Weissenbacher, Matthias (2015): On geometric corrections to effective actions of string theory. Dissertation, LMU München: Faculty of Physics 

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Abstract
In this thesis we study geometric corrections to the lowenergy effective actions of string theory. More concretely, we compute higherderivative corrections to the couplings of threedimensional, N = 2 supergravity theories and interpret the induced α′corrections in N = 1, minimal supergravity theories in four dimensions, in the framework of Ftheory. These allow for chiral spectra and are therefore phenomenological relevant. We analyzed higherderivative corrections to Mtheory, accessible through its lowenergy effective theory, given by elevendimensional supergravity. The next to leading order terms to elevendimensional supergravity carry eightderivatives, and are suppressed by lM6 compared to the classical terms, with lM being the elevendimensional PlanckLength  the only scale in eleven dimensions. These corrections are lifted from IIA supergravity corrections, which are derived from string scattering amplitudes. The common theme of this thesis is to compactify the bosonic sector of the elevendimensional supergravity action, including all known eightderivative corrections, on a supersymmetric background to find a 3d, N = 2 theory, which then can be lifted to a 4d, N = 1 theory. This goal is approached in several steps. In the classical reduction of elevendimensional supergravity the metric background is a direct product of the external space, consisting of two space and one time dimension and the internal eight spacelikedimensional CalabiYau manifold. However, when considering higherderivative corrections the background has to be altered by introducing a dependence of the external space on the warp factor, which is a function of the internal space. We find an explicit warped background solution to the elevendimensional E.O.M.’s including nonvanishing flux. To check the background for its supersymmetry features one would need to consider the elevendimensional gravitino variations at this order in lM . However, these are not known, which leads us to propose higherorder lM corrected gravitino variations consistent with our background solution. As a next step we dimensionally reduce the bosonic sector of the elevendimensional supergravity action including all eightderivative terms on this warped background and analyze the resulting three dimensional theory. In this context the interplay of the warpfactor and the higherderivative terms is of crucial importance. To identify the N = 2 properties of the resulting threedimensional theory obtained by dimensional reduction, we compare it to the canonical from of threedimensional N = 2 supergravtiy. We conclude that the reduced action is compatible with N = 2 supersymmetry and give a proposal for the K ̈ahler potential and the complex coordinates, which receive lM6 corrections. Besides a warpfactor contribution, the K ̈ahler potential receives a correction proportional to the third Chern 2 ￼form of the zeroth order internal background, being the CalabiYau fourfold. The complex coordinates are defined as divisorintegrals and are corrected by a warpfactor dependent term as well as one related to the nonharmonic part of the fourth Chernform, of the zeroth order CalabiYau manifold. Thus the couplings of the resulting theory receive besides the warpfactor, in particular geometric corrections of order lM6 . In the first part of this thesis we study a simplified setup, only considering a subset of the relevant eightderivative corrections in eleven dimensions. Furthermore, we do compactify on the classical background, consisting of the internal CalabiYau fourfold without warping and fluxes, to gain a threedimensional theory. However, we use the M/Ftheory duality to uplift the yielded corrections, which results in corrections to the couplings of the fourdimensional theory. In the weak coupling limit we find that these are sourced by the selfintersection curves of D7branes.
Item Type:  Thesis (Dissertation, LMU Munich) 

Keywords:  Ftheory, HigherDerivative, Supergravity 
Subjects:  500 Natural sciences and mathematics 500 Natural sciences and mathematics > 530 Physics 
Faculties:  Faculty of Physics 
Language:  English 
Date of oral examination:  23. September 2015 
1. Referee:  Lüst, Dieter 
MD5 Checksum of the PDFfile:  f71c3716b0e706e392e4a2af2fdb569f 
Signature of the printed copy:  0001/UMC 23282 
ID Code:  18713 
Deposited On:  21. Oct 2015 13:27 
Last Modified:  21. Oct 2015 13:27 