Complex Analysis meets Statistical Mechanics: Applications to Kernel Methods and Conformal Field Theory

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Flux correlators and semiclassics

Riccardo Rattazzi, Alexander Monin, Eren Clément Firat, Matthew Thomas Walters

We consider correlators for the flux of energy and charge in the background of operators with large global U(1) charge in conformal field theory (CFT). It has recently been shown that the corresponding Euclidean correlators generically admit a semiclassica ...

Springer Nature2024

Null energy constraints on two-dimensional RG flows

Grégoire Olivier Mathys

We study applications of spectral positivity and the averaged null energy condition (ANEC) to renormalization group (RG) flows in two-dimensional quantum field theory. We find a succinct new proof of the Zamolodchikov c-theorem, and derive further independ ...

Springer Nature2024

Bootstrapping smooth conformal defects in Chern-Simons-matter theories

Barak Gabai, Amit Sever

The expectation value of a smooth conformal line defect in a CFT is a conformal invariant functional of its path in space-time. For example, in large N holographic theories, these fundamental observables are dual to the open-string partition function in Ad ...

Springer Nature2024

Bootstrapping amplitudes of scalar particles

Jan Krzysztof Marucha

Quantum Field Theories are a central object of interest of modern physics, describing fundamental interactions of matter. However, current methods give limited insight into strongly coupling theories. S-matrix bootstrap program, described in this thesis, a ...

EPFL2024

Transition to chaos in extended systems and their quantum impurity models

Camille Didier Georges Aron

Chaos sets a fundamental limit to quantum-information processing schemes. We study the onset of chaos in spatially extended quantum many-body systems that are relevant to quantum optical devices. We consider an extended version of the Tavis-Cummings model ...

Iop Publishing Ltd2024

Identifying Large Charge operators

Riccardo Rattazzi, Alexander Monin, Gil Badel

The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on U(1) invariant Wilson-Fisher fixed points, we study the spectrum of spinning l ...

Springer Nature2023

The Källén-Lehmann representation in de Sitter spacetime

Kamran Salehi Vaziri, Manuel Loparco, João Miguel Augusto Penedones Fernandes

We study two-point functions of symmetric traceless local operators in the bulk of de Sitter spacetime. We derive the Kallen-Lehmann spectral decomposition for any spin and show that unitarity implies its spectral densities are nonnegative. In addition, we ...

Springer Nature2023

Twist Accumulation in Conformal Field Theory: A Rigorous Approach to the Lightcone Bootstrap

Jiaxin Qiao

We prove that in any unitary CFT, a twist gap in the spectrum of operator product expansion (OPE) of identical scalar quasiprimary operators (i.e. phi x phi) implies the existence of a family of quasiprimary operators O t,l with spins l ->.infinity and twi ...

SPRINGER2023

Nonperturbative aspects of scattering amplitudes

Miguel Alexandre Ribeiro Correia

In this thesis we study how physical principles imposed on the S-matrix, such as Lorentz invariance, unitarity, crossing symmetry and analyticity constrain quantum field theories at the nonperturbative level. We start with a pedagogical introduction to the ...

EPFL2023

Exact quantum conformal symmetry, its spontaneous breakdown, and gravitational Weyl anomaly

Mikhail Chapochnikov, Anna Tokareva

The classical Lagrangian of the Standard Model enjoys the symmetry of the full conformal group if the mass of the Higgs boson is put to zero. This is a hint that conformal symmetry may play a fundamental role in the ultimate theory describing nature. The o ...

American Physical Society2023

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