Starting from the study of a 2-dimensional non-linear sigma model with N=(2,2) supercharges one can show that supersymmetry cannot be preserved on a curved target space. Thus, it is useful to perform a topological twisting of the theory which allows to keep at least one supercharge; moreover the resulting theory is topological, which means that it does not depend on the worldsheet metric. Thanks to this one can study physical operators and correlation functions and in turns out that they are deeply connected to "Gromov-Witten" invariants which can be computed by studying the moduli space of stable maps. Finally, one can try to treat the metric as a dynamical variable, and reducing the target space to be a point, one can show that correlators of gravitational observables in two dimensions can be computed studying the moduli space of Riemann surfaces.
Partendo dallo studio di un una teoria di campo bidimensionale con N=(2,2) supercariche e cercando di generalizzare tale teoria ad un modello in cui i campi prendono valori in una varietà target di Kahler, si nota come la supersimmetria non venga preservata. Si effettua quindi un "twisting" topologico ed in tal modo almeno una supercarica viene preservata; inoltre la teoria risultante è topologica, ovvero non dipende dalla metrica della varietà di base. Si cercano quindi quali sono gli operatori e i correlatori rilevanti, ottenendo che quest'ultimi sono legati agli invarianti di "Gromov-Witten" i quali si possono calcolare studiando lo spazio dei moduli delle mappe stabili. Infine si cerca di rendere la metrica una variabile dinamica e, prendendo come varietà target un punto, si giunge alla conclusione che correlatori di osservabili gravitazionali in due dimensioni si possono calcolare studiando lo spazio dei moduli delle superfici di Riemann.
Arising of the moduli space of Riemann surfaces from the study of topological strings
MATHEUS ROCHA, SANTIAGO JAVIER
2022/2023
Abstract
Starting from the study of a 2-dimensional non-linear sigma model with N=(2,2) supercharges one can show that supersymmetry cannot be preserved on a curved target space. Thus, it is useful to perform a topological twisting of the theory which allows to keep at least one supercharge; moreover the resulting theory is topological, which means that it does not depend on the worldsheet metric. Thanks to this one can study physical operators and correlation functions and in turns out that they are deeply connected to "Gromov-Witten" invariants which can be computed by studying the moduli space of stable maps. Finally, one can try to treat the metric as a dynamical variable, and reducing the target space to be a point, one can show that correlators of gravitational observables in two dimensions can be computed studying the moduli space of Riemann surfaces.File | Dimensione | Formato | |
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https://hdl.handle.net/20.500.12608/61043