Academic Year 2022/2023

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

I will review some recent progress in the context of geometric engineering limits of M-theory and their interplay with higher symmetries of (supersymmetric) field theories.

I will show that self-dual gravity in Euclidean four-dimensional Anti-de Sitter space (AdS4​) can be described by a scalar field with a cubic interaction written in terms of a deformed Poisson bracket, providing a remarkably simple generalisation of the Plebanski action for self-dual gravity in flat space. This implies a novel symmetry algebra in self-dual gravity, notably an AdS4​ version of the so-called kinematic algebra. This provides a concrete starting point for defining the double copy for Einstein gravity in AdS4​ by expanding around the self-dual sector. Moreover, I will show that the new kinematic Lie algebra can be lifted to a deformed version of the w1+∞​ algebra, which plays a prominent role in celestial holography.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

In recent years various unifying frameworks for understanding 2d integrable field theories have emerged. In this talk I will review the approach based on 4d Chern-Simons theory, due to Costello and Yamazaki, and describe recent progress towards extracting general 2d integrable field theories from 4d Chern-Simons theory.

In this talk we will study solutions of the cylindrical KdV equation built up by using the Janossy densities of the thinned shifted and dilated Airy determinantal point process. We will see how they can be interpreted as Darboux transformations of known solutions obtained in terms of the Fredholm determinant of the so called finite temperature Airy kernel. Finally we will describe their asymptotic behavior in different regimes. This is based on a joint work with T. Claeys, G. Glesner, G. Ruzza available at ArXiv2303.09848.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

In this talk I will introduce some basic ideas about entanglement measures in many-body quantum systems and I will present one of the leading approaches to computing such measures in 1D quantum field theory. This approach is based on relating entanglement measures to correlations functions of a special class of fields called branch point twist fields. Once this connection has been made, the problem of computing entanglement measures is reduced to computing correlation functions, which is generally technically difficult. I will explain how these correlation functions become especially simple for certain types of excited states of quantum field theory and how this simplicity allows us to compute many different measures very explicitly, including a measure that has attracted a lot of interest recently: the symmetry resolved entanglement entropy. My talk contains input from work I have done with many people over the years including Pasquale Calabrese, Luca Capizzi, John L. Cardy, Cecilia De Fazio, Benjamin Doyon, David X. Horváth, Michele Mazzoni, Lucía Santamaría-Sanz and István Szécsény.

Supersymmetric theories with 8 supercharges in dimensions 3 through 6 have a large moduli space of vacua, and the Higgs branches are one of the most significant parts of this space. These (singular) hyper-Kahler spaces can be characterised by a combinatorial object known as the magnetic quiver. By using this technique, we can fully encode the Higgs branch geometry for both the low energy effective description and the strongly coupled conformal fixed point. A simple algorithm on the magnetic quiver allows us to access the stratification of the Higgs branch, which physically corresponds to the generalised Higgs mechanism. In this talk, I will discuss this construction in the context of 5d and 6d theories.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

High Tc cuprate strange metals are noted for a DC-resistivity that scales linearly with T from the onset of superconductivity to the crystal melting temperature, indicative of a Planckian dissipation life time τℏ≃ℏ/(kBT). At the same time, the optical conductivity ceases to be of the Drude form at high temperatures, suggesting a change in dynamics that surprisingly leaves the T-linear DC-resistivity unaffected. We use the AdS/CFT correspondence that describes strongly coupled, densely entangled states of matter to study the DC and optical conductivities of the local quantum critical Gubser-Rocha holographic strange metal in 2+1D in the presence of a lattice potential, a prime candidate to compare with experiment. We find that the DC-resistivity is linear in T at low temperatures for a range of potential strengths and wavevectors, even as it transitions between different dissipative regimes. At weak lattice potential the optical conductivity evolves with temperature from a Drude form to a bad metal characterized by a mid-IR resonance without changing the DC transport, similar to that seen in cuprate strange metals. This mid-IR peak can be understood as a consequence of Umklapp hydrodynamics: i.e. hydrodynamic perturbations are Bloch modes in the presence of a lattice. At strong lattice potential an incoherent metal is realized where momentum conservation no longer plays a role in transport. In this regime the thermal diffusivity appears insensitive to the breaking of translations and can be explained by Planckian dissipation originating in universal microscopic chaos. The charge diffusivity cannot be explained this way, though the continuing linear-in-T DC resistivity saturates to an apparent universal slope, numerically equal to a Planckian rate. We conjecture that this may originate in chaos properties that differ between charged and neutral operators.

The symbol bootstrap has proven to be a powerful tool in the calculation of polylogarithmic Feynman integrals and scattering amplitudes in planar maximally supersymmetric Yang-Mills theory that bypasses the direct integration of loop integrals. In this talk I will discuss a generalisation of this approach to an elliptic case: the symbol bootstrap of the 12-point two-loop double-box integral in four dimensions. The bootstrapping ansatz is obtained from an elliptic generalisation of a Schubert-type analysis of the leading singularities of the double box. After imposing mathematical and physical constraints on this ansatz, one obtains a compact one-line formula for the (2,2)-coproduct of the double-box integral.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

We propose a twistor description of non-self-dual Kähler metrics and black hole space-times in general relativity. We first focus on complex coordinate transformations between different real solutions, suggesting that they are different real sections of the same complex space. Then we describe how the full non-linear solutions can be understood as deformed twistor quadrics.

