Lecture

String Theory: Lectures 14-17

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In course

PHYS-739: Conformal Field theory and Gravity

This course is an introduction to holography, the modern approach to quantum gravity. ...

Description

This lecture covers topics related to string theory, including AdS/CFT correspondence, critical points in 3D Ising model, and the behavior of gravitons. It discusses the expansion of AdS radius, critical points in the Ising model, and the ordering of coincident points. The lecture also explores stress tensor Ward identities, scalar fields, and the concept of holographic CFTs. It delves into the asymptotic behavior of correlators, the role of D-branes, and the constraints on holographic CFTs. The instructor explains the observables in CFTs, the concept of conformal invariance, and the interactions of different particles in string theory.

Instructors (2)

Grégoire Olivier Mathys

Kyriakos Papadodimas

Official source

Ontological neighbourhood

Physics

Quantum mechanics: Quantum gravity

Related concepts (32)

Conformal field theory

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.

String theory

In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string.

Conformal symmetry

In mathematical physics, the conformal symmetry of spacetime is expressed by an extension of the Poincaré group, known as the conformal group. The extension includes special conformal transformations and dilations. In three spatial plus one time dimensions, conformal symmetry has 15 degrees of freedom: ten for the Poincaré group, four for special conformal transformations, and one for a dilation. Harry Bateman and Ebenezer Cunningham were the first to study the conformal symmetry of Maxwell's equations.

String field theory

String field theory (SFT) is a formalism in string theory in which the dynamics of relativistic strings is reformulated in the language of quantum field theory. This is accomplished at the level of perturbation theory by finding a collection of vertices for joining and splitting strings, as well as string propagators, that give a Feynman diagram-like expansion for string scattering amplitudes. In most string field theories, this expansion is encoded by a classical action found by second-quantizing the free string and adding interaction terms.

Scale invariance

In physics, mathematics and statistics, scale invariance is a feature of objects or laws that do not change if scales of length, energy, or other variables, are multiplied by a common factor, and thus represent a universality. The technical term for this transformation is a dilatation (also known as dilation). Dilatations can form part of a larger conformal symmetry. In mathematics, scale invariance usually refers to an invariance of individual functions or curves.

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Covers the concept of holography in classical gravity and its relation to string theory.

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Covers the Easing model conformal theory, focusing on scaling limits and correlation functions.

Black Holes and String Theory

Explores black holes and string theory solutions in higher-dimensional space.

Conformal Field Theory Basics

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

Renormalization Group in Field Theory