Journal clubs take place online on Tuesdays from 13:00 to 14:00.
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Spring semester 2021
Journal Club 20-07-2021
- Andrea Manenti (Uppsala U.), "Bootstrapping mixed correlators in N=4 Super Yang Mills"
I will discuss the numerical bootstrap of the system of correlators containing the half-BPS operators of dimension 2 and 3 in N=4 Super Yang Mills. After reviewing the solution of the N=4 Ward identitis and showing the crossing equations I will present a few plots and comment on the results. I will mostly focus on the regime of large N and compare with known AdS_5×S^5 supergravity predictions.
Journal Club 13-07-2021
- Alan Rios Fukelman (ICC, Barcelona U.), "The planar limit of N=2 superconformal field theories"
In this talk I will review some recent developments that allow us to completely solve a large family of Matrix models in the planar limit. Armed with these new techniques, we will characterize the full pertubative series of relevant observables of N=2 Lagrangian superconformal field theories on S^4 such as the planar free energy, the Wilson loop and n-point functions. Finally we will obtain the exact expression for the maximally transcendental part of the 2 and 3-point function of Chiral Primary Operators.
Journal Club 29-06-2021
- Jingxiang Wu (Perimeter), "Integrable Kondo line defect, 4D Chern Simons, and ODE/IM correspondence"
I will discuss the integrability and wall-crossing properties of Kondo line defects in 2d conformal field theories. It provides a large class of interesting defect RG flows interpolating between topological line defects. I will discuss its embeding in the four dimensional Chern Simons theory and how it can make the integrability properties of the Kondo lines manifest. As a surprise, I will discuss how ODE/IM correspondence might arise from 4d Chern Simons constructions and provide new examples of the ODE/IM correspondence.
Journal Club 15-06-2021
- Aleix Gimenez Grau, "Aspects of CFTs on Real Projective Space" Slides: slides.pdf
We present an analytic study of conformal field theories on the real projective space, focusing on the two-point functions of scalar operators. After reviewing basic facts about the structure of correlators on RPd, we study a simple holographic setup which captures the essential features of boundary correlators on RPd. In particular, we argue that the structure of the conformal block decomposition of the exchange Witten diagrams suggests a natural basis of analytic functionals, whose action on the conformal blocks turns the crossing equation into certain sum rules. We test this approach in the canonical example of φ4 theory in dimension d= 4− eps, extracting the CFT data to second order. This talk is a summary of 2009.03290.
Journal Club 8-06-2021
- Sylvain Lacroix, "Renormalisation of integrable sigma-models"
It is a long standing belief that classically integrable sigma-models define renormalisable QFTs. In this journal club, I will review some recent developments related to this question. For instance, I will discuss some checks of this conjecture in new types of examples and the emergence from these results of a common simple structure in the 1-loop RG flow of a very broad class of integrable sigma-models. Moreover, I will also give a brief summary of some recent works on the renormalisation of these models at higher-loops and the question of their quantum \alpha'-corrections. This review will cover elements from 1907.04737, 1910.00397, 1911.02027, 2010.07879, 2012.10451 and 2103.10513.
Journal Club 25-05-2021
- Ilija Buric, "Partial Waves in Defect CFTs from the Iwasawa decomposition"
I will introduce a new model for correlation functions in defect conformal field theories, based on the "induced picture" realisation of bulk fields. One arrives at such a realisation through the study of decompositions of the defect conformal group and in particular, its Iwasawa decomposition. In the second part, the model will be used to compute conformal partial waves for the correlation function of one defect and two scalar bulk fields, expressing them in terms of Appell's function F_4. This talk is based on the joint work with Volker Schomerus, [2012.12489].
