Bertozzi, Luca
(2024)

*Integrability structures in SU(2) supersymmetric gauge theory with four flavours and AdS black holes.*
[Laurea magistrale], Università di Bologna, Corso di Studio in

Physics [LM-DM270], Documento ad accesso riservato.

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## Abstract

In this thesis we study through the Ordinary Differential Equation/Integrable Model
(ODE/IM) correspondence the deformed Seiberg-Witten curve of four flavour N = 2
SU(2) supersymmetric Yang-Mills theory. This theory, compared with the ones with
fewer flavours of quarks, is very different as there is no dinamically generated scale and
thus the theory is asymptotically conformal. At the ODE level this is manifested in the
absence of irregular singular points in the equation and thus no Stokes phenomenon is
present. While in the eyes of the AGT correspondence this is the most natural setting,
for the ODE/IM correspondence this leads to the absence of the transfer matrices of
integrability. However we introduce the monodromy group of the ODE into the problem
and show its equivalence with the system of Q-functions. We stress how the gauge theory prepotential should be seen as the generating function of a canonical transformation
on the space of monodromy data which is endowed with a symplectic structure. Using
this fact we achieve a definition of the prepotential directly from the differential equation, using the Matone relation, without requiring, in principle, the usage, but only the
matching with gauge theory. The same differential equation shows up as the equation
describing a scalar perturbation in the five-dimensional AdS-Schwarzschild background.
The applications of this is two-fold: first integrability could be used to derive Bethe
ansatz equation for the quasi-normal modes of AdS black holes. Second this gravity
theory is the holographic dual of four-dimensional N = 4 SYM and the connection coefficients for the ODE can then be connected to an exact expression for the two-point
function at finite temperature in this theory

Abstract

In this thesis we study through the Ordinary Differential Equation/Integrable Model
(ODE/IM) correspondence the deformed Seiberg-Witten curve of four flavour N = 2
SU(2) supersymmetric Yang-Mills theory. This theory, compared with the ones with
fewer flavours of quarks, is very different as there is no dinamically generated scale and
thus the theory is asymptotically conformal. At the ODE level this is manifested in the
absence of irregular singular points in the equation and thus no Stokes phenomenon is
present. While in the eyes of the AGT correspondence this is the most natural setting,
for the ODE/IM correspondence this leads to the absence of the transfer matrices of
integrability. However we introduce the monodromy group of the ODE into the problem
and show its equivalence with the system of Q-functions. We stress how the gauge theory prepotential should be seen as the generating function of a canonical transformation
on the space of monodromy data which is endowed with a symplectic structure. Using
this fact we achieve a definition of the prepotential directly from the differential equation, using the Matone relation, without requiring, in principle, the usage, but only the
matching with gauge theory. The same differential equation shows up as the equation
describing a scalar perturbation in the five-dimensional AdS-Schwarzschild background.
The applications of this is two-fold: first integrability could be used to derive Bethe
ansatz equation for the quasi-normal modes of AdS black holes. Second this gravity
theory is the holographic dual of four-dimensional N = 4 SYM and the connection coefficients for the ODE can then be connected to an exact expression for the two-point
function at finite temperature in this theory

Tipologia del documento

Tesi di laurea
(Laurea magistrale)

Autore della tesi

Bertozzi, Luca

Relatore della tesi

Correlatore della tesi

Scuola

Corso di studio

Indirizzo

THEORETICAL PHYSICS

Ordinamento Cds

DM270

Parole chiave

integrability,supersymmetry,gauge theory,quantum field theory,holography,ode/im

Data di discussione della Tesi

27 Marzo 2024

URI

## Altri metadati

Tipologia del documento

Tesi di laurea
(NON SPECIFICATO)

Autore della tesi

Bertozzi, Luca

Relatore della tesi

Correlatore della tesi

Scuola

Corso di studio

Indirizzo

THEORETICAL PHYSICS

Ordinamento Cds

DM270

Parole chiave

integrability,supersymmetry,gauge theory,quantum field theory,holography,ode/im

Data di discussione della Tesi

27 Marzo 2024

URI

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