Abstract
Nonlinear supersymmetry is used to compute the general form of the effective D-brane action in type I string theory compactified to four dimensions in the presence of internal magnetic fields. In particular, the scalar potential receives three contributions: (1) a nonlinear part of the D-auxiliary component, associated to the Dirac–Born–Infeld action; (2) a Fayet–Iliopoulos (FI) D-term with a moduli-dependent coefficient; (3) a D-auxiliary independent (but moduli dependent) piece from the D-brane tension. Minimization of this potential leads to three general classes of vacua with moduli stabilization: (i) supersymmetric vacua allowing in general FI terms to be cancelled by non-trivial vacuum expectation values (VEV's) of charged scalar fields; (ii) anti-de Sitter vacua of broken supersymmetry in the presence of a non-critical dilaton potential that can be tuned at arbitrarily weak string coupling; (iii) if the dilaton is fixed in a supersymmetric way by three-form fluxes and in the absence of charged scalar VEV's, one obtains non-supersymmetric vacua with positive vacuum energy.
Highlights
D -branes break dynam ically half ofthe bulk supersym m etries w hich are realized on their world-volum e in a nonlinear way
M inim ization of this potential leads to three general classes of vacua w ith m oduli stabilization: (i) supersym m etric vacua allow ing in generalFIterm s to be cancelled by non-trivialvacuum expectation values (V EV ’s) ofcharged scalar elds;(ii) anti-de Sitter vacua ofbroken supersym m etry in the presence of a non-criticaldilaton potentialthatcan be tuned atarbitrarily weak string coupling; (iii) if the dilaton is xed in a supersym m etric way by threeform uxes and in the absence ofcharged scalar V EV ’s,one obtains non supersym m etric vacua w ith positive vacuum energy
For generic C alabi-Yau com pacti cations of type I string theory to four dim ensions, m agnetic uxes generate a potential for closed string K ahler class m oduli and play com plem entary role to three-form uxes that generate a potential for the com plex structure m oduliand the dilaton [2,3],in orderto stabilize allclosed string m oduli[4] w ithout introducing non-perturbative e ects [5,6,7,8]
Summary
D -branes break dynam ically half ofthe bulk supersym m etries w hich are realized on their world-volum e in a nonlinear way. Elim inating the form er,one obtains the D BI action for the latter w hich is identi ed w ith the G oldstino m ultiplet ofthe second supersym m etry thatbecom esnonlinearly realized [1].,thecorresponding transform ationsare m odi ed by an additive constantpiece. W e construct the N = 2 superspace and derive the generalform of an N = 2 supersym m etric action w ith arbitrary prepotential and FI term s of both electric and m agnetic type,as wellas the vector-tensor m ultiplet couplings. By im posing a nonlinear constraint,we derive the m odi cation in the supersym m etry transform ations,the D BI action and the corresponding o -shellscalar potentialas a function ofthe D -auxiliary eld.
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