I will introduce the partial Bondi gauge for 4 dimensional spacetimes. This partial gauge includes the usual Bondi gauge and Newman-Unti gauge, designed to approach asymptotic boundaries along null rays. This new gauge is only specified by 3 conditions on the metric (g_{rr}=0=g_{rA}). I will discuss the solution space and asymptotic symmetries. Most importantly by relaxing the gauge we uncovered new symmetries of asymptotically flat spacetimes.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

We consider theories of gravity where a more "finite" holographic theory is relevant. From a Lorentzian perspective we comment on properties of gravity in the presence of finite timelike boundaries, and holographic realisations. Time permitting, we also discuss Euclidean gravity on manifolds with no boundary, like Euclidean de Sitter.

I will describe G-algebroids, a class of Leibniz algebroids carrying an "extended inner product", which generalise Lie algebroids, Courant algebroids, and the structures appearing in exceptional geometry. I will show how they provide an efficient tool for the study of consistent truncations of M-theory and type II string theory, and of dualities of the Poisson-Lie type. This is a joint work with M. Bugden, O. Hulik, and D. Waldram.

A session during which speakers will give a short introduction to their talks for PhD students and postdocs.

Landau's theory of Fermi liquids is a cornerstone of theoretical physics. I will show how to formulate Fermi liquid theory as an effective field theory of bosonic degrees of freedom, using the mathematical formalism of coadjoint orbits. While at the linear level, this theory reduces to existing multidimensional bosonization approaches, it necessarily features nonlinear corrections that are fixed by the geometry of the Fermi surface. These are crucial to reproduce nonlinear response, such as higher-point functions of currents. The effective field theory framework furthermore systematically parametrizes corrections to Fermi liquid behavior, and provides a computationally advantageous approach for non-Fermi liquids -- strongly interacting fixed points obtained by deforming Fermi liquids with relevant interactions.

A spacetime is said to satisfy the Penrose property if every pair of points on past and future null infinity can be connected by a timelike curve. Penrose showed that this property fails in Minkowski spacetime of any dimension but is satisfied in 3+1 dimensional positive mass Schwarzschild. I will consider the Penrose property in more detail and discuss how it is related to the ADM mass and dimensionality of the spacetime. I will then show how some of the ideas arising in the study of this property can be used to prove a version of the positive mass theorem. Finally, I will discuss how the apparent failure of the Penrose property in higher dimensions (regardless of the ADM mass) may be linked to the greater regularity of possible conformal completions of the spacetime at spacelike infinity.

A pre-seminar is a session during which speakers will give a short introduction to their talks.

In this talk, we will discuss QED at finite temperature from a hydrodynamic viewpoint. In the first part of the talk we shall discuss the symmetries of QED using the notion of higher-form symmetries. In the second part of the talk, we will discuss a holographic model which has the same higher-form symmetry structure. We will also very briefly touch upon work in progress regarding an effective hydrodynamic description of QED at T>0, using non-invertible symmetries.

Deformations of the algebra of quantum operators lead to a description of fundamental interactions that generalizes (and in a sense unifies) the principles of gauge theory and the geometric description of gravity as free fall in curved spacetime. This is quite well established for electromagnetism and is for example useful for the description of charged particles in a magnetic monopole background. We shall show that also gravitational interactions find such an algebraic description, but the construction requires a graded geometry setting. The construction suggests a novel somewhat more algebraic interpretation of key ingredients of general relativity. Generalized Geometry arises in this context via the derived bracket formalism and yields a symmetry-based approach to string effective gravity actions. Further examples of applications of graded geometry and deformation methods in (quantum) field theory include e.g. non-commutative gauge theory, tensor gauge theories, non-local interactions.

A pre-seminar is a session during which speakers will give a short introduction to their talks.

The flat space holography program aims at describing quantum gravity in asymptotically flat spacetime in terms of a dual lower-dimensional field theory. Two different roads to construct flat space holography have recently emerged. The first consists of a 4d bulk / 3d boundary duality, called Carrollian holography, where 4d gravity is suggested to be dual to a 3d Carrollian CFT living on the null boundary of the spacetime. The second is a 4d bulk / 2d boundary duality, called celestial holography, where 4d gravity is dual to a 2d CFT living on the celestial sphere. I will argue that these two seemingly contradictory proposals are actually related. The Carrollian amplitudes will be mapped to the celestial amplitudes using an appropriate integral transform. The Ward identities of the sourced Carrollian CFT, encoding the gravitational flux-balance laws, will be shown to reproduce those of the 2d celestial CFT, encoding the bulk soft theorems.

