Quantum integrability as a new method for exact results on N=2 supersymmetric gauge theories and black holes

Gregori, Daniele (2022) Quantum integrability as a new method for exact results on N=2 supersymmetric gauge theories and black holes, [Dissertation thesis], Alma Mater Studiorum Università di Bologna. Dottorato di ricerca in Fisica, 34 Ciclo. DOI 10.48676/unibo/amsdottorato/10485.
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In this thesis I show a triple new connection we found between quantum integrability, N=2 supersymmetric gauge theories and black holes perturbation theory. I use the approach of the ODE/IM correspondence between Ordinary Differential Equations (ODE) and Integrable Models (IM), first to connect basic integrability functions - the Baxter’s Q, T and Y functions - to the gauge theory periods. This fundamental identification allows several new results for both theories, for example: an exact non linear integral equation (Thermodynamic Bethe Ansatz, TBA) for the gauge periods; an interpretation of the integrability functional relations as new exact R-symmetry relations for the periods; new formulas for the local integrals of motion in terms of gauge periods. This I develop in all details at least for the SU(2) gauge theory with Nf=0,1,2 matter flavours. Still through to the ODE/IM correspondence, I connect the mathematically precise definition of quasinormal modes of black holes (having an important role in gravitational waves’ obervations) with quantization conditions on the Q, Y functions. In this way I also give a mathematical explanation of the recently found connection between quasinormal modes and N=2 supersymmetric gauge theories. Moreover, it follows a new simple and effective method to numerically compute the quasinormal modes - the TBA - which I compare with other standard methods. The spacetimes for which I show these in all details are in the simplest Nf=0 case the D3 brane in the Nf=1,2 case a generalization of extremal Reissner-Nordström (charged) black holes. Then I begin treating also the Nf=3,4 theories and argue on how our integrability-gauge-gravity correspondence can generalize to other types of black holes in either asymptotically flat (Nf=3) or Anti-de-Sitter (Nf=4) spacetime. Finally I begin to show the extension to a 4-fold correspondence with also Conformal Field Theory (CFT), through the renowned AdS/CFT correspondence.

Tipologia del documento
Tesi di dottorato
Gregori, Daniele
Dottorato di ricerca
Settore disciplinare
Settore concorsuale
Parole chiave
Integrability, Gauge theory, Supersymmetry, N=2 SUSY, Black holes, ODE/IM correspondence, ODE/IQFT correspondence, exact methods, non-perturbative methods, Seiberg-Witten theory, Thermodynamic Bethe Ansatz, Quasinormal modes, Gravitational waves, AdS/CFT correspondence
Data di discussione
18 Ottobre 2022

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