Abstract
We study profiles and gauge invariant observables of classical solutions corresponding to a constant magnetic field on a torus in open string field theory. We numerically find that the profile is not discontinuous on the torus, although the solution describes topologically nontrivial configurations in the context of low energy effective theory. From the gauge invariant observables, we show that the solution provide correct couplings of closed strings to a D-brane with constant magnetic field.
Highlights
We study profiles and gauge invariant observables of classical solutions corresponding to a constant magnetic field on a torus in open string field theory
From the gauge invariant observables, we show that the solution provide correct couplings of closed strings to a D-brane with constant magnetic field
We need to divide the torus into some patches to describe the U(1) gauge field with a constant magnetic field on a torus, so that the smooth gauge fields on different patches are related by gauge transformations
Summary
We would like to consider the configuration with a constant background Fμν. We concentrate on the spatial directions X1 and X2, since a real antisymmetric tensor Fμν can be transformed into a block diagonal form with 2 × 2 blocks. To find the classical solution corresponding to a constant F12 background, we need to prepare the BCC operators which changes the open string boundary conditions for X1, X2 from the Neumann boundary condition to the one with F12 and vice versa. Following Erler-Maccaferri’s method, we multiply σ∗k, σ∗k by the vertex operators e±i hX0 and appropriate normalization factors and construct |N | pairs of modified BCC operators σk, σk They are primary fields with conformal weight zero and satisfy the OPEs σk(s)σl(0) ∼ δk,l, σl(s)σk(0) ∼ δl,k = | cos πλ|. Having these BCC operators, the classical solution corresponding to the constant magnetic field background [2] are given as follows: Ψ0 = Ψtv + Ak,lΦk,l, k,l (2.4). These are useful in checking the correctness of the profile calculation presented later
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