T-dualizacija bozonske strune i tip IIB superstrune u prisustvu koorinatno zavisnih pozadinskih polja

[D. Obrić]

VIII, 58 listova

Physics - High energy theoretical physics / Fizika - Тeorijska fizika visokih energija

Topic of this disertation is examination of non-commutative and non-associative properties that emerge in context of closed string theory. This examination will be carried out on two distinct models. One where we work with bosonic string and other where we work with type IIB superstring. Furthermore, both of these models will be analyzed in presence of coordinate dependent background fields. Subjecting these models to T-dualization we will be able to obtain both T-dual theories and transformation laws that connect coordinates of starting theory with T-dual one. Utilizing transformation laws and commutative relations of starting theory we will be able to deduce non-commutative properties of T-dual theories. Method for obtaining T-duality will be based on Buscher procedure and its extensions. Main idea of Buscher procedure lies in localization of translational symmetry by replacing partial derivatives and coordinates that appear in action with covariant derivatives and invariant coordinates. This substitution inevitably introduces additional degrees of freedom which are encoded in gauge fields. By elimination of newly introduced degrees of freedom with method of Lagrange multipliers and subsequently finding equations of motion for gauge fields we obtain transformation laws. Inserting these laws into the action we will obtain T-dual theory. In examination of bosonic string theory, we will work with 3D space where Kalb- Ramond background field will have infinitesimal linear dependence on one coordi- nate, z coordinate. Dualization will be carried along two distinct chains, one where coordinate that appears in background fields will be dualized last and other where it will be dualized first. By comparing these two approaches we will be able do discern what are necessary components for emergence of non-commutative properties. Second part of thesis will be concerned with T-duality of type II superstring that propagates in linearly coordinate dependent Ramond-Ramond field. Unlike previous case, this theory possesses both bosonic and fermionic coordinates, however back- ground field will only depend on bosonic part. T-duality will first focus only on bosonic part and later we will also incorporate fermionic part. We will also present alternative chain of duality where first we dualize fermionic coordinates and later bosonic ones. It will be shown that both chains produce same non-commutative relations. Finally, at the end of the thesis, we will also make analysis of same case when we have more general Ramond-Ramond field.

Tema ove disertacije je bazirana na izuˇcavanju nekomutativnih i neasocijativnih os- obina koje se javljaju u kontekstu teorije struna. Ovo izuˇcavanje ´ce biti obavljeno na dva razliˇcita modela. Prvi model sa kojim ´cemo raditi je model bozonske strune dok je drugi model za tip IIB superstrunu. Oba modela ´ce biti analizirana u prisustvu koordinatno zavisnih pozadinskih polja. Podvrgavanjem ovih modela T-dualizaciji bi´cemo u stanju da dobijemo T-dualne teorije i zakone transfromacija koji povezuju koordinate poˇcetnih i T-dualnih teorija. Koriˇs´cenjem datih zakona transformacije, kao i komutativnih osobina poˇcetnih teorija bi´cemo u stanju da dedukujemo neko- mutativne osobine T-dualnih teorija. Metoda za dobijanje T-dualnosti je bazirana na Buˇserovoj proceduri i njenom upoˇstenju. Glavna ideja Buˇserove procedure leˇzi u lokalizaciji translacione simetrije, gde mi zamenjujemo parcijalne izvode i koor- dinate koje se javljaju u dejstvu sa kovarijantnim izvodima i invarijantnim koordi- natama. Ova smena sa sobom povlaˇci i uvoženje dodatnih stepeni slobode koji su izraˇzeni preko kalibracionih polja. Eliminacijom novih stepeni slobode preko metode Lagranˇzevih mnoˇzitelja a zatim pronalaˇzenjem jednaˇcina kretanja za kalibraciona polja, dobijamo zakone transformacija izmežu koordinata. Ubacivanjem ovih zakona transformacija u dejstvo dobijamo T-dualnu teoriju. Prouˇcavanje bozonske teorije struna, radi´cemo sa 3D prostorom gde uzimamo da Kalb-Ramondovo pozadinsko polje ima infinitezimalu linearnu koordinatnu zavis- nost od samo jedne koordinate, z koordinate. Dualizacija ´ce biti sprovedena duˇz dva razliˇcita lanca, jedan gde tek na kraju dualizujemo duˇz koordinate koja se javlja u pozadinskom polju a druge gde ovu koordinatu prvu dualizujemo. Poreženjem ova dva pristupa bi´cemo u stanju da zakljuˇcimo koji su sastojci neophodni za javljanje nekomutativnih osobina. Drugi deo disertacije tiˇce se T-dualizacije tip II superstrune koja se kre´ce u lin- earno koordinatno zavisnom Ramon-Ramon polju. Za razliku od ploˇslog sluˇcaja, ova teorija poseduje i bozonske i fermionske koordinate, doduˇse pozadinska polja zavise samo od bozonskih koordinata. T-dualizacija ´ce se prvo fokusirati samo na bozonski deo, nakon toga ´cemo ukljuˇciti i fermionske koordinate. Kao i u proˇslom sluˇcaju, predstavi´cemo i jos jedan alternativan lanac dualizacije, lanac gde prvo du- alizujemo fermionske a zatim bozonske koordinate. Pokaza´cemo da oba lanca vode do istih nekomutativnih relacija. Konaˇcno, na kraju disertacije, izvrˇsi´cemo analizu iste teorije ali sa opˇstijim sluˇcajem Ramon-Ramon polja.

String theory, non-commutativity, non-associativity, Buscher procedure

Teroija struna, nekomutativnost, neasocijativnost, Bušerova procedura

539.121.667(043.3)

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