Publications

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• Minimal lectures on two-dimensional conformal field theory

  Sylvain Ribault

  SciPost Phys. Lect. Notes 1 (2018) · published 10 June 2018 | Toggle abstract · pdf

  We provide a brief but self-contained review of conformal field theory on the Riemann sphere. We first introduce general axioms such as local conformal invariance, and derive Ward identities and BPZ equations. We then define minimal models and Liouville theory by specific axioms on their spectrums and degenerate fields. We solve these theories by computing three- and four-point functions, and discuss their existence and uniqueness.

  8 citations

• Dark matter in astrophysics/cosmology

  Anne M. Green

  SciPost Phys. Lect. Notes 37 (2022) · published 25 January 2022 | Toggle abstract · pdf

  These lecture notes aim to provide an introduction to dark matter from the perspective of astrophysics/cosmology. We start with a rapid overview of cosmology, including the evolution of the Universe, its thermal history and structure formation. Then we look at the observational evidence for dark matter, from observations of galaxies, galaxy clusters, the anisotropies in the cosmic microwave background radiation and large scale structure. To detect dark matter we need to know how it's distributed, in particular in the Milky Way, so next we overview relevant results from numerical simulations and observations. Finally, we conclude by looking at what astrophysical and cosmological observations can tell us about the nature of dark matter, focusing on two particular cases: warm and self-interacting dark matter.

  8 citations

• Statistical mechanics of integrable quantum spin systems

  Frank Göhmann

  SciPost Phys. Lect. Notes 16 (2020) · published 17 August 2020 | Toggle abstract · pdf

  This script is based on the notes the author prepared to give a set of six lectures at the Les Houches School "Integrability in Atomic and Condensed Matter Physics" in the summer of 2018. The school had its focus on the application of integrability based methods to problems in non-equilibrium statistical mechanics. The lectures were meant to complement this subject with background material on the equilibrium statistical mechanics of quantum spin chains from a vertex model perspective. The author was asked to provide a minimal introduction to quantum spin systems including notions like the reduced density matrix and correlation functions of local observables. He was further asked to explain the graphical language of vertex models and to introduce the concepts of the Trotter decomposition and the quantum transfer matrix. This was basically the contents of the first four lectures presented at the school. In the remaining two lectures these notions were filled with life by deriving an integral representation of the free energy per lattice site for the Heisenberg-Ising chain (alias XXZ model) using techniques based on non-linear integral equations.

  8 citations

• Phase transitions above the upper critical dimension

  Bertrand Berche, Tim Ellis, Yurij Holovatch, Ralph Kenna

  SciPost Phys. Lect. Notes 60 (2022) · published 12 August 2022 | Toggle abstract · pdf

  These lecture notes provide an overview of the renormalization group (RG) as a successful framework to understand critical phenomena above the upper critical dimension $d_{\rm uc}$. After an introduction to the scaling picture of continuous phase transitions, we discuss the apparent failure of the Gaussian fixed point to capture scaling for Landau mean-field theory, which should hold in the thermodynamic limit above $d_{\rm uc}$. We recount how Fisher's dangerous-irrelevant-variable formalism applied to thermodynamic functions partially repairs the situation but at the expense of hyperscaling and finite-size scaling, both of which were, until recently, believed not to apply above $d_{\rm uc}$. We recall limitations of various attempts to match the RG with analytical and numerical results for Ising systems. We explain how the extension of dangerous irrelevancy to the correlation sector is key to marrying the above concepts into a comprehensive RG scaling picture that renders hyperscaling and finite-size scaling valid in all dimensions. We collect what we believe is the current status of the theory, including some new insights and results. This paper is in grateful memory of Michael Fisher who introduced many of the concepts discussed and who, half a century later, contributed to their advancement.

