KdV equation on riemann surfaces
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KdV equation on riemann surfaces
SISSAISASSCUOLA INTERNAZIONALE SUPERIORS DI STUDI AVANZATIINTERNATIONAL SCHOOL FOR ADVANCED S TUDIESD-branes, Rolling Tachyons and Vacuum String Field KdV equation on riemann surfaces d TheoryThesis submitted for the degree of “Doctor Philosophise’1Candidate:Carlo MaccaferriSupervisor:Prof. Loriano BonoraExternal referee:Prof. Cainillo Imbimbo38626AcknowledgmentsIwould like to warmly thank my supervisor Loriano Bonora- His unconditioned enthusiasm, careful guidance, strong persev KdV equation on riemann surfaces erance and friendly character made most of this work possible.I thank all of my collaborators for having enjoyed with me ideas, discussions, computa tKdV equation on riemann surfaces
ions (and sometimes frustrations...): Loriano Bonora. Davide Mamonc. Predrag Prester. Mario Salizzoni, Ricardo s. Santos and Driba D. Tolla.I thank mySISSAISASSCUOLA INTERNAZIONALE SUPERIORS DI STUDI AVANZATIINTERNATIONAL SCHOOL FOR ADVANCED S TUDIESD-branes, Rolling Tachyons and Vacuum String Field KdV equation on riemann surfaces sions on the blackboard or in front of some beer.I thank Stefano Profumo and Martin '0 Loughlin for our music and jazz sessions.I thank all of my friends in SISSA: my years in Trieste wouldn't have been so exciting without them.I thank my sweet wife Emica for her love and support throughout the past KdV equation on riemann surfaces six years: she is the living proof that Physics Is not enough...I thank my family Luciano. Daniela and Giorgio for their love and their enthusiasm abKdV equation on riemann surfaces
out my job.•2AbstractIll this thesis we discuss classical solutions and open string vacua of open String Field Theory.After a brief introduction whichSISSAISASSCUOLA INTERNAZIONALE SUPERIORS DI STUDI AVANZATIINTERNATIONAL SCHOOL FOR ADVANCED S TUDIESD-branes, Rolling Tachyons and Vacuum String Field KdV equation on riemann surfaces ndary Conformal Field Theories.We then concentrate on the ^-product, that makes the string Hilbert space a non-commutative algebra. We review the construction of the three string vertex for the matter and the ghost sector, for t he latter case we provide a new formulation which allows to treat ghost KdV equation on riemann surfaces zero modes on the same footing as non zero modes, thus providing a more compact and economical structure. All the Neumann coefficients are then diagoKdV equation on riemann surfaces
nalized and the corresponding eigenvalues and eigenvectors are derived. This preliminary technical part is necessary for the explicit computations thaSISSAISASSCUOLA INTERNAZIONALE SUPERIORS DI STUDI AVANZATIINTERNATIONAL SCHOOL FOR ADVANCED S TUDIESD-branes, Rolling Tachyons and Vacuum String Field KdV equation on riemann surfaces um and we define the Vacuum String Field Theory model. We show how our formulation of the ghost *-product allows for a simple derivation of the universal ghost solution, common to all the classical solutions of VSFT that represent D-branes systems of any kind.We then proceed with the construction of KdV equation on riemann surfaces a solution in the matter sector (the Dressed Sliver) which represents a D25~brane background, as seen from the tachyon vacuum. We derive a deformatioKdV equation on riemann surfaces
n technique (dressing) which allows for an unambiguous definition of the string coupling constant as an emergent quantity from the regularization procSISSAISASSCUOLA INTERNAZIONALE SUPERIORS DI STUDI AVANZATIINTERNATIONAL SCHOOL FOR ADVANCED S TUDIESD-branes, Rolling Tachyons and Vacuum String Field KdV equation on riemann surfaces ).The next topic we address is the systematic study of the linearized equations of motion around the Dressed Sliver background. We show, up to level 3, that all the open string spectrum arises with the correct Virasoro constraints: this is possible thanks to the dressing deformation (as far as the t KdV equation on riemann surfaces ransversality condition for the (7(1) gauge field is concerned) and due to a regularization of the midpoint degrees of freedom which allows for a propKdV equation on riemann surfaces
er definition of the massive modes. We indeed show in detail that all the physical excitat ions arise from the midpoint and that our regularization alSISSAISASSCUOLA INTERNAZIONALE SUPERIORS DI STUDI AVANZATIINTERNATIONAL SCHOOL FOR ADVANCED S TUDIESD-branes, Rolling Tachyons and Vacuum String Field KdV equation on riemann surfaces rallel Dp-branes, showing how Chan Paton factors are automatically generated from the equation of motions and how they are related to the Icft/right splitting of VSFT classical solutions. We then derive the open string spectrum on the Higgs phase given by jV parallel separated Dp-branes: the shift i KdV equation on riemann surfaces n the mass formula for strings stretched between different branes emerges from a breakdown of associativity at the midpoint degree of freedom. We evalKdV equation on riemann surfaces
uate this anomaly by means (if wedge-states regularization, obtaining perfect agreement with the known result. We elaborate on the fact that the dynamSISSAISASSCUOLA INTERNAZIONALE SUPERIORS DI STUDI AVANZATIINTERNATIONAL SCHOOL FOR ADVANCED S TUDIESD-branes, Rolling Tachyons and Vacuum String Field KdV equation on riemann surfaces nt change in boundary conditions between the left/right parts of the string.https://khothuvien.cori!The* remaining part of the presented material is devoted to the derivation of timedependent solutions which represent the rolling tachyon BCFT in the VSFT framework. This new kind of solutions are obt KdV equation on riemann surfaces ained from Wick rotation of codimension 1 lump solutions: however wo show that we have to use an unconventional lump solution with a Neumann coefficieKdV equation on riemann surfaces
nt which is inverted w.r.t. the conventional case in the discrete spectrum. We generalize our rolling tachyon solution to the case of an E-field backgSISSAISASSCUOLA INTERNAZIONALE SUPERIORS DI STUDI AVANZATIINTERNATIONAL SCHOOL FOR ADVANCED S TUDIESD-branes, Rolling Tachyons and Vacuum String Field KdV equation on riemann surfaces by the background E-field.We conclude this dissertation with a number of important unsolved questions that, in our opinion, merit further effort.The material wo are presenting is extracted from the publications [1, 2. 3. 4. 5, 6, 7, 8].2 KdV equation on riemann surfaces SISSAISASSCUOLA INTERNAZIONALE SUPERIORS DI STUDI AVANZATIINTERNATIONAL SCHOOL FOR ADVANCED S TUDIESD-branes, Rolling Tachyons and Vacuum String FieldGọi ngay
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