-Zumino-Witten term, making some comments about its topological…
Following on from earlier work relating modules of meromorphic bosonic conformal field theories to states representing solutions of certain simple equations inside the theories, we show, in the context of orbifold theories, that the…
We consider the structure of current and stress tensor two-point functions in conformal field theory with a boundary. The main result of this paper is a relation between a boundary central charge and the coefficient of a displacement…
In this short expository note, we present a selection of classic and recent ideas in free boundary theory, with a focus on the vectorial case, referred to here as constraint maps. The note includes a brief historical perspective and…
In a recent work, R. Pandharipande, J. P. Solomon and the second author have initiated a study of the intersection theory on the moduli space of Riemann surfaces with boundary. They conjectured that the generating series of the intersection…
We discuss the extent to which solutions to one-phase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by…
We derive boundary states which describe configurations of multiple parallel branes with arbitrary open string states interactions in bosonic string theory. This is obtained by a careful discussion of the factorization of open/closed string…
The massless bosonic field compactified on the circle of rational $R^2$ is reexamined in the presense of boundaries. A particular class of models corresponding to $R^2=\frac{1}{2k}$ is distinguished by demanding the existence of a…
We comment on the conformal boundary states of the c=1 free boson theory on a circle which do not preserve the U(1) symmetry. We construct these Virasoro boundary states at a generic radius by a simple asymmetric shift orbifold acting on…
We apply the background charged bosonic free-field approach to the rational principal quantum Drinfeld-Sokolov (QDS) $\mathcal{W} \big[ \widehat{g} \big](p,p')$ minimal models with boundaries, where $g$ is a finite bosonic simple Lie…