Neil B. Copland
These lecture notes introduce the multiple membrane theories known as BLG and ABJM. We assume the reader is familiar with string theory, but not with M-theory, 11-dimensional supergravity or membranes. We therefore start with a background on M-theory and its extended objects before discussing BLG and ABJM. The link to string theory via dimensional reduction will be maintained throughout.
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These are short notes of three introductory lectures on recently proposed matrix models of Superstrings and M theory given at 5th Nordic Meeting on Supersymmetric Field and String Theories in Helsinki (March 10-12, 1997). Contents: M(atrix) theory of BFSS, From IIA to IIB with IKKT, The NBI matrix model.
In an ungauged supergravity theory, the presence of a \emph{scalar potential} is allowed only for the minimal $\N=1$ case. In extended supergravities, a non-trivial scalar potential can be introduced without explicitly breaking supersymmetry only through the so-called \emph{gauging procedure}. The latter consists in promoting a suitable global symmetry group to local symmetry to be gauged by the vector fields of the theory. Gauged supergravities provide a valuable approach to the study of superstring flux-compactifications and the construction of phenomenologically viable, string-inspired mode…
This is a pedagogical introduction to D-branes, addressed to graduate students in field theory and particle physics and to other beginners in string theory. I am not going to review the most recent results since there are already many good papers on web devoted to that. Instead, I will present some old techniques in some detail in order to show how some basic properties of strinfs and branes as the massless spectrum of string, the effective action of D-branes and their tension can be computed using QFT techniques. Also, I will present shortly the boundary state description of D-branes. The det…
We give an elementary introduction to classical and quantum bosonic string theory.
We give a standard introduction to loop quantum gravity, from the ADM variables to spin network states. We include a discussion on quantum geometry on a fixed graph and its relation to a discrete approximation of general relativity.
Introductory Lectures on Resurgence: CERN Summer School 2024
本文通过四讲介绍 resurgence 方法，涵盖连续基础、非线性 Stokes 现象、QFT 有效作用及 resurgence 续续与求和，强调物理动机的例子和练习。
In these lectures we present a few topics in Quantum Field Theory in detail. Some of them are conceptual and some more practical. They have been selected because they appear frequently in current applications to Particle Physics and String Theory.
An elementary, pedagogical introduction to the large-N limit of QCD and to its phenomenological implications is presented, and a survey of lattice results in the 't Hooft limit is briefly discussed.
Notes of my 14 `lectures on everything' given at the 1995 Les Houches school. An introductory course in topological and conformal field theory, strings, gauge fields, supersymmetry and more. The presentation is more mathematical then usual and takes a modern point of view stressing moduli spaces, duality and the interconnectedness of the subject. An apocryphal lecture on BPS states and D-branes is added.
These lecture notes are based on a course on string theories given by Hirosi Ooguri in the first week of TASI 96 Summer School at Boulder, Colorado. It is an introductory course designed to provide students with minimum knowledge before they attend more advanced courses on non-perturbative aspects of string theories in the School. The course consists of five lectures: 1. Bosonic String, 2. Toroidal Compactifications, 3. Superstrings, 4. Heterotic Strings, and 5. Orbifold Compactifications.
These notes were prepared for the introductory lectures on Higher Spin Holography presented at the Twelfth Modave Summer School in Mathematical Physics 2016, aimed at Ph.D. students and researchers new to this topic. Contents: 1. Higher spin particles in AdS 2. The AdS/CFT correspondence and higher spins 3. The ambient space formalism 4. Witten diagrams for higher spin fields / higher spin interactions from CFT
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the definition in terms symmetric monoidal categories, and we highlight the algebraic formulation emerging from a formal generators-and-relations description. This allows one to understand (oriented, closed) 1- and 2-dimensional TQFTs in terms of a finite amount of algebraic data, while already the 3-dimensional case needs an infinite amount of data. We evade these …
In these introductory lectures we summarize some basic facts and techniques about perturbative string theory (sections 1 to 6). These are further developed (sections 7 and 8) for describing string propagation in the presence of gravitational or gauge fields. We also remind some solutions of the string equations of motion, which correspond to remarkable (NS or D) brane configurations. A part II by Emilian Dudas will be devoted to orientifold constructions and applications to string model building.
