Conformal field theory | EPFL Graph Search

Are you an EPFL student looking for a semester project?

Work with us on data science and visualisation projects, and deploy your project as an app on top of GraphSearch.

A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations, and conformal field theories can sometimes be exactly solved or classified. Conformal field theory has important applications to condensed matter physics, statistical mechanics, quantum statistical mechanics, and string theory. Statistical and condensed matter systems are indeed often conformally invariant at their thermodynamic or quantum critical points. In quantum field theory, scale invariance is a common and natural symmetry, because any fixed point of the renormalization group is by definition scale invariant. Conformal symmetry is stronger than scale invariance, and one needs additional assumptions to argue that it should appear in nature. The basic idea behind its plausibility is that local scale invariant theories have their currents given by where is a Killing vector and is a conserved operator (the stress-tensor) of dimension exactly . For the associated symmetries to include scale but not conformal transformations, the trace has to be a non-zero total derivative implying that there is a non-conserved operator of dimension exactly . Under some assumptions it is possible to completely rule out this type of non-renormalization and hence prove that scale invariance implies conformal invariance in a quantum field theory, for example in unitary compact conformal field theories in two dimensions. While it is possible for a quantum field theory to be scale invariant but not conformally invariant, examples are rare. For this reason, the terms are often used interchangeably in the context of quantum field theory. The number of independent conformal transformations is infinite in two dimensions, and finite in higher dimensions. This makes conformal symmetry much more constraining in two dimensions. All conformal field theories share the ideas and techniques of the conformal bootstrap.

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Related publications (58)

Related people (12)

Related units (1)

Related concepts (33)

Related courses (17)

Related lectures (147)

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. An

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

SPRINGER2022

Level crossings and chiral transitions in transverse-field Ising models of adatom and Rydberg chains

Ivo Aguiar Maceira

This thesis is motivated by recent experiments on systems described by extensions of the one-dimensional transverse-field Ising (TFI) model where (1) finite-size properties of Ising-ordered phases --

EPFL2022

Ising model

The Ising model (ˈiːzɪŋ) (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors.

Wightman axioms

In mathematical physics, the Wightman axioms (also called Gårding–Wightman axioms), named after Arthur Wightman, are an attempt at a mathematically rigorous formulation of quantum field theory. Arthur Wightman formulated the axioms in the early 1950s, but they were first published only in 1964 after Haag–Ruelle scattering theory affirmed their significance. The axioms exist in the context of constructive quantum field theory and are meant to provide a basis for rigorous treatment of quantum fields and strict foundation for the perturbative methods used.

Conformal field theory

PHYS-739: Conformal Field theory and Gravity

This course is an introduction to the non-perturbative bootstrap approach to Conformal Field Theory and to the Gauge/Gravity duality, emphasizing the fruitful interplay between these two ideas.

MATH-605: Conformal bootstrap and Liouville conformal field

The course will focus on a probabilistic construction of a conformal field theory related to random Riemann surfaces, called the Liouville conformal field theory. The symmetries of the theory allow to

PHYS-435: Statistical physics III

This course introduces statistical field theory, and uses concepts related to phase transitions to discuss a variety of complex systems (random walks and polymers, disordered systems, combinatorial o

Conformal Field Theory Basics

Covers the basics of Conformal Field Theory, focusing on Large N CFTs and correlation functions.

Operator Product Expansion

Explores Operator Product Expansion (OPE) and its role in Conformal Bootstrap.

Conformal Transformations: Symmetries and Correlation Functions

Explores conformal transformations and correlation functions in quantum field theory, emphasizing symmetry preservation and fixed correlation functions.