Journal Club 18-05-2021
- Lorenzo Quintavalle, "An introduction to logarithmic CFTs in d>2" Slides Slides with live annotations
As their name suggest, Logarithmic Conformal Field Theories are CFTs whose correlators, starting from two-point functions, are not bound to behave as power laws, but can also contain logarithmic dependence on the coordinates of the fields. We will start by spelling out the crucial representation-theoretic differences that distinguishes log CFTs from regular CFTs, to then review the consequences that these have on n-point functions. We will then move to the construction of conformal partial waves and conformal blocks, and finally conclude with examples of log CFTs and their holographic duals. This discussion is mainly based on https://arxiv.org/abs/1605.03959 .
Journal Club 11-05-2021
- Xinyu Zhang, "Instantons in supersymmetric quantum mechanics (II): Beyond the BPS sector"
We describe supersymmetric quantum mechanics on a Kahler manifold with a holomorphic Killing vector. We show how the theory dramatically simplifies in the Frenkel-Losev-Nekrasov limit. The space of states in the Hilbert space can be determined, but the Hamiltonian is not diagonalizable. The correlation functions of all observables, not necessary in the BPS sector, may be computed explicitly in terms of integrals over finite-dimensional instanton moduli spaces.
E. Frenkel, A. Losev and N. Nekrasov, “Instantons Beyond Topological Theory. I,” arXiv:hep-th/0610149.
Journal Club 27-04-2021
- Xinyu Zhang, "Instantons in supersymmetric quantum mechanics (I): the BPS sector"
We consider the supersymmetric quantum mechanical model describing maps from one-dimensional space to target spaces that are Kahler manifolds. The theory possesses a particular limit, in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We study the spectrum and the correlation functions of all observables. An interesting feature is that the Hamiltonian is not always diagonalizable, but may have Jordan blocks, which leads to the appearance of logarithms in the correlation functions.
(1) E. Witten, “Supersymmetry And Morse Theory,” J. Diff. Geom. 17 (1982) 661-692.
(2) K. Hori, S. Katz, A. Klemm, R. Pandharipande, R. Thomas, C. Vafa, R. Vakil, E. Zaslow, "Mirror symmetry", 2003.
(3) E. Frenkel, A. Losev and N. Nekrasov, “Instantons Beyond Topological Theory. I,” arXiv:hep-th/0610149.
Fall semester 2020
Journal Club 03-09-2021
- Philine van Vliet, "Superconformal boundaries in 4-epsilon dimensions", https://arxiv.org/abs/2012.00018
Journal Club 02-23-2021
- Felix Tellander, "Anomaly-free Models and Fermion Masses", https://arxiv.org/abs/1902.08529
Journal Club 02-16-2021
- Philipp Tontsch, "Holographic Correlators at Finite Temperature", https://arxiv.org/pdf/2009.10062.pdf
Journal Club 02-09-2021
- Jeremy Mann, "Twisted Supergravity and Koszul Duality: A case study in AdS_3", https://arxiv.org/abs/2001.02177
Journal Club 02-02-2021
- Niklas Henke, “Stringy Canonical Forms", https://arxiv.org/abs/1912.08707
Journal Club 26-01-2021
- Nicole Righi, “Hybrid and Winding Inflation in Type IIB”
I will present my works on two different models of inflation, namely hybrid and winding inflation, which are both embedded in Type IIB string theory. For this purpose, I will start by reviewing the problems related to stabilising the moduli and getting dS vacua and explain how they can (partially) be solved. Then I will introduce the role of inflation in string theory. Finally, I will explain how hybrid and winding inflation fit in this landscape and highlight their different features.
Journal Club 19-01-2021
- QU day
- Apratim Kaviraj, "Supersymmetry in Random Field Ising Model"
The Ising Model coupled to a random field demonstrates a fixed point, characterized by a certain emergent supersymmetry (Parisi-Sourlas SUSY). This feature gives rise to the interesting property of dimensional reduction of critical exponents, which can be established from general CFT axioms. Numerical results verify this in d=5 but show a violation in d<=4. This is explained from an RG flow analysis that reveals SUSY-breaking deformations. I show how the RG flow is consistent with the standard replica description for Random Field models, and present a classification of the deforming operators. Finally I present a list of dangerous operators that can destabilize the SUSY fixed point, explaining numerical predictions.
