Renormalisation group (RG) interfaces were introduced by I. Brunner and D. Roggenkamp in 2007. To construct such an interface consider perturbing a UV fixed point, described by a conformal field theory (CFT), by a relevant operator on a half space. Renormalising and letting the resulting QFT flow along the RG flow we obtain a conformal interface between the UV and IR fixed point CFTs. Although enjoying a full conformal symmetry this interface carries information about the RG flow it originated from. In this talk I will consider a rather special case of the RG interface between two boundary conditions of a 2D CFT which is obtained from a boundary RG flow interpolating between two conformal boundary conditions. This interface is zero-dimensional and is thus described by a local boundary-condition changing operator. I investigate its properties in concrete models and formulate a number of general conjectures that can help charting phase diagrams of boundary RG flows.

We construct new supersymmetric solutions of 11D supergravity, preserving 1/4 of the supersymmetry, that are dual to the ABJM Chern-Simons-matter theory deformed by mass terms which depend on one spatial direction. The BPS equations boil down to solving the Helmholtz equation on the complex plane giving rise to rich classes of new solutions. In particular, the construction gives rise to infinite classes of new supersymmetric “boomerang” RG flows, as well as generalising other previously known solutions.

I will describe simple models of holography that can display some of the thermodynamics associated to small black holes. These phenomena include negative specific heat and localization on additional dimensions of the geometry. I will also explain how the dynamics of these states should naturally be thought of as partial deconfinement on a submatrix set of degrees of freedom of the model.

Ultra-planckian collisions represent a fertile arena where to test quantum theories of gravity such as string theory. Glimpses of black hole formation and evaporation can be taken. For suitably defined infrared-safe observables, we show that the `classicalization' approach to high-multiplicity processes agrees with the ACV approach based on the resummation of ladder diagrams. Since a significant fraction of energy is lost in gravitational bremsstrahlung, we re-derived the zero-frequency limit (ZFL) of the GW flux using soft graviton theorems at leading order and compute the corrections at sub- and sub-sub-leading order. For massless two-particle elastic collisions the former is shown to vanish, while the latter takes an explicit expression which is checked against a simple tree-level process.However, if the tree-level form of the soft theorems is used at sub-sub-leading order even when the elastic amplitude needs resummation, an unphysical IR singularity occurs due to the infinite Coulomb phase. We briefly discuss a recent proposal as how to deal with these divergences and find agreement with the eikonal approach.

I will give an overview of my recent research on the definition of asymptotic charges in asymptotically flat spacetimes, including the definition of subleading BMS charges and the relation to the conserved Newman-Penrose charges at null infinity.

I will discuss some old and new relations between the characters, modular data and braiding and fusing matrices of rational conformal field theories and their associated modular tensor categories. These relations involve concepts from number theory which I will explain in the talk.

We probe a generic two dimensional conformal interface via a collider experiment. We measure the energy and charges which are reflected and transmitted through the interface. We find that the average transmitted energy is independent of the way the state is constructed and determined by the central charge and a single piece of CFT data. We comment on the universality of the result and discuss some examples.

I will show how large logarithms arise in a perturbative calculation and how resummation solves the issue of having these large logarithms. If there is some time left, I want to show some recent progress that we have made on pinning down the origin of the next-to-leading class of logarithms.

Understanding most basic thermodynamic properties of liquids such as energy and heat capacity turned out to be a long-standing problem in physics [1]. Landau&Lifshitz textbook states that no general formulas can be derived for liquid thermodynamic functions because the interactions are both strong and system-specific. Phrased differently, liquids have no small parameter. Recent results have opened a new way to understand liquid thermodynamics on the basis of collective modes (phonons) as is done in the solid state theory. There are important differences between phonons in solids and liquids, and we have recently started to understand and quantify this difference. One striking difference is the emergence of a gap in the liquid phonon spectrum in the reciprocal space [2]. This brings an interesting question of what kind of field theory describes this gap. We recently proposed a two-field Lagrangian which accounts for dissipation and predicts the gap in momentum space [3]. The dissipative and mass terms compete by promoting gaps in k-space and energy, respectively (when bare mass is close to the field hopping frequency, both gaps close and the dissipative term annihilates the bare mass.) I will also discuss the recent attempt to canonically quantize this theory where I attempted to describe quantum dissipation which has been of interest recently. The Hamiltonian is quantized in terms of particles and antiparticles as in the complex scalar field theory and has the energy spectrum with the gap in momentum space. Finally, I will discuss the emergence of ultraviolet and infrared cutoffs in this theory due to dissipation. [1] K. Trachenko and V. V. Brazhkin, Collective modes and thermodynamics of the liquid state, Reports on Progress in Physics 79, 016502 (2016). [2] C. Yang, M. T. Dove, V. V. Brazhkin and K. Trachenko, Physical Review Letters 118, 215502 (2017). [3] K. Trachenko, Physical Review E 96, 062134 (2017).

