Abstract
The topological calculation of Aharonov-Bohm phases associated with D-branes in the absence of a Neveu-SchwarzB-field is explored. The K-theoretic classification of Ramond-Ramond fields in Type II and Type I theories is used to produce formulae for the Aharonov-Bohm phase associated with a torsion flux. A topological construction shows that K-theoretic pairings to calculate such phases exist and are well defined. An analytic perspective is then taken, obtaining a means for determining Aharonov-Bohm phases by way of the reduced eta-invariant. This perspective is used to calculate the phase for an experiment involving the (−1) −8 system in Type I theory and compared with previous calculations performed using different methods.
Highlights
It is well known that the existence of a magnetic field will affect the phase of electrically charged particles, even when the particles do not pass through the region containing the magnetic field
In this paper we have developed formulae to calculate the Aharonov-Bohm phase of torsion Ramond-Ramond fluxes in the Type II and Type I string theories based upon the Ktheoretic classification of Ramond-Ramond fields and D-brane charges
The analytic perspective was used to calculate the phase for the −1 − 8 system in Type I theory, allowing us to test our formulae by comparison with independent calculations
Summary
It is well known that the existence of a magnetic field will affect the phase of electrically charged particles, even when the particles do not pass through the region containing the magnetic field. We see that the Aharonov-Bohm phase is given by a pairing H1 X × H1 X; U 1 → U 1 defined as Φ A, γ. In 2, 3 it was shown that D-brane charges and Ramond-Ramond RR fields in Types IIA, IIB, and I theories are classified by K-theory. The calculation of Aharonov-Bohm phases for D-branes will necessarily involve some sort of K-theoretic pairing. It is shown that our result agrees with a calculation performed in 5 using different methods
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
