Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Boundary Deformation Theory and Moduli Spaces of D-Branes

A. Recknagel, V. Schomerus

TL;DR

This work develops a comprehensive boundary conformal field theory framework for D-brane moduli, introducing a large class of truly marginal self_local boundary operators and providing all_order deformation formulas. By separating chiral from non_chiral marginal perturbations and employing boundary state techniques, it derives explicit deformations of gluing maps, 1_point functions, and partition functions, enabling global insights into D-brane moduli spaces. The c=1 example illustrates rich stringy phenomena, including band structures, Dirichlet_like points, and nongeometric moduli, and connects boundary deformations to target space geometry via T_duality and orbifold structures. These results offer a robust CFT-based approach to analyzing D-brane dynamics in diverse backgrounds and set the stage for applications to supersymmetric and Gepner-model settings, as well as potential links to open string tachyon condensation and noncommutative brane geometry.

Abstract

Boundary conformal field theory is the suitable framework for a microscopic treatment of D-branes in arbitrary CFT backgrounds. In this work, we develop boundary deformation theory in order to study the changes of boundary conditions generated by marginal boundary fields. The deformation parameters may be regarded as continuous moduli of D-branes. We identify a large class of boundary fields which are shown to be truly marginal, and we derive closed formulas describing the associated deformations to all orders in perturbation theory. This allows us to study the global topology properties of the moduli space rather than local aspects only. As an example, we analyse in detail the moduli space of c=1 theories, which displays various stringy phenomena.

Boundary Deformation Theory and Moduli Spaces of D-Branes

TL;DR

This work develops a comprehensive boundary conformal field theory framework for D-brane moduli, introducing a large class of truly marginal self_local boundary operators and providing all_order deformation formulas. By separating chiral from non_chiral marginal perturbations and employing boundary state techniques, it derives explicit deformations of gluing maps, 1_point functions, and partition functions, enabling global insights into D-brane moduli spaces. The c=1 example illustrates rich stringy phenomena, including band structures, Dirichlet_like points, and nongeometric moduli, and connects boundary deformations to target space geometry via T_duality and orbifold structures. These results offer a robust CFT-based approach to analyzing D-brane dynamics in diverse backgrounds and set the stage for applications to supersymmetric and Gepner-model settings, as well as potential links to open string tachyon condensation and noncommutative brane geometry.

Abstract

Boundary conformal field theory is the suitable framework for a microscopic treatment of D-branes in arbitrary CFT backgrounds. In this work, we develop boundary deformation theory in order to study the changes of boundary conditions generated by marginal boundary fields. The deformation parameters may be regarded as continuous moduli of D-branes. We identify a large class of boundary fields which are shown to be truly marginal, and we derive closed formulas describing the associated deformations to all orders in perturbation theory. This allows us to study the global topology properties of the moduli space rather than local aspects only. As an example, we analyse in detail the moduli space of c=1 theories, which displays various stringy phenomena.

Paper Structure

This paper contains 26 sections, 114 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Boundary conditions in conformal field theory
  3. The bulk conformal field theory.
  4. Boundary theories and the gluing map.
  5. One-point functions.
  6. Boundary fields.
  7. Marginal perturbations of boundary conditions
  8. The general prescription.
  9. Truly marginal operators.
  10. Chiral marginal boundary perturbations.
  11. Deformation of the gluing map.
  12. Deformation of the 1-point functions.
  13. Partition function and cluster property.
  14. The boundary state formalism.
  15. Non-chiral analytic perturbations.
  16. ...and 11 more sections

Figures (3)

  • Figure 1: With the help of operator product expansions in the bulk, the computation of $n$-point functions in a boundary theory can be reduced to computing 1-point functions on the half-plane. Consequently, the latter must contain all information about the boundary condition.
  • Figure 2: The curve $\gamma^\nu_{\nu+1}$ along which correlation functions are analytically continued to exchange the position of two neighboring boundary fields. In most cases the result depends on the orientation of the curve.
  • Figure 3: For chiral deformations the original curves $\gamma_p$ in the contour integrals (\ref{['analdef']}) can be deformed into small circles surrounding the insertion points of two bulk fields. The result is expressible through descendants of the original bulk fields.