Non-linear electrodynamics from quantized strings

Decay of Unstable D-branes with Electric Field

“…It has been noti ced i n vari ous works [ 1,2,3,4,5,6,7]that sw i tchi ng on an el ectri c el d on the worl d-vol um e ofa D -brane l eads to vari ous new physi cale ects w hi ch are absent i n the m agneti c case [ 1,8,9] . In parti cul ar,unl i ke the m agneti c case the strength ofthe el ectri c el d can not be i ncreased beyond a cri ti calval ue keepi ng the open stri ng theory stabl e. T he sol uti ons carryi ng el ectri c ux [ 10,11,12,13]are parti cul arl y i nteresti ng i n the tachyon vacuum ofan unstabl e D -brane [ 14,15] ,si nce i n thi svacuum the ful lPoi ncare i nvari anceofthebul k i sexpected to berestored and al ltheperturbati vedegreesoffreedom are unphysi cal [ 16] .…”

“…Proceedi ng al ong the sam e l i ne,we rst nd the sol uti on to the l i neari sed equati on ofm oti on i n presence of the background el ectri c el d, and use i t to i denti fy the rol l i ng tachyon perturbati on i n presence of background el d. H avi ng i denti ed the rel evant BC FT we anal yse i t fol l ow i ng the approach of [ 18,19] ,nam el y W i ck-rotate the ti m e di recti on to go to a theory w i th al lspati aldi recti ons. T he resul ti ng theory w i thout the perturbati on term i sequi val entto the standard m agneti c BC FT anal ysed i n [ 1,2,31,9]w i th an i m agi nary m agneti c el d. W e do al lthe expl i ci t anal ysi s w i th a realm agneti c el d and atthe end recoverresul tsi n the ori gi nalel ectri c theory by perform i ng the i nverse W i ck-rotati on and an anal yti c conti nuati on w hi ch m akes the m agneti c el d i m agi nary. W e study the perturbati on descri bi ng the rol l i ng tachyon i n thi s m agneti c BC FT and argue,usi ng the i dea ofl ocal ity ofboundary operators i ntroduced i n [ 33] ,that thi s deform ati on i s exactl y m argi nal .…”

p−p′ system with B field and projection operator noncommutative solitons

“…These coordinates are expanded in an integral power series of z and z [6][7] [13]. The two-point functions of these string coordinates are given in [1] 4) where R stands for the radial ordering, G µν and θ µν are the inverse of the open string metric G µν and the noncommutativity parameter defined in [8] respectively, and (x) denotes the sign function.…”

“…String theory with a constant NS-NS two-form B field background has several interesting features [1][2] [3]. Among others, it has been found out that when D-branes accompany this system the worldvolume of the D-branes becomes noncommutative [4][5] [6] [7] [8].…”

Singularities of the Seiberg-Witten map

“…For slowly varying fields on a D-brane, the effective action is described by the Dirac-BornInfeld (DBI) Lagrangian [3] which depends on B, F and the closed string metric g. Using the above equations for δ θ A i and δ θ F ij , Seiberg and Witten established that this action is equivalent (up to a total derivative and O(∂F ) terms) to a non-commutative version of the DBI action. The latter has no explicit B-dependence, but it involves the non-commutative curvature F (θ) with 6) where g α = g/(2πα ), α is the inverse to the string tension.…”