In this thesis we study 2dimensional N=(4,4) superconformal field theories and their application to superstring theories. More specifically, we would like to analyze the behaviour of the fields under a certain set of discrete symmetries of a nonlinear sigma model whose target space is a K3 surface, in particular, the T^4/Z_2 orbifold. A good way to understand this is to compute the Elliptic Genus and some Twining Genera obtained by inserting in the Elliptic Genus one of the allowed discrete symmetries of the model. More in detail, the set of discrete symmetries we are going to consider are the ones that respect the OPEs of the fields and fix the N=4 superconformal algebra. The peculiarity of K3 surfaces is that, when a d=10 IIA or IIB superstring theory with 32 supercharges is compactified on them, only 16 supercharges are preserved and this gives birth to 6dimensional lowenergy theories of supergravity. If we compactify on (K3 x T^2) surfaces, what we obtain are lowenergy 4dimensional theories of supergravity with 16 preserved supercharges. The Twining Genera we are going to compute, have been conjectured for a certain set of K3 surfaces with different metrics and different discrete symmetries, therefore, since they should not depend on the choice of the metric as long as the symmetry remains a symmetry of the orbifold, we expect to confirm the conjectured value. In conclusion, the study of nonlinear sigma models living on K3 surfaces is useful to understand 6dimensional and 4dimensional supergravity theories with, at least, 16 supercharges.
Discrete symmetries of N = 4 String models
Gorini, Nicola
2017/2018
Abstract
In this thesis we study 2dimensional N=(4,4) superconformal field theories and their application to superstring theories. More specifically, we would like to analyze the behaviour of the fields under a certain set of discrete symmetries of a nonlinear sigma model whose target space is a K3 surface, in particular, the T^4/Z_2 orbifold. A good way to understand this is to compute the Elliptic Genus and some Twining Genera obtained by inserting in the Elliptic Genus one of the allowed discrete symmetries of the model. More in detail, the set of discrete symmetries we are going to consider are the ones that respect the OPEs of the fields and fix the N=4 superconformal algebra. The peculiarity of K3 surfaces is that, when a d=10 IIA or IIB superstring theory with 32 supercharges is compactified on them, only 16 supercharges are preserved and this gives birth to 6dimensional lowenergy theories of supergravity. If we compactify on (K3 x T^2) surfaces, what we obtain are lowenergy 4dimensional theories of supergravity with 16 preserved supercharges. The Twining Genera we are going to compute, have been conjectured for a certain set of K3 surfaces with different metrics and different discrete symmetries, therefore, since they should not depend on the choice of the metric as long as the symmetry remains a symmetry of the orbifold, we expect to confirm the conjectured value. In conclusion, the study of nonlinear sigma models living on K3 surfaces is useful to understand 6dimensional and 4dimensional supergravity theories with, at least, 16 supercharges.File  Dimensione  Formato  

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https://hdl.handle.net/20.500.12608/25100