Journal Club 08-12-2020
- Anne Spiering, Trinity College Dublin, "Integrability and chaos in N=4 SYM from the anomalous dimension spectrum"
The discovery of integrability in planar N=4 SYM theory led to considerable advances in the computation of the planar anomalous dimension spectrum. Less is known at the non-planar level where the theory is assumed to be non-integrable. I will show how statistical properties of numerical anomalous dimension spectra can give insight into the symmetries of the underlying model and that the N=4 SYM non-planar spectrum is well described by random matrix theory, indicating its quantum-chaotic nature. I will finish by showing analytical results for perturbative 1/N-corrections to non-planar anomalous dimensions.
Journal Club 01-12-2020
- Gleb Kotousov, "Density matrix for the 2D black hole sigma model from an integrable spin chain"
I report on the results of my recent work. The latter concerns a certain integrable critical spin chain whose universal behaviour, according to the 2011 paper of Ikhlef, Jacobsen and Saleur, is governed by the 2D Euclidean black hole Non-Linear Sigma Model (NLSM). The study of the spin chain yields a density matrix which reproduces the modular invariant partition function for the NLSM. I'll also clear up some confusion in the proposals of
Ikhlef, Jacobsen and Saleur as well as the results in the literature concerning the Euclidean black hole NLSM.
Journal Club 24-11-2020
- Aleix Gimenez-Grau, Information Paradox Part IV: slides.pdf
Journal Club 10-11-2020
- Ilija Buric, Information Paradox Part III: The entropy of Hawking radiation Journal_club__The_entropy_of_Hawking_radiation.pdf
Journal club 03-11-2020
- Maxime Trepanier, King's College, "Defect CFT techniques in the 6d N=(2,0) theory"
"Surface operators are among the most important observables of the 6d N=(2,0) theory, where they play a role analogous to the Wilson loops of gauge theories. In this talk I will introduce a description of these surface operators using the framework of defect CFT, which consists in inserting local operators into a surface operator defined over a plane. To illustrate the power of this description, I will first show how to relate the 2-point function of the displacement operator, an operator which describes the geometric deformation of the plane, to the expectation value of the stress tensor. This relation has an interesting consequence for the Weyl anomaly of surface operators. Secondly, I will discuss how to find some of the operators of the defect CFT using the defect operator expansion. This talk is based on arXiv:2009.10732."
Defect CFT (desy).pdf
Journal club 27-10-2020
- Paul Ryan, Trinity College, "Wave functions and correlators in high-rank integrable systems via separation of variables"
The Heisenberg XXX spin chain is an important model appearing in many different areas of theoretical physics. Remarkably, the same set of functional equations which describe the energy spectrum of the XXX model also determine the spectrum of anomalous dimensions in planar N=4 SYM, the only difference being in the analytic properties of the solutions - the Q functions. Recently it has become apparent that certain correlators in N=4 SYM have very simple expressions in terms of Q functions closely resembling spin chain correlators expressed using Sklyanin’s separation of variables (SoV). Motivated by this, in this talk I will review the recent progress towards extending Sklyanin’s construction beyond the simplest SU(2) spin chains to the higher rank SU(n) and SL(n) cases needed for N=4 SYM. I will explain how to construct highly compact expressions for the wave functions in separated variables and a remarkable link between their structure and quantum group representation theory. I will also discuss how to easily extract the SoV measure and compute various observables in the SoV representation using one of the key equations of quantum integrable systems - the Baxter equation.