I give an overview of work with Aasen and Mong on topological defects in two-dimensional classical lattice models, quantum spin chains and tensor networks. The partition function in the presence of a topological defect is invariant under any local deformation of the defect. By using results from fusion categories, we construct topological defects in a wide class of lattice models, and show how to use them to derive exact properties of field theories by explicit lattice calculations. In the Ising model, the fusion of duality defects allows Kramers-Wannier duality to be enacted on the torus and higher genus surfaces easily, implementing modular invariance directly on the lattice. In other models, the construction leads to generalised dualities previously unknown. A consequence is an explicit definition of twisted boundary conditions that yield the precise shift in momentum quantization and for critical theories, the spin of the associated conformal field. Other universal quantities we compute exactly on the lattice are the ratios of g-factors for conformal boundary conditions

I will introduce the framework of 4D scattering equations for calculating tree level super amplitudes in a variety of different theories, including Einstein supergravity and super Yang-Mills theory. I will discuss my work on numerical solutions to these equations by Monte Carlo methods, and work with Arthur Lipstein on calculating N=4 conformal supergravity amplitudes in this framework.

The infrared fixed point of graphene under the renormalization group flow is a relatively under studied yet important example of a boundary conformal field theory with a number of remarkable properties. It has a close relationship with three dimensional QED. It maps to itself under electric-magnetic duality. Moreover, it along with its supersymmetric cousins all possess an exactly marginal coupling -- the charge of the electron -- which allows for straightforward perturbative calculations in the weak coupling limit. I will review past work on this model and also discuss my own contributions, which focus on understanding the boundary contributions to the anomalous trace of the stress tensor and their role in helping to understand the structure of boundary conformal field theory.

Given two copies of any quantum mechanical system, one may want to prepare them in the thermofield double state for the purpose of studying thermal physics or black holes. However, the thermofield double is a unique entangled pure state and may be difficult to prepare. We propose a local interacting Hamiltonian for the combined system whose ground state is approximately the thermofield double. The energy gap for this Hamiltonian is of order the temperature. Our construction works for any quantum system satisfying the Eigenvalue Thermalization Hypothesis.

I will discuss walking behavior in gauge theories and weakly first order phase transition in statistical models. Despite being phenomena appearing in very different physical systems, they both show a region of approximate scale invariance. They can be understood as a RG flow passing between two fixed points living at complex couplings, which we call complex CFTs. By using conformal perturbation theory, knowing the conformal data of the complex CFTs allows us to make predictions on the observables of the walking theory. As an example, I will discuss the two dimensional Q-state Potts model with Q>4.

Quantum error correction provides a convenient setup where bulk operators are defined only on a code subspace of the physical Hilbert space of the conformal field theory. I will first reformulate entanglement wedge reconstruction in the language of operator-algebra quantum error correction with infinite-dimensional physical and code Hilbert spaces. I will streamline my proof that for infinite-dimensional Hilbert spaces, the entanglement wedge reconstruction is identical to the equivalence of the boundary and bulk relative entropies. I will discuss its implications for holographic theories with the Reeh-Schlieder theorem.

To any four-dimensional N=2 super-conformal field theory (SCFT) one can canonically associate a two-dimensional vertex operator algebra (VOA). This provides a powerful framework for the analysis of SCFTs and leads to surprising predictions for a large new class of VOAs. In this talk I will present remarkable free field realizations of the relevant VOAs which mirror the effective field theory description of the corresponding four dimensional theory on the Higgs branch of its moduli space of vacua.

Supersymmetric localization is a powerful technique to evaluate a class of functional integrals in supersymmetric field theories. It reduces the functional integral over field space to ordinary integrals over the space of solutions of the off-shell BPS equations. The application of this technique to supergravity suffers from some problems, both conceptual and practical. I will discuss one of the main conceptual problems, namely how to construct the fermionic symmetry with which to localize. I will show how a deformation of the BRST technique allows us to do this. As an application I will then sketch a computation of the one-loop determinant of the super-graviton that enters the localization formula for BPS black hole entropy.

Even if one knows everything for a conformal field theory on the infinite plane, new data are required to place the same theory in finite geometries. This is a physically relevant question for finite-temperature/finite-size critical systems. I will show in this talk how to apply an OPE inversion formula to thermal two-point functions of bosonic and fermionic CFTs in general odd dimensions. This allows us to analyze in detail the operator spectrum of these theories. The main result is that nontrivial thermal CFTs arise when the thermal mass satisfies an algebraic transcendental equation that ensures the absence of an infinite set of operators from the spectrum. The solutions of these gap equations for general odd dimensions are in general complex numbers and follow a particular pattern. I will argue that this pattern unveils the large-N vacuum structure of the corresponding theories at zero temperature.