Celestial holography is the proposal of a codimension two correspondence between quantum gravity in 4d Minkowski space and some putative celestial conformal field theory on the 2d celestial sphere at the asymptotic boundary of Minkowski space. In this talk, I'll start with what the basics of the correspondence is and how the loop algebra of the wedge algebra of $w_{1+\infty}$ algebra with augmented indices emerges, then move on to review the famous family of W-algebras. After identifying the members of this family that are relevant in the context of celestial holography, I'll describe the physical theory in which W-algebra appears and its derivation.

A pre-seminar is a session during which speakers will give a short introduction to their talks.

Every textbook on general relativity states that light propagates along null geodesics. Although there are many senses in which this is true at sufficiently-high frequencies, it breaks down more generally. This talk will focus on the motion "as a whole" of electromagnetic pulses with large (but not infinitely-large) frequencies. Angular momentum then affects the motion, resulting in null but non-geodesic trajectories. Precise answers depend, however, on what exactly is meant by the "pulse as a whole": its centroid. There are many apparently-reasonable centroid definitions, but surprisingly, some of these result in positions which are nowhere near the pulse itself! This turns out to be an unphysical artifact of the fact that electromagnetic wavepackets are only approximately massless. Using this approximation uncritically turns out to result in some predictions which are not even qualitatively correct. The underlying problem is that eikonal approximations break standard features of Maxwell theory, such as the fact that exact electromagnetic stress-energy tensors satisfy positive-energy conditions.

TBA

A pre-seminar is a session during which speakers will give a short introduction to their talks.

When an external magnetic field is applied to a superconductor, unlike in a normal metal, the field penetrates the material in localised flux tubes. These flux tubes can be modelled as vortex (topological soliton) solutions of an effective U(1) gauged Ginzburg-Landau (abelian Higgs) model in 2-dimensions with a complex order parameter. The solutions of this model has a rich mathematical structure and understanding their properties has interested mathematicians for several decades. However, in the hunt for high temperature superconductivity, physicists have recently become interested in unconventional materials that exhibit a C^n order parameter. I will explore the topological soliton solutions of these unconventional models and their properties. I will then demonstrate that doubly periodic solutions exhibit peculiar magnetic structures, finally proposing experimental signatures that could be used to measure these structures in the lab.

Fractons are quasiparticles with the distinctive feature of having only limited mobility. This bizarre trait and their unusual symmetries also make the coupling to curved spacetime nontrivial. I will highlight the underlying exotic symmetries and show how aristotelian geometry provides the right framework for placing them on curved space. I will also emphasize that the very definition of isolated fractons requires a careful study of asymptotic symmetries. Analog to electrodynamics and general relativity, fractons have infinitely many soft charges which hint at a rich infrared structure and a fracton infrared triangle. Based on: 2111.03668, 2203.02817, 2206.11806, work in progress

I will be discussing certain dynamical and integrability properties of certain set-theoretical solutions of the (parametric) Yang-Baxter equation. These solutions are bi-rational maps with several invariants and a Lax representation (re-factorisation of two elements of a loop group). We show that we can use these maps to construct higher dimensional bi-rational maps which admit nice properties and we prove their integrability in the Liouville sense. These maps can be seen as higher dimensional generalisations of the famous integrable QRT maps, known as Adler's Triad maps. If we have enough time, we will present two different generalisations, namely the above picture in the case of the entwining Yang-Baxter equation and also for maps with Grassmann variables.

Models with large supersymmetry are unrealistic, but over the years they have proven to be a very fruitful playground for improving our understanding of quantum field theory. In this talk we will consider a new class with eight supercharges in three spacetime dimensions. The simplest example gives a way to enhance the supersymmetry of a model with three Chern--Simons gauge fields (which generically only allows for six supercharges), when the inverses of the levels sums up to zero. We will also see evidence that our class arises by compactifying the mysterious six-dimensional 'M5' model on a three-manifold. Our method reproduces for example the condition for a Seifert manifold to have enhanced holonomy. More generally our class should be related to so-called graph-manifolds. The condition for enhancement is related to a jump in homology groups, and seems to suggest a non-abelian analogue of the theory of 'transversely holomorphic foliations'.

A pre-seminar is a session during which speakers will give a short introduction to their talks.

We will study the relation among Galileii dynamical systems, without extensions, and some Carroll dynamical systems. The construction of the Galilei invariant systems will be done from the knowledge of Carroll dynamical models.

In recent years, the surprising relations between asymptotic symmetries and soft theorems have led to a promising candidate for flat holography: celestial holography. The central objects in this program are celestial amplitudes, which behave as correlation functions of primary operators in a putative conformal field theory: celestial CFT (CCFT). In this talk, we will first introduce some basics of celestial amplitudes and CCFT. We then discuss some aspects of celestial amplitudes and CCFT, including operator product expansions (OPEs), how soft theorems are related to symmetries in CCFT, and differential equations for celestial amplitudes. We will describe the recent ideas of top-down approaches in celestial holography and show one specific example, the celestial Liouville theory for Yang-Mills amplitudes. We will conclude with some open questions and future directions.