Journal club 20-10-2020
- Philine van Vliet, Information Paradox Part II: Entropy in gravitational systems - Journal_Club_Information_Paradox 4.pdf
Journal club 13-10-2020
- Lorenzo Quintavalle, Information Paradox Part I: A Black Holes refresher - Slides with pen input
Spring semester 2020
Journal club 14-07-2020
- Alexander T. Kristensson (Niels Bohr Institute), "Thermodynamics of N=4 SYM at finite N"
Abstract: The maximally Supersymmetric Yang Mills (SYM) theory is an SU(N) gauge theory that occurs many places in theoretical high-energy physics -- most notably in the famous AdS/CFT duality. On a compact space RxS^3, N=4 SYM theory exhibits a phase transition similar to the confinement/deconfinement phase transition of Quantum Chromo Dynamics (QCD). On the gravity side of the duality, this phase transition is believed to be dual to the Hawking-Page phase transition between a gas of gravitons and a black hole. In the last twenty years, there has been much progress in understanding the planar limit of the theory, where one takes N -> infinity. This progress has shown strong hints of the theory being integrable. The main focus of our research is to push this understanding beyond the planar limit to finite values of N. In this talk I will present our ongoing research on the thermodynamics of N=4 SYM at finite N. In particular, I will discuss various sub-sectors of the full algebra and show how to compute the exact partition functions for small values of N. In the su(2) sector, I will present the claim that the Hagedorn behaviour at N -> infinity is replaced by a phase transition of Lee-Yang type at finite N, characterized by a condensation of zeros in the complex fugacity plane.
Journal club 07-07-2020
- Matthias Volk (Niels Bohr Institute), "Geometry of Feynman Integrals in Twistor Space"
Abstract: To compute scattering amplitudes in quantum field theory perturbatively, one has to evaluate integrals over loop momentum space known as Feynman integrals. In simpler cases (e.g. for low loop order) the integrals can often be expressed in terms of so-called multiple polylogarithms. However, explicit computations have shown that this fails for more complicated amplitudes and that new functions will be needed. One approach to a better understanding of these functions has been to analyze the geometry associated to a Feynman integral and interesting geometric objects such as elliptic curves, K3 surfaces and Calabi-Yau manifolds have been found. In this talk, we construct and analyze the geometry of a certain class of Feynman integrals known as traintracks that occur for example in N = 4 SYM or \phi^4 theory. In contrast to previous work, we describe the geometry directly in momentum twistor space. At two loops, we obtain an elliptic curve as the intersection of two quadrics. At three loops, we find a K3 surface as a branched surface over two elliptic curves in P^1 x P^1. Based on arXiv:2005.08771 together with C. Vergu.
Journal club 19-05-2020
- Junchen Rong, "Bootstrap and deconfined phase transition""
Abstract: I will discuss how using conformal bootstrap to study the deconfined quantum
critical point (DQCP), which describes the phase transition between anti-ferromagnetic Neel phase and the valence bond solid state phase. The continuum limit of the model is described by the three dimensional Abelian Higgs model.
Journal club 21-04-2020
- Niklas Henke, How tropical are seven-, eight- and nine-particle scattering amplitudes?
Using the symbol bootstrap, loop amplitudes of planar N=4 SYM theory can be obtained from their alphabet, the list of their singularities, whose letters coincide with the variables (rational functions) of certain cluster algebras. However, at eight and more particles these cluster algebras become infinite, whereas it is believed that the amplitudes only have finitely many distinct singularities. First discussing the application of cluster algebras to the seven-particle (N)MHV amplitude, I will show how the recently introduced mathematics of tropical geometry gives rise to a selection rule and present the thus obtained finite alphabets for eight and nine particles. Furthermore, I will discuss how infinite mutation sequences in cluster algebras also give rise to the algebraic singularities at eight particles.
Journal club 07-04-2020
- Fabrizio Neri: Physics and geometry of knots-quivers correspondence
Journal club 09-03-2020
- Matteo Parisi, Amplituhedra: Scattering Amplitudes from Geometry
The Amplituhedra A(n,k,m) are generalisations of polytopes introduced as a geometric construction encoding scattering amplitudes in planar N=4 supersymmetric Yang-Mills theory (SYM). These are extracted from a differential form, the canonical form of the Amplituhedron, which emerges from a purely geometric definition.
