The main purpose of the present talk is to lay the foundations of generalizing the AdS/CFT (holography) idea beyond the conformal setting, where it is very natural. The main tool is to find suitable realizations of the bulk and boundary via group theory. We use all ten families of classical real semisimple Lie groups G and Lie algebras g. For this are used several group and algebra decompositions: the global Iwasawa decomposition and the local Bruhat and Sekiguchi decomposititions, which we introduce first on easy examples. The same analysis is applied to the exceptional real semisimple Lie algebras. We present the boundary-to-bulk operators first in the Euclidean conformal setting and then outline the various generalizations.

Note unusual time. part of London TQFT Journal Club (please register at https://london-tqft.co.uk);

Since the existence of interacting SCFTs in six dimensions was first inferred by string theory, many have sought a Lagrangian construction of such models. With this goal in mind, in this talk I will introduce some curious supersymmetric Lagrangian gauge theories in five dimensions. These models exhibit an Omega-deformed non-relativistic conformal symmetry, and have a single, discrete coupling. Crucially, I will argue that these models in fact capture the dynamics of six-dimensional (2,0) and (1,0) SCFTs, through a solitonic enhancement mechanism analogous to that of the ABJM model. I will finally speculate on the utility of the models, including through the fashionable paradigms of integrability and localisation.

Quantum mechanical theories describing large N by N matrices of oscillators can lead to an emergent space as N -> infinity. In the most fully fledged version, the emergent space is dynamical and gravitating. However, there are also simpler, lower dimensional versions of this phenomenon. One of the simplest occurs in the so-called quantum Hall matrix model, in which a 2 dimensional space emerges and supports Chern-Simons dynamics. I will describe how this solvable model leads to insights about the emergence of space from matrices. In particular, I will describe how the emergent spatial locality is reflected in the entanglement structure of the ground state of theory.

I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). I will first review the definitions and some properties of defect CFTs and defect RG flows, including a recent result on the monotonicity of the defect RG flow. I will then discuss in detail two examples relevant for three-dimensional critical systems: magnetic field defects, which arise from a localized external field in a lattice system, and spin defects, that describe doping impurities in magnets. I will show in particular that impurities with large spin are “effectively’’ equivalent to a magnetic field defect. I will close with a comment on Wilson lines in conformal gauge theories; part of London TQFT Journal Club (please register at https://london-tqft.co.uk);

Topological phases can be divided into two classes corresponding to whether the microscopic degrees of freedom supporting the phase are purely bosonic (e.g., spins or qubits) or whether they include fermions (e.g., electrons). Imposing a symmetry on a topological phase enriches the classification by restricting and possibly fracturing the phase space. Fermionic topological phases additionally include an underlying fermionic particle of the system, the physical fermion. This talk will present recent results on the algebraic structure and classification of fermionic topological phases with on-site unitary symmetry using G-crossed braided tensor categories. I will emphasize the new obstructions which appear, contrast them with their bosonic counterparts, and provide a complete characterization of all symmetric unobstructed invertible fermionic phases. [for zoom link please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]

QCD undergoes a transition from the confined phase (hadron gas) to a deconfined quark-gluon plasma at a temperature of about 155 MeV. This phenomenon can be investigated in relativistic heavy-ion experiments and studied theoretically, using e.g. simulations of QCD discretised on a space-time lattice. In this talk, I will review some aspects of QCD at nonzero temperature, with an emphasis on results obtained by our lattice QCD collaboration. Very recently, machine learning has been introduced as a new tool to study lattice field theory. In the final part, I will present some results of applications of machine learning to phase transitions in statistical field theory.

In this talk I will review the basic ingredients which allows one to formulate 10D super-Yang-Mills on pure spinor superspace. The respective pure spinor master action in the gauge b_{0}V = QΞ, will then be used to show that tree-level scattering amplitudes calculated via perturbiner methods, match those obtained from pure spinor CFT techniques. I will also discuss how to compute pure spinor kinematic numerators through the use of standard Feynman rules, and show these are described by compact expressions involving the b-ghost operator. Remarkably, it will be shown how color-kinematics duality immediately emerges in this pure spinor framework after imposing the Siegel gauge condition b_{0}V = 0. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]

Email m.godazgar@qmul.ac.uk for zoom link. Abstract: I will present the derivation of the antipodal matching relations used to demonstrate the equivalence between soft graviton theorems and BMS charge conservation across spatial infinity. To this end I will provide a precise map between Bondi data at null infinity and Beig-Schmidt data at spatial infinity in a context appropriate to the gravitational scattering problem and celestial holography. I will also demonstrate that, among various proposals of BMS charges at null infinity found in the literature, only a subset match the conserved charges at spatial infinity and are therefore preferred from that perspective.

