I will review recent progress in our understanding of light-ray operators in abstract CFTs. Light-ray operators first appeared in QCD and were later studied in N=4 Super Yang-Mills theory and holography by Hofman and Maldacena. More recently, they attracted new interest due to an important role played by the averaged null energy condition (ANEC) operator in various contexts. However, it is only during the last few years it became possible to start developing a more general theory of light-ray operators. I will explain a nonperturbative, convergent operator product expansion (OPE) for null-integrated operators on the same null plane in a CFT. I will discuss its application to energy-energy correlators in N=4 Super Yang-Mills theory.

Certain quantum field theories possess generalized global symmetries; just as ordinary global symmetries enforce the conversation of particle number, generalized global symmetries enforce the conservation of extended objects, such as strings. I will review this symmetry principle and argue that it governs the long-distance physics of conventional 4d electromagnetism, where the strings in question are magnetic field lines. I will then apply it to construct a novel effective theory for the description of strongly magnetized plasmas. One potential application of this new effective theory is to astrophysical pulsars, which are thought to be surrounded by strong magnetic fields as well as a high density of charged particles; the resulting zero temperature system is highly nonlinear. At leading order in derivatives our new effective theory agrees with the standard treatment in terms of ``force-free electrodynamics''. The inclusion of higher derivative terms however generically results in new and potentially observationally relevant effects, such as electric fields that accelerate charges to high energies along magnetic field lines. If time permits I will describe some recent work towards describing such energetic charges in terms of bosonization along magnetic field lines.

In this talk, I will describe new mathematical structures in the low-energy expansion of one-loop string amplitudes. The insertion of external states on the open- and closed-string worldsheets requires integration over punctures on a cylinder boundary and a torus, respectively. Suitable bases of such integrals will be shown to obey simple first-order differential equations in the modular parameter of the surface. These differential equations will be exploited to perform the integrals order by order in the inverse string tension, similar to modern strategies for dimensionally regulated Feynman integrals. Our method manifests the appearance of iterated integrals over holomorphic Eisenstein series in the low-energy expansion. Moreover, infinite families of Laplace equations can be generated for the modular forms in closed-string low-energy expansions.

I discuss the dependence of supersymmetric partition functions on continuous parameters for the flavour symmetry group. In the presence of the 't Hooft anomalies, the supersymmetric Ward identities imply that the partition function computed in the Wess-Zumino gauge has a non-holomorphic dependence on the flavour parameters. I show this explicitly for a large class of 4d N=1 partition functions on half-BPS four manifolds. I propose a new expression for the partition functions on M3 x S1, which differs from earlier holomorphic results by a non-holomorphic Casimir pre-factor.

Costello, Witten, and Yamazaki have recently proposed a new description of quantum integrable systems using a variant of Chern-Simons theory defined on the product of a two dimensional real manifold and a Riemann surface. I'll review their work, and show how to extend it to describe integrable systems with boundary. In particular I'll discuss how it can be used to generate solutions of the boundary Yang-Baxter equation, and how to realise twisted Yangians in the theory. If there is enough time I will explore the result of applying this construction when the Riemann surface is chosen to be a torus.

A large class of 4d SCFTs can be engineered by wrapping a stack of M5-branes on a compact space, possibly with defects. ‘t Hooft anomalies are crucial observables for such theories, which often do not admit any known Lagrangian description. Building on the seminal work of Freed, Harvey, Minasian, Moore, we develop systematic tools for extracting the ‘t Hooft anomalies of a geometrically engineered 4d theory using anomaly inflow from the M-theory bulk. We exemplify our tools by studying a class of setups with M5-branes probing a C^2/Z_2 singularity. We argue that these setups define 4d SCFTs which are dual to a class of AdS_5 solutions­—first discussed by Gauntlett, Martelli, Sparks, Waldram—whose field theory interpretation has been a longstanding puzzle.

This is a two day meeting, please see the website for details. www.tinyurl.com/kcldef19 Registration is required as King's has a new policy on attendance. Supported by the LMS and the IoP

AdS/CFT provides a consistent non-perturbative definition of quantum gravity in asymptotically AdS space. Black holes should correspond to ensembles of states in the boundary field theory. By analyzing the superconformal index of 4d N=4 SU(N) Super-Yang-Mills, with the help of a new Bethe Ansatz type formula, we are able to exactly reproduce the Bekenstein-Hawking entropy of BPS black holes in AdS5 x S5. The large N limit exhibits many competing contributions and Stokes phenomena, hinting at new physics.

In flat space, four point scattering amplitudes at weak coupling can be fully determined from Lorentz symmetry, unitarity and causality. The resulting scattering amplitude depends on model details only through coupling constants and the particle content of the theory. I will show how the analogous story works in the case of inflationary fluctuations. We found explicit expressions for inflationary three and four-point functions, whose shapes depend on the field content of the theory, and do not depend on the specific inflationary model, as long as the fluctuations minimally break de Sitter symmetry. This ``cosmological bootstrap” is a first step towards classifying all possible shapes of primordial non-gaussianity, which can be searched for in experimental data.

