A Stable Non-BPS Configuration From Intersecting Branes and

We describe a tachyon-free stable non-BPS brane configuration in type IIA string theory. The configuration is an elliptic model involving rotated NS5 branes, D4 branes and anti-D4 branes, and is dual to a fractional brane-antibrane pair placed at a conifol

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ahep-th/0003219TIFR/TH/00-12AStableNon-BPSCon gurationFromIntersectingBranesandAntibranesSunilMukhiandNemaniV.SuryanarayanaTataInstituteofFundamentalResearch,HomiBhabhaRd,Mumbai400005,IndiaABSTRACTWedescribeatachyon-freestablenon-BPSbranecon gurationintypeIIAstringtheory.Thecon gurationisanellipticmodelinvolvingrotatedNS5branes,D4branesandanti-D4branes,andisdualtoafractionalbrane-antibranepairplacedataconifoldsingularity.Thiscon gurationexhibitsaninterestingbehaviouraswevarytheradiusof

thecompactdirection.BelowacriticalradiustheD4andanti-D4branesarealigned,butastheradiusincreasesabovethecriticalvaluethepotentialbetweenthemdevelopsaminimumawayfromzero.Thissignalsaphasetransitiontoacon gurationwith nitelyseparatedbranes.

March2000

We describe a tachyon-free stable non-BPS brane configuration in type IIA string theory. The configuration is an elliptic model involving rotated NS5 branes, D4 branes and anti-D4 branes, and is dual to a fractional brane-antibrane pair placed at a conifol

IntroductionandReview

Muchhasbeenlearnedinrecenttimesaboutthephysicsofbrane-antibranepairsandnon-BPSbranesinsuperstringtheory[1-32].Parallel,in nitelyextendedpairsattracteachother,andcanannihilateintothevacuumbyaprocessoftachyoncondensationintoaconstantminimum.Ananalogousdecayprocesstakesplaceforsingleormultiplenon-BPSbranes.Condensationofthetachyonasakink,vortexormoregeneralsolitonisassociatedtobrane-antibraneannihilationintobranesoflowerdimension.

Theaboveconsiderationshavebeenextendedtobackgroundswithlowersupersym-metry(orientifolds,orbifoldsandsmoothCalabi-Yaumanifolds),whereone ndsnewphenomenaincludingtheexistenceofstable,non-BPSbranes.Asparametersoftheback-groundarevaried,therecanalsobephasetransitionsbetweenqualitativelydi erentcon- gurations.ThereadermayconsultthereviewsinRefs.[33-36].

Adi erentdirection,exploredinRef.[37],istoconsidernon-BPScon gurationsofintersectingbranesandantibranesinthefullysupersymmetrictypeIIspacetimeback-ground.Hereoneencountersnovelphenomenaincludingbothattractiveandrepulsiveinteractionsamongbranesandantibranes.Suchcon gurationscouldbeusefultostudynon-supersymmetric eldtheories,andalsotounderstandbetterthebasicunderlyingstructureofsuperstringtheory.

Inthepresentnoteweexamineavariantofacon gurationof“adjacentbrane-antibranepairs”thatwasdiscussedinRef.[37].Letusdescribetheoriginalcon gura-tion.IntypeIIAtheorywestartwithapairofparallelNS5-branesextendedalongx1,x2,x3,x4,x5andseparatedalongx6.Thex6directioniscompact,withcircumference2L.NowstretchaD4-branealongx6fromthe rstNS5-branetothesecond,anda

D4betweenparallelbranes.

We describe a tachyon-free stable non-BPS brane configuration in type IIA string theory. The configuration is an elliptic model involving rotated NS5 branes, D4 branes and anti-D4 branes, and is dual to a fractional brane-antibrane pair placed at a conifol

InRef.[37]itwasarguedthattheD4-braneand

D4endontheNS5branefromoppositesides,andtheirendsarecharged

3-branesintheNS5worldvolume.Ifwedimensionallyreduceeverythingoverthesethreedirections,thentheendsbecomevorticeslivingonthereducedNS5worldvolume.Thesevorticescarrythesamechargeunderthegauge eld,hencetheyrepel,andsincethecon gurationisnon-supersymmetricthereisnoreasontoexpectthatthisrepulsioniscancelledbyexchangeofothermassless elds.BecausetheNS5-branesareparallel,therepellingD4-and

D4-branesareactuallytwotypesoffractionalbranes(denoted1fand

D4inthe

other,sothatthe4-branesextendalongx1,x2,x3andx6(Fig.2).Thiscon gurationbreaksallthesupersymmetriesofTypeIIA,thougheachoftheD4and

We describe a tachyon-free stable non-BPS brane configuration in type IIA string theory. The configuration is an elliptic model involving rotated NS5 branes, D4 branes and anti-D4 branes, and is dual to a fractional brane-antibrane pair placed at a conifol

D4D4

NS5NS5’NS5

Fig.2:AdjacentD4and

D4-branesrepel.InthecaseofparallelNS5-branes,

therepulsionwasidenti edascomingfromlikechargescarriedbytheendsofthe4-branes.Inthispicturetherepulsivee ectislocalisedoneachNS5-braneseparately,henceintroducingarelativerotationshouldnotmatter.Moreover,fromthestringtheorypointofview,therepulsionbetweentheD4and

D4acrossanyoneNS5brane.Thisagain

http://doc.guandang.netingthesearguments,weconcludethattheD4-and

D4-braneswhentheNS5-branesarenot

rotatedwithrespecttoeachother.

WithrotatedNS5-branes,theimportantdi erenceisthatthetheD4-branesnolongerhavemodulitomoveawayfromeachother.AstheymovewiththeirendsontheNS5-branes,theD4-branesgetstretched.Intheprocesstheire ective3-branetensionincreases,providingarestoringforcefortherepellingendsoftheadjacentD4

D4pairexactlycancel,givingrisetoacon guration

thatisstableatleastundersmallperturbations.

Infact,aswenowshowexplicitly,suchastablecon gurationexistsforsomerangeofvaluesofthecircumferenceR6.Forsimplicity,letusassumethattheNS5andNS5’-branesarelocatedatdiametricallyoppositepointsonthecompactx6direction,withthe

We describe a tachyon-free stable non-BPS brane configuration in type IIA string theory. The configuration is an elliptic model involving rotated NS5 branes, D4 branes and anti-D4 branes, and is dual to a fractional brane-antibrane pair placed at a conifol

separationbetweenthembeingL=1

D4-branewillalsobedisplacedbyanequalamountr,andthe

displacementoftheotherendsofthe4-branesalongx8(orx9)willalsober

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