Ensemble averaging in quantum field theory is a well-defined procedure which is also of much recent interest in the context of the AdS/CFT correspondence. In this talk we present a stringy realization of quantum field theory ensembles in D \leq 4 spacetime dimensions. This provides a UV completion of a recent proposal of Marolf and Maxfield that there is a high-dimensional Hilbert space for baby universes, but one that is compatible with the proposed Swampland constraints of McNamara and Vafa. We identify two ways in which our construction breaks down, one of which is sensitive to short distance effects, and one which is an entropic effect for objects with a large number of microstates. The construction thus provides an explicit set of counterexamples to the claim that holography can be fully decoupled from top down considerations. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]

Please email m.godazgar@qmul.ac.uk for zoom link. Abstract: To date, gravitational waves from tens of merging stellar-mass black holes have been observed. These observations provide us with a unique opportunity to probe the fundamental properties of astrophysical black holes. The precise measurement of the masses and spins of black holes is particularly crucial to determine the evolutionary pathways of these binaries. This requires, however, highly accurate theoretical models of the emitted gravitational-wave signal. The signal complexity grows with the number of degrees of freedom and the accurate modelling general-relativistic spin-induced precession has proven to be challenging. In this talk, I will first discuss the current approaches to modelling waveforms from precessing black hole binaries. I will then demonstrate the limitations and how they translate into systematic measurement uncertainties.

M-theory on spaces with codimension 11-d singularities gives rise to a rich class of d-dimensional field theories. I will discuss how (d+1)-dimensional topological field theories (TFTs) encode the higher symmetries and anomalies of these d-dimensional theories, and how these TFTs can be extracted from the geometry of the singular space. I will illustrate the discussion by analysing some simple examples explicitly. [for zoom link please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]

(Email m.godazgar@qmul.ac.uk for zoom link) Abstract: The exterior dynamics of black holes has played a major role in holographic duality, describing the approach to thermal equilibrium of strongly coupled media. The interior dynamics of black holes in a holographic setting has, in contrast, been largely unexplored. I will describe recent work investigating the classical interior dynamics of various holographic black holes. I will discuss the nature of the singularity, the absence of Cauchy horizons and a new kind of chaotic behavior that emerges in the presence of charged scalar fields.

I will present a way to promote the anomalous axial U(1) in 4d QED to an exact symmetry, with the price of losing its invertibility. I will then discuss some applications of this non-invertible U(1) symmetry. In particular, I will show how to couple this non-invertible symmetry to a gauge field. By taking this gauge field to be dynamical, we get a new type of gauge theory with unconventional interactions and constraints. By taking this gauge field to be background, we can study 't-Hooft anomalies of the non-invertible symmetry.

We demonstrate that the dynamics of neural networks trained with gradient descent and the dynamics of scalar fields in a flat, vacuum energy dominated Universe are structurally profoundly related. This duality provides the framework for synergies between these systems, to understand and explain neural network dynamics and new ways of simulating and describing early Universe models. Working in the continuous-time limit of neural networks, we analytically match the dynamics of the mean background and the dynamics of small perturbations around the mean field, highlighting potential differences in separate limits. We perform empirical tests of this analytic description and quantitatively show the dependence of the effective field theory parameters on hyperparameters of the neural network. As a result of this duality, the cosmological constant is matched inversely to the learning rate in the gradient descent update. [for zoom link, please contact jung-wook(dot)kim(at)qmul(dot)ac(dot)uk]

After a brief introduction to some of the impact which integrable methods and the Bethe ansatz have had on the study of the AdS/CFT correspondence in string theory, we will focus on the axiomatic approach to S-matrix theory in 1+1 dimensions. We will highlight the issues that arise when the particles are massless, and how this is in fact connected to Zamolodchikov's way of describing two-dimensional conformal field theories by means of integrability techniques. We will then mention how the axiomatic approach extends to form-factors, which are the gate to access the n-point functions of the theory. If time permits, we will briefly depict how this finds a contemporary application in the area of the AdS_3/CFT_2 correspondence; part of London TQFT Journal Club (please register at https://london-tqft.vercel.app);

Celestial conformal field theory (CCFT) is a conjectured theory living on the celestial sphere of the asymptotic boundary of Minkowski. In analogy to the usual AdS/CFT dictionary, CCFTs would be dual to gravitational theories in the bulk, with bulk scattering amplitudes being dual to correlation functions on the celestial sphere. OPE coefficients are basic building blocks of CFTs which should also have an analogue in CCFTs. It has been shown that CCFT OPEs can be extracted from amplitudes with appropriate wavefunctions for external states, but there's still no direct computation using the CCFT itself since we lack a first principles definition. I will talk about recent work I have done computing these OPEs directly by using twistor strings, circumventing the issue of the target space theory. I will show how the worldsheet CFT of the twistor string gives a realization of the algebra of operators of the CCFT, reproducing the known leading OPE terms, as well as how it can be used to compute further regular terms in the OPE, beyond what is currently known. As a bonus, the worldsheet OPE also organizes the spectrum naturally in terms of the infinite dimensional symmetry algebras of CCFTs. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]

The Standard Model extended with non-renormalisable operators is increasingly becoming THE theory of the elementary particles and their interactions. A large part of current and future research is devoted to test this theory to the best possible accuracy. To this aim, though, substantial knowledge on its quantum structure is needed, both for theoretical reasons (constraints on the basis of relativity+quantum mechanics) and experimental ones (combine data gathered at very different energies). In this talk I will discuss the progress made over the years in this respect, with particular emphasis on major obstacles.

I will describe the space of effective field theories consistent with local, unitary, and analytic UV completions, which was termed the EFThedron. Recently the EFThedron was generalized to a non-projective geometry, which can be used to implement new constraints on spectral functions. These include the unitarity bound, which leads to analytic bounds on single Wilson coefficients (instead of bounds only on ratios), or the low spin dominance condition, which drastically reduces the landscape of allowed theories. [for zoom link please contact h(dot)jiang(at)qmul(dot)ac(dot)uk]