Planning to explore the beginning of the Universe? A lightweight introductory guide to the theory of Inflation.
The purpose of these lecture notes is to give a quick and introductory overview of holographic superconductors. Besides the actual description of the standard holographic superconductor, attention is paid to the motivations and the relation with the previous, non-holographic context.
This is the written version of a set of introductory lectures on string theory.
These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds. The last section provides a short introduction to toric geometry, aimed at constructing Calabi-Yau manifolds in two different ways; as hypersurfaces in toric varieties and as local toric Calabi-Yau threefolds. These lecture notes supplement a mini-course that was given by the author at the Modave Summer School in Mathematical Physics 2005, and at CERN in …
Section I contains introductory remarks about surface motions. Section II gives a detailed derivation of $H=-Δ-Tr\sum_{i<j}[X_i,X_j]^2$ as describing a quantized discrete analogue of relativistically invariant membrane dynamics. Section III concerns the question of zero-energy bound-states in SU(N)-invariant supersymmetric matrix models. Section IV discusses the space of solutions of some differential matrix equations on $(-\infty,+\infty)$, interpolating between different representations of $su(2)$. Some exercises are added, and one remark/conjecture concerning 5-commutators.
Introductory lectures on Extra Dimensions delivered at TASI 2004. The emphasis is on basic mechanisms rather than specific models.
The curse of dimensionality associated with the Hilbert space of spin systems provides a significant obstruction to the study of condensed matter systems. Tensor networks have proven an important tool in attempting to overcome this difficulty in both the numerical and analytic regimes. These notes form the basis for a seven lecture course, introducing the basics of a range of common tensor networks and algorithms. In particular, we cover: introductory tensor network notation, applications to quantum information, basic properties of matrix product states, a classification of quantum phases usin…
These notes represent approximately one semester's worth of lectures on introductory general relativity for beginning graduate students in physics. Topics include manifolds, Riemannian geometry, Einstein's equations, and three applications: gravitational radiation, black holes, and cosmology.
These lecture notes provide an introduction to cosmic inflation. In particular I will review the basic concepts of inflation, generation of density perturbations, and reheating after inflation.
These are introductory lectures on loop quantum gravity. The theory is presented in self-contained form, without emphasis on its derivation from classical general relativity. Dynamics is given in the covariant form. Some applications are described.
Introductory lectures on the relations between the thermodynamics of gauge theory on branes and black holes, including the correspondence principle of Horowitz and Polchinski, the AdS/CFT conjecture, and matrix theory.
Les Houches lectures on non-perturbative topological strings
本文介绍了非微扰拓扑弦理论的概览，涵盖 resurgence 理论、非微扰幅推导以及 TS/ST 对应关系的核心贡献。
Introductory lectures on classical and quantum string black holes (supergravity, branes and dualities) given at the VII School "La Hechicera" of Relativity, Fields and Astrophysics, held in the University of Los Andes, Merida (Venezuela) 2001. Fully in Spanish.
This is a set of introductory lecture notes devoted to the Wess-Zumino-Witten model of two-dimensional conformal field theory. We review the construction of the exact solution of the model from the functional integral point of view. The boundary version of the theory is also briefly discussed.
In this lecture we review some of the recent developments in string theory on an introductory and qualitative level. In particular we focus on S-T-U dualities of toroidally compactified ten-dimensional string theories and outline the connection to M-theory. Dualities among string vacua with less supersymmetries in six and four space-time dimensions is discussed and the concept of F-theory is briefly presented. (Lecture given by J. Louis at the Workshop on Gauge Theories, Applied Supersymmetry and Quantum Gravity, Imperial College, London, UK, July 5--10, 1996.)
In these lectures, we review the D=11 supermembrane and supersymmetric matrix models at an introductory level. We also discuss some more recent developments in connection with non-perturbative string theory.
Three introductory lectures: on Yangians and their representations; on Yangian symmetry in 1+1D integrable (bulk) field theory; and on the effect of a boundary upon this symmetry.