  7 citations

• Lectures on faster-than-light travel and time travel

  Barak Shoshany

  SciPost Phys. Lect. Notes 10 (2019) · published 1 October 2019 | Toggle abstract · pdf

  These lecture notes were prepared for a 25-hour course for advanced undergraduate students participating in Perimeter Institute's Undergraduate Summer Program. The lectures cover some of what is currently known about the possibility of superluminal travel and time travel within the context of established science, that is, general relativity and quantum field theory. Previous knowledge of general relativity at the level of a standard undergraduate-level introductory course is recommended, but all the relevant material is included for completion and reference. No previous knowledge of quantum field theory, or anything else beyond the standard undergraduate curriculum, is required. Advanced topics in relativity, such as causal structures, the Raychaudhuri equation, and the energy conditions are presented in detail. Once the required background is covered, concepts related to faster-than-light travel and time travel are discussed. After introducing tachyons in special relativity as a warm-up, exotic spacetime geometries in general relativity such as warp drives and wormholes are discussed and analyzed, including their limitations. Time travel paradoxes are also discussed in detail, including some of their proposed resolutions.

  7 citations

• Celestial holography: Lectures on asymptotic symmetries

  Prema B. Aneesh, Geoffrey Compère, Leonardo Pipolo de Gioia, Igor Mol, Bianca Swidler

  SciPost Phys. Lect. Notes 47 (2022) · published 13 April 2022 | Toggle abstract · pdf

  The aim of these Lectures is to provide a brief overview of the subject of asymptotic symmetries of gauge and gravity theories in asymptotically flat spacetimes as background material for celestial holography.

  7 citations

• Introduction to the nested algebraic Bethe ansatz

  N. A. Slavnov

  SciPost Phys. Lect. Notes 19 (2020) · published 2 September 2020 | Toggle abstract · pdf

  We give a detailed description of the nested algebraic Bethe ansatz. We consider integrable models with a $\mathfrak{gl}_3$-invariant $R$-matrix as the basic example, however, we also describe possible generalizations. We give recursions and explicit formulas for the Bethe vectors. We also give a representation for the Bethe vectors in the form of a trace formula.

  6 citations

• Notes on 8 Majorana Fermions

  David Tong, Carl Turner

  SciPost Phys. Lect. Notes 14 (2020) · published 30 March 2020 | Toggle abstract · pdf

  Eight Majorana fermions in $d=1+1$ dimensions enjoy a triality that permutes the representation of the $SO(8)$ global symmetry in which the fermions transform. This triality plays an important role in the quantization of the superstring, and in the analysis of interacting topological insulators and the associated phenomenon of symmetric mass generation. The purpose of these notes is to provide an introduction to the triality and its applications, with careful attention paid to various ${\bf Z}_2$ global and gauge symmetries and their coupling to background spin structures.

  6 citations

• Birdtracks for SU(N)

  Stefan Keppeler

  SciPost Phys. Lect. Notes 3 (2018) · published 27 September 2018 | Toggle abstract · pdf

  I gently introduce the diagrammatic birdtrack notation, first for vector algebra and then for permutations. After moving on to general tensors I review some recent results on Hermitian Young operators, gluon projectors, and multiplet bases for SU(N) colour space.

  6 citations

• Nested Algebraic Bethe Ansatz in integrable models: recent results

  Stanislav Pakuliak, Eric Ragoucy, Nikita Slavnov

  SciPost Phys. Lect. Notes 6 (2018) · published 29 October 2018 | Toggle abstract · pdf

  This short note summarizes the works done in collaboration between S. Belliard (CEA, Saclay), L. Frappat (LAPTh, Annecy), S. Pakuliak (JINR, Dubna), E. Ragoucy (LAPTh, Annecy), N. Slavnov (Steklov Math. Inst., Moscow) and more recently A. Hutsalyuk (Wuppertal / Moscow) and A. Liashyk (Kiev / Moscow). It presents the construction of Bethe vectors, their scalar products and the form factors of local operator for integrable models based on the (super)algebras $gl_n$, $gl_{m|p}$ or their quantum deformations. It corresponds to two talks given by E.R. and N.S. at \textsl{Correlation functions of quantum integrable systems and beyond}, in honor of Jean-Michel Maillet for his 60's (ENS Lyon, October 2017).

  6 citations