Following my recent works, I will explain how the Jeffrey-Kirwan residue, a powerful concept in symplectic and algebraic geometry, computes the canonical form for whole families of objects, namely for Amplituhedra of type A(n,1,m), which are cyclic polytopes and for their conjugates A(n,n-m-1,m) for even m, which are not polytopes.
This method connects to the rich combinatorial structure of triangulations of Amplituhedra, captured by what we refer to as ‘Secondary Geometry’. For polygons, this is the `Associahedron', explored by Stasheff in the sixties; for polytopes, it is the `secondary polytope' constructed by the Gelfand's school in the nineties. Whereas, for Amplituhedra, we are the first to initiate the studies of what we called the ‘Secondary Amplituhedra’. The latter encodes all representations of scattering amplitudes, many not obtainable with any physical method, together with their algebraic relations produced by global residue theorems.
Finally, I will briefly illustrate some of the recent geometric directions in my work on the Amplituhedron in momentum space and new exciting developments connecting the (secondary geometry of) m=2 amplituhedron with the positive tropical Grassmannian. This object has been appearing in dozens of papers in the physics community in the last year, both in bootstrapping loop amplitudes in planar N=4 SYM and in computing (a generalisation of) biadjoint scalar amplitudes.
Journal club 03-03-2020
- Lorenzo Quintavalle, Celestial Sphere Amplitudes
Over the recent years there has been many developments in the study of four-dimensional Quantum Field Theories through a CFT description on the Celestial sphere. The aim of this Journal club is to review the basic ideas behind Celestial sphere amplitudes. We will start from the discussion of asymptotic symmetries in electrodynamics, to then describe soft theorems taking the case of Scalar QED as an example. We will see how this suggests a 2D CFT interpretation, and therefore introduce the concept of Celestial sphere amplitudes.
Journal club 25-02-2020 (TBA)
Journal club 18-02-2020
- Madalena Lemos (CERN), Surface defects in 4d superconformal theories and chiral algebras (This seminar will take place in Building 3 Seminar room BAH 2)
We study symmetry constraints on BPS surface defects in four-dimensional superconformal field theories, showing how supersymmetry imposes relations on anomaly coefficients. Turning to dynamics, we analyze a protected subsector of N=(2,2) surface defects that is captured by a two-dimensional chiral algebra. We discuss how to compute observables of interacting defects from the chiral algebra, including the aforementioned anomaly coefficients.
Journal club 11-02-2020 (Integrability school)
Journal club 04-02-2020
- Taro Kimura (Bourgogne U.), Yet another affinization of geometric Langlands correspondence
One of the implications of the geometric Langlands correspondence is the isomorphism between conformal blocks of W-algebra and affine Lie algebra. This correspondence has a natural q-deformation, providing a relation between q-deformation of W-algebra and quantum affine algebra. In this talk, I'll discuss yet another affinization of this correspondence between doubly affine W-algebra and quantum toroidal algebra, based on the formalism of quiver W-algebra. I'll also mention its possible physical interpretation in gauge theory with the surface defects.
Journal club 28-01-2020
- Federico Carta (DESY), Supersymmetry Enhancement
Journal club 21-01-2020
- Lorenzo Quintavalle (DESY), Celestial sphere amplitudes
Journal club 10-12-2019
- Fabrizio del Monte (SISSA), Class S theories and isomonodromic deformations on the torus.
In the last few years there have been many new results connecting (linear quiver) N=2 class S theories, and the topological strings that engineeer them, to the theory of isomonodromic deformations on the sphere and their q-deformations. These gauge theories are constructed by compactifying the 6d N=(0,2) SCFT on a punctured Riemann Sphere, whose moduli, which are the marginal deformations of the gauge theory, are the times of the isomonodromic flows. The aim of this talk is to show how this connection can be extended beyond the case of genus zero, for more general (asymptotically superconformal) class S theories. We will discuss in detail the case of circular quiver gauge theories, that are obtained from the N=(0,2) SCFT on punctured tori, and see how the genus one case displays new qualitative features that are absent on the sphere, due to the possibility of various inequivalent vector bundles, and how this actually provides new interesting relations satisfied by the gauge theory partition function.