A four-dimensional abelian gauge theory can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFTs) parametrized by the gauge coupling \tau and by the choice of the CFT in the decoupling limit. Upon performing an Electric-Magnetic duality in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action. In particular the cusps on the real \tau axis correspond to the 3d gauging of the original CFT. We study general properties of this family of BCFTs. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. Finally, upon assuming particle-vortex duality (and its fermionic version), we show how to turn this machinery into a powerful computational tool to study 3d gauge theories.

We show that supersymmetry is anomalous in N = 1 superconformal quantum field theories (SCFTs) with an anomalous R-symmetry. This anomaly was originally found in holographic theories: here we show that this anomaly is present in general and demonstrate it for the massless superconformal Wess-Zumino model via a one loop computation of four-point functions of two supercurrents with either R-currents. In fact, the Wess-Zumino consistency conditions together with the standard R-symmetry anomaly imply the existence of the anomaly. We outline the implications of this anomaly.

KCL TPPC Seminar

KCL TPPC Seminar Abstract: Black hole (BH) mergers can be viewed as cosmological “scattering experiments” resulting in an excited BH, which then decays to its ground state by emitting gravitational waves (GW). I will present general arguments, based on fundamental physics principles, as to why we should expect additional quantum ringdown modes to those predicted by general relativity. Then, I will discuss the spectrum of the predicted ringdown modes, the resulting emitted GW and the prospects for their detection in LIGO/VIRGO.

TBA

I will first review the Batalin-Vilkovisky formalism and its mathematical foundations with an emphasis on higher algebraic structures and classical field theories. I will then move on and discuss recent developments in formulating higher gauge theory with Lie quasi-groupoids as gauge structure. Finally, I will explain how all these ideas can be combined with those of twistor theory to formulate maximally superconformal gauge theories in four and six dimensions by means of quasi-isomorphisms.

I will talk about the formalism of supersymmetric localization in supergravity using the deformed BRST algebra defined in the presence of a supersymmetric background. The gravitational functional integral localizes onto the cohomology of a global supercharge Q_eq, obeying (Q_eq)²=H, where H is a global symmetry of the background. This construction naturally produces a twisted version of supergravity whenever supersymmetry can be realized off-shell. I will present the details of the twisted graviton multiplet and ghost fields for the superconformal formulation of four-dimensional N=2 supergravity. As an application of our formalism, we systematize the computation of the exact quantum entropy of supersymmetric black holes. In particular, we compute the one-loop determinant of the Qeq deformation operator for the off-shell fluctuations of the Weyl multiplet around the AdS₂×S² saddle.

A four-dimensional abelian gauge theory can be coupled to a 3d CFT with a U(1) symmetry living on a boundary. This coupling gives rise to a continuous family of boundary conformal field theories (BCFTs) parametrized by the gauge coupling Ï„ and by the choice of the CFT in the decoupling limit. Upon performing an Electric-Magnetic duality in the bulk and going to the decoupling limit in the new frame, one finds a different 3d CFT on the boundary, related to the original one by Witten's SL(2, Z) action. In particular the cusps on the real Ï„ axis correspond to the 3d gauging of the original CFT. We study general properties of this family of BCFTs. We show how to express bulk one and two-point functions, and the hemisphere free-energy, in terms of the two-point functions of the boundary electric and magnetic currents. Finally, upon assuming particle-vortex duality (and its fermionic version), we show how to turn this machinery into a powerful computational tool to study 3d gauge theories.

In the first part of my talk I will give a brief introduction to the main features of the Entaglement Entropy of a bipartite system in Integrable Quantum Field Theories and Conformal Field Theories. Secondly I will discuss the results my collaborators and I obtained in our two papers. In particular, I will consider the Entaglement Entropy of a single connected region of a finite bipartite system in excited states described by one-dimensional massive free theories with finite numbers of particles. I will show that in the limit of large volume and large length of the region the excess of entanglement due to the presence of the particles with respect to the ground state takes a simple form and admits a "q-bit interpretation".

This will be presenting mainly some of my recent work, and also aspects of recent work of Herbert Spohn, both developed in parallel. The classical Toda system is a one-dimensional integrable many-body system, which can be seen either as a gas of particles or as a chain of degrees of freedom. Herbert has shown how the generalised Gibbs ensembles of the Toda chain can be obtained from a certain limit of the beta-ensemble in random matrix theory. Analysing and connecting the gas and chain viewpoints, I have obtained both the generalised Gibbs ensembles and generalised hydrodynamics from a quasiparticle scattering description. Thus we make a connection between quasiparticle scattering and random matrix theory.

This talk will explore topological invariants of susy gauge theories, with some emphasis on index-like quantities and the notion of holonomy saddles. We start with 1d refined Witten index computations where the twisted partition functions typically show rational, rather than integral, behavior. We will explain how this oddity is a blessing in disguise and propose a universal tool for extracting the truely enumerative Witten indices. In part, this finally put to the rest a two-decade-old bound state problems which had originated from the M-theory hypothesis. Along the way, we resolve an old and critical conflict between Kac+Smilga and Staudacher/Pestun, circa 1999~2002, whereby the notion of holonomy saddles emerges and plays a crucial role. More importantly, the holonomy saddle prove to be universal features of supersymmetric gauge theories when the spacetime include a small circle. We explore them further for d=4, N=1 theories, with much ramifications on recent claims on Cardy exponents of their partition functions.