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Identifier

000440997

Title

Exploring field theories via the Conformal Bootstrap

Alternative Title

Εξερευνώντας θεωρίες πεδίου μέσω Conformal Bootstrap

Author

Κούσβος, Στέφανος Ρόμπερτ Ν

Thesis advisor

Τομαράς, Θεόδωρος

Reviewer

Κυρίτσης, Ηλίας
Νιάρχος, Βασίλειος
Παυλίδου, Βασιλική
Rychkov, Slava
Stergiou, Andreas
Τούμπας, Νικόλαος
Τσάμης, Νικόλαος

Abstract

We study conformal field theories of interest due to phenomenological as well as purely theoretical considerations. This is done with the use of consistency conditions. The program of studying (conformal) field theories with the use of self consistency conditions is referred to as "the bootstrap". In the present thesis we will make use of the numerical bootstrap as envisioned in its modern revival. That is, we will impose crossing symmetry on certain correlators and demand unitarity/reflection positivity, from which we will derive constraints on the parameter space. The parameter space is spanned by an in general infinite set of scaling dimensions and OPE coefficients. These determine various observables, such as the critical exponents observed at critical points. With the use of the numerical bootstrap we will provide strong constraints on the space of allowed critical exponents for various universality classes. The constraints in certain circumstances will be in fact so strong that they actually compute the critical exponents. In other words, only small isolated regions of parameter space will be found to be compatible with the imposed consistency conditions. Some examples of theories we will consider are (hyper) cubic , O(m) × O(n)/Z₂ and “MN” theories. We will find isolated allowed regions in parameter space for all of these. As a side effect of our analysis we will also work out tensor structures for various global symmetries, which can be useful beyond the numerical bootstrap.

Language

English

Subject

Conformal field theory

Critical point

Phase transitions

Αλλαγές φάσης

Κρίσιμο σημείο

Σύμμορφη θεωρία πεδίου

Issue date

2021-07-12

Collection