Journal club 03-12-2019
Jack Foster (Southampton University): Cluster Adjacency, Tropical Geometry, and Scattering Amplitudes
Abstract: I will discuss two new areas of interest in scattering amplitudes: cluster adjacency and tropical geometry. The former describes how the analytic structure of planar amplitudes in N=4 Super Yang-Mills is controlled by mathematical objects called cluster algebras. The latter has been used to calculate amplitudes in the biadjoint phi^3 theory, which I will discuss briefly, but it also has implications for cluster adjacency.
Journal club 26-11-2019
- Francesco Galvano (Torino): Emitted radiation and geometry (This seminar will take place in Building 3 Seminar room BAH 2)
Abstract: We discuss the computation of the radiated energy by an accelerated heavy particle. This quantity is captured by the one-point function of the stress energy tensor in presence of a Wilson line. In a N=2 superconformal theory we prove that this observable is exactly related to a small geometric deformation of the background geometry. In a four dimensional case, supersymmetric localization allows to express the emitted energy in terms of a matrix model on a squashed sphere.
Journal club 19-11-2019
- No seminar scheduled.
Journal club 12-11-2019
- Zhengwen Liu: Scattering Equations and Multi-Regge Kinematics
Abstract: The scattering equations, a system of algebraic equations connecting the space of kinematic invariants and the moduli space of punctured Riemann spheres, provide a novel way to construct scattering amplitudes. In this framework, the tree-level S-matrix in many quantum field theories can be reformulated as a multiple integral that is entirely localized on the zeroes of the scattering equations. After presenting a very minimal introduction to the scattering equations, I will discuss the asymptotic behavior of the scattering equations in the so-called Multi-Regge kinematic regime and the corresponding factorizations of amplitudes in gauge theory and gravity.
Multi-Regge kinematics and the scattering equations
Gravitational Scattering in the High-Energy Limit
Journal club 05-11-2019
- Yuta Sekiguchi (U. Bern, AEC), O(d,d) transformations preserve classical integrability.
Abstract: We studied the classical integrability of O(d,d) transformations including not only O(d,d;Z) duality but also global O(d,d;R) deformation. The latter is known in the traditional literature to generate so-called current-current (JJbar) deformations of 2D CFTs. In this talk, I first plan to give brief reviews Yang-Baxter deformations of string backgrounds as well as the doubled sigma model. Then I will present how to construct the Lax pairs in the O(d,d) deformed WZNW models via O(d,d) map through very easy examples. The resulting Lax connections are in general non-local because they depend on the winding modes. Finally I will briefly comment on open questions under consideration in relation to the recent irrelevant integrable deformation. This talk is based on the recent work [1907.03759] with Domenico Orlando, Susanne Reffert and Kentaroh Yoshida.
Journal club 29-10-2019
Till Bargheer: Exact Four-Point Functions: Genus Expansion and Strong Coupling (This seminar will take place in Building 3 Seminar room BAH 2)
Using integrability, correlation functions of local operators in planar N=4 super Yang-Mills theory can be computed by reconstructing the dual worldsheet from a set of "hexagon" patches via "gluing" (performing complete state sums over mirror Bethe states). After reviewing this general procedure, I will explain how it can be used to compute a certain class of four-point correlators as an exact function of the coupling at any order in the 1/Nc genus expansion, and how the resulting series can be re-summed (via a suitable matrix model) to recover the full Nc dependence. If time permits, I will also comment on the strong-coupling limit of these correlators.
Journal club 22-10-2019
Gleb Kotousov: "Reflection operators in integrable QFT".
Journal club 15-10-2019
Sylvain Lacroix, Gauge Theory And Integrability, III (focusing on the second part about "disorder defects").
Journal club 08-10-2019
Alessandro Pini, Extremal Correlators and Random Matrix Theory.