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BPS D-branes on Non-supersymmetric Cycles

Ashoke Sen

TL;DR

The work investigates stable non-supersymmetric D-branes wrapped on non-supersymmetric cycles in K3 and Calabi–Yau manifolds, showing that in the orbifold limit these configurations are captured by solvable boundary conformal field theories. It demonstrates moduli-dependent stability and identifies exactly marginal boundary deformations that interpolate between non-BPS branes and pairs of BPS branes on supersymmetric cycles, with detailed analyses for D-strings on circles and orbifolds. The paper further derives the world-volume theories on coincident non-BPS branes, explores generalizations to other non-supersymmetric cycles, and establishes descent relations among BPS and non-BPS D-branes via tachyon condensation and $(-1)^{F_L}$ projections, highlighting the interconnected D-brane landscape in type II theories.

Abstract

In certain regions of the moduli space of K3 and Calabi-Yau manifolds, D-branes wrapped on non-supersymmetric cycles may give rise to stable configurations. We show that in the orbifold limit, some of these stable configurations can be described by solvable boundary conformal field theories. The world-volume theory of N coincident branes of this type is described by a non-supersymmetric U(N) gauge theory. At the boundary of the region of stability, there are marginal deformations connecting the non-supersymmetric brane to a pair of D-branes wrapped on supersymmetric cycles. We also discuss various relationships between BPS and non-BPS D-branes of type II string theories.

BPS D-branes on Non-supersymmetric Cycles

TL;DR

The work investigates stable non-supersymmetric D-branes wrapped on non-supersymmetric cycles in K3 and Calabi–Yau manifolds, showing that in the orbifold limit these configurations are captured by solvable boundary conformal field theories. It demonstrates moduli-dependent stability and identifies exactly marginal boundary deformations that interpolate between non-BPS branes and pairs of BPS branes on supersymmetric cycles, with detailed analyses for D-strings on circles and orbifolds. The paper further derives the world-volume theories on coincident non-BPS branes, explores generalizations to other non-supersymmetric cycles, and establishes descent relations among BPS and non-BPS D-branes via tachyon condensation and projections, highlighting the interconnected D-brane landscape in type II theories.

Abstract

In certain regions of the moduli space of K3 and Calabi-Yau manifolds, D-branes wrapped on non-supersymmetric cycles may give rise to stable configurations. We show that in the orbifold limit, some of these stable configurations can be described by solvable boundary conformal field theories. The world-volume theory of N coincident branes of this type is described by a non-supersymmetric U(N) gauge theory. At the boundary of the region of stability, there are marginal deformations connecting the non-supersymmetric brane to a pair of D-branes wrapped on supersymmetric cycles. We also discuss various relationships between BPS and non-BPS D-branes of type II string theories.

Paper Structure

This paper contains 8 sections, 37 equations, 2 figures.

Table of Contents

  1. Introduction and Summary
  2. Type IIA D-string on a Circle
  3. Type IIA D-string on an Orbifold
  4. World-volume Theory on Coincident D-branes
  5. Some Generalizations
  6. Branes wrapped on other non-supersymmetric cycles of K3
  7. Branes wrapped on non-supersymmetric 2- and 3-cycles of a Calabi-Yau manifold
  8. Descent Relations Among D-branes

Figures (2)

  • Figure 1: The tachyon background corresponding to $(T_{1}-T_{-1})$ excitation.
  • Figure 2: The relationship between different D-branes. The horizontal arrows represent the result of modding out the theory by $(-1)^{F_L}$, where the vertical arrows represent the effect of constructing a tachyonic kink solution.