This is an introductory lecture note aiming at providing an overview of the AdS-CFT correspondence at weak 't Hooft coupling at finite temperature. The first aim of this note is to describe the equivalence of three interesting thermodynamical phenomena in theoretical physics, namely, Hawking-Page transition to black hole geometry, deconfinement transition in gauge theories, and vortex condensation on string worldsheets. The Hawking-Page transition and the deconfinement transition in weakly coupled gauge theories are briefly reviewed. Emphasis is on the study of 't Hooft-Feynman diagrams in the…
An introductory review, based on a series of lectures delivered at the XXXI SERC School, Kalyani University, 9--18 January 2017.
Introduction to String Theory
本文为都灵大学理论物理硕士课程弦理论入门的讲义，系统介绍玻色弦与超弦框架下的世界面方法。
This is an introductory set of lectures on elliptic differential operators and boundary problems, and their associated spectral functions. The role of zeta functions and traces of heat kernels in the regularization of Casimir energies is emphasized, and the renormalization issue is discussed through simple examples.
Branes in String/M-Theory
本文基于2006年北京亚太超弦入门学校及2023年南京弦、场与全息暑期学校讲座内容，从历史与教学角度阐述第二次弦革命早期1/2 BPS扩展弦孤子的发展，并讨论膜/反膜系统等非超对称解。
The first part of these lectures contains an introductory review of the AdS/CFT duality and of its tests. Applications to thermal gauge theory are also discussed briefly. The second part is devoted to a review of gauge-string dualities based on various warped conifold backgrounds, and to their cosmological applications.
Lecture notes: Introduction to the Off-shell Double Copy Program
本文为研究生课程讲义，基于经典场论基础，系统介绍离壳单拷贝和双拷贝的现代框架，并探讨T-对偶不变框架下的重新诠释。
This is a write-up of introductory lectures on black holes in string theory given at TASI-99. Topics discussed include: Black holes, thermodynamics and the Bekenstein-Hawking entropy, the information problem; supergravity actions, conserved quantum numbers, supersymmetry and BPS states, units and duality, dimensional reduction, solution-generating; extremal M-branes and D-branes, smearing, probe actions, nonextremal branes, the Gregory-Laflamme instability; breakdown of supergravity and the Correspondence Principle, limits in parameter space, singularity resolution; making black holes with bra…
Introductory visual lecture on QCD at large-$N_{c}$: bound states, chiral models, and phase diagram
该讲座利用类NJL束缚态方程研究QCD大$N_c$极限下介子、胶球、重子等的行为与标度律，分析手征模型特性，探讨介质中QCD的相图、退禁闭相变及大$N_c$对原子核和中子星的启示。
These notes accompany an introductory lecture course on the twistor approach to supersymmetric gauge theories aimed at early-stage PhD students. It was held by the author at the University of Cambridge during the Michaelmas term in 2009. The lectures assume a working knowledge of differential geometry and quantum field theory. No prior knowledge of twistor theory is required.
Lecture Notes on Symmetry Reduction via the Dressing Field Method
本文通过着装场方法系统提取广义相对论规范场论中的规范与微分同胚不变、显式关系的物理可观测量和自由度，并举例应用于非阿贝尔陈-西蒙斯理论、麦克斯韦电磁学、非阿贝尔希格斯模型、超对称场论、广义相对论和标量坐标化。
In these introductory lectures we discuss the topic of Yangian symmetry from various perspectives. Forming the classical counterpart of the Yangian and an extension of ordinary Noether symmetries, first the concept of nonlocal charges in classical, two-dimensional field theory is reviewed. We then define the Yangian algebra following Drinfeld's original motivation to construct solutions to the quantum Yang-Baxter equation. Different realizations of the Yangian and its mathematical role as a Hopf algebra and quantum group are discussed. We demonstrate how the Yangian algebra is implemented in q…
Lecture notes on Nichols algebras
本文从范畴论视角介绍了Nichols代数的定义、性质及其在量子群表示范畴构建中的作用，同时探讨其在共形场论中的应用。
These lecture notes are a systematic and self-contained exposition of the cohomological theories naturally related to partial differential equations: the Vinogradov C-spectral sequence and the C-cohomology, including the formulation in terms of the horizontal (characteristic) cohomology. Applications to computing invariants of differential equations are discussed. The lectures contain necessary introductory material on the geometric theory of differential equations and homological algebra.
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