Superconnections, Anomalies and Non-BPS Brane Charges

Abstract

The properties of brane-antibrane systems and systems of unstable D-branes in Type II superstring theory are investigated using the formalism of superconnections. The low-energy open string dynamics is shown to be probed by generalized Dirac operators. The corresponding index theorems are used to compute the chiral gauge anomalies in these systems, and hence their gravitational and Ramond-Ramond couplings. A spectral action for the generalized Dirac operators is also computed and shown to exhibit precisely the expected processes of tachyon condensation on the brane worldvolumes. The Chern-Simons couplings are thereby shown to be naturally related to Fredholm modules and bivariant K-theory, confirming the expectations that D-brane charge is properly classified by K-homology.

57 pages LaTeX; Typos corrected, references added, various clarifying comments on derivations of superconnection actions in section 3 added

References in corpus (8)

• Boundary String Field Theory of the DDbar System
• Brane-Antibrane Action from Boundary String Field Theory
• Boundary Superstring Field Theory
• On Superconnections and the Tachyon Effective Action
• Anomaly Analysis of Brane-Antibrane Systems
• Non-commutative Branes from M-theory
• On Unification of RR Couplings
• Projector Equivalences in K theory and Families of Non-commutative Solitons

Cited by in corpus (18)

• Cosmological Creation of D-branes and anti-D-branes
• D-branes, Matrix Theory and K-homology
• K-Theory from a physical perspective
• Quiver Gauge Theory of Nonabelian Vortices and Noncommutative Instantons in Higher Dimensions
• Rank Two Quiver Gauge Theory, Graded Connections and Noncommutative Vortices
• Noncommutative Instantons in Higher Dimensions, Vortices and Topological K-Cycles
• D-Branes, Tachyons and K-Homology
• Geometric K-Homology of Flat D-Branes
• D-branes and Azumaya/matrix noncommutative differential geometry,II: Azumaya/matrix supermanifolds and differentiable maps therefrom -- with a view toward dynamical fermionic D-branes in string theory
• Anomaly and Superconnection
• Worldsheet Description of Tachyon Condensation in Open String Theory
• KO-Homology and Type I String Theory
• Confinement and Non-perturbative Tachyons in Brane-Antibrane Systems
• D-branes and $K$-homology
• $N=1$ fermionic D3-branes in RNS formulation I. $C^{\infty }$-Algebrogeometric foundations of $d=4$, $N=1$ supersymmetry, SUSY-rep compatible hybrid connections, and $\hat{D}$-chiral maps from a $d=4$ $N=1$ Azumaya/matrix superspace
• Quillen superconnections and connections on supermanifolds
• Dimensional Reduction of Seiberg-Witten Monopole Equations, N=2 Noncommutative Supersymmetric Field Theories and Young Diagrams
• K-homology in algebraic geometry and D-branes