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Differential operators for superconformal correlation functions

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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 ...

SPRINGER2023

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

Semiclassical methods in conformal field theories scrutinized by the epsilon-expansion

Gil Badel

Conformal Field Theories (CFTs) are crucial for our understanding of Quantum Field Theory (QFT). Because of their powerful symmetry properties, they play the role of signposts in the space of QFTs. Any method that gives us information about their structure ...

EPFL2022

Conformal Field Theory at the Lattice Level: Discrete Complex Analysis and Virasoro Structure

Clément Hongler

Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin et al. (Nucl Phys B 241(2):333-380, 1984). Both exhibit exactly solvable structures in two dimensions. A long-standing question ( ...

SPRINGER2022

Nonperturbative Mellin Amplitudes

João Pedro Alves Da Silva

Conformal field theory lies at the heart of two central topics in theoretical high energy physics: the study of quantum gravity and the mapping of quantum field theories through the renormalization group. In this thesis we explore a technique to study conf ...

EPFL2021

Applications of dispersive sum rules: epsilon-expansion and holography

Alexander Zhiboedov, João Pedro Alves Da Silva, Din Carmi

We use Mellin space dispersion relations together with Polyakov conditions to derive a family of sum rules for Conformal Field Theories (CFTs). The defining property of these sum rules is suppression of the contribution of the double twist operators. First ...

SCIPOST FOUNDATION2021

Bootstrapping superconformal field theories in four dimensions

Andrea Manenti

The conformal bootstrap is a non-perturbative technique designed to study conformal field theories using only first principles, such as unitarity, crossing symmetry and the existence of an Operator Product Expansion. In this thesis we discuss an applicatio ...

EPFL2020

Numerical investigations of 3D CFTs using conformal bootstrap methods

Marten Jan Reehorst

Conformal field theories (CFTs) play a very significant role in modern physics, appearing in such diverse fields as particle physics, condensed matter and statistical physics and in quantum gravity both as the string worldsheet theory and through the AdS/C ...

EPFL2020

A conformal dispersion relation: correlations from absorption

Din Carmi

We introduce the analog of Kramers-Kronig dispersion relations for correlators of four scalar operators in an arbitrary conformal field theory. The correlator is expressed as an integral over its "absorptive part", defined as a double discontinuity, times ...

2020

Convergent momentum-space OPE and bootstrap equations in conformal field theory

Marc Gillioz

General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a dist ...

SPRINGER2020