Quantum gravity is undoubtfully one of the most important missing pieces in the understanding of the mathematical structure of our universe. The impossibility of consistently quantizing gravity via perturbative quantum field theory has led to a plethora of different proposals, from asymptotically safe gravity to non-local gravity, loop quantum gravity, and string theory. Different approaches face different problems and have succeeded in different areas. Yet, on the conceptual side, it is not obvious that all these frameworks are inequivalent or unrelated: some theories may be low-energy approximations of others, or could even provide different mathematical descriptions of the same physics. On the technical side, the knowledge gained in an approach could be useful to investigate certain aspects of others. In this spirit, I will review progress in connecting and contrasting two theories: asymptotically safe gravity and string theory. Specifically, I will discuss how to test asymptotic safety using stringy swampland constraints, and how techniques developed in the context of asymptotically safe gravity can be exploited to compute cosmological higher-derivative corrections to all orders in string theory.

Quantum coherence plays essential role in diverse phenomena of relevance in the early universe. Examples include activation of sterile neutrinos, electroweak baryogenesis, resonant leptogenesis and particle production in phase transitions and during the (p)reheating stage after inflation. After a general introduction I will concentrate on the particle production problem. I will show how one can derive coupled, renormalized and tractable quantum kinetic equations for the scalar field 1- and 2-point functions starting from the CTP-formalism, working in the Hartree approximation of the 2PI-action. I will then apply these equations to study particle production and the back-reaction from the non-equilibrium modes on the dynamics of the one-point function. We will see both spinodal and parametric resonances taking place and sometimes overlapping in a novel way, and we follow the process of decoherence and thermalization. Overall, I argue that advanced quantum transport equations are necessary for an accuarate description of many systems of acute interest in cosmology.

Scalar condensates are very common objects in cosmology. For example, the inflaton field can be viewed as a scalar condensate before it completely dissipates into ordinary particles during reheating. Axion condensates may have been formed through the vacuum-misalignment mechanism. In this talk, I will discuss the dissipation of oscillating homogeneous scalar backgrounds in flat spacetime and an expanding universe using nonequilibrium quantum field theory. The latter naturally captures the thermal effects and backreaction effects. For quasi-harmonic oscillations, we adopt the multi-scale analysis to obtain analytical approximate expressions for the self-consistent evolution of the scalar condensates in terms of the retarded self-energy and retarded proper four-vertex function, whose imaginary parts characterize different condensate decay channels. At finite temperatures, there are many new condensate decay channels that would be absent at zero temperature. These new channels could play an important role in ensuring a complete dissipation in an expanding universe. The talk is based on the following two papers: JHEP 11 (2021) 160 [arXiv:2108.00254 [hep-ph]]; JHEP 11 (2022) 075 [arXiv:2202.08218 [hep-ph]]

In this talk I will develop Rafael D. Sorkin’s heuristic that a partially ordered process of the birth of spacetime atoms in causal set quantum gravity can provide an objective physical correlate of our perception of time passing. I will argue that one cannot have an external, fully objective picture of the birth process because the order in which the spacetime atoms are born is a partial order. I propose that live experience in causal set theory is an internal “view” of the objective birth process in which events that are neural correlates of consciousness occur. In causal set theory, what “breathes fire” into a neural correlate of consciousness is that which breathes fire into the whole universe: the unceasing, partially ordered process of the birth of spacetime atoms.

Topological recursion has become known as a powerful recursive formalism to compute a variety of invariants in mathematics and physics. The list of applications includes matrix model correlation functions, 2d gravity amplitudes, topological string theory amplitudes, and more. Interestingly, recent study has shown that by introducing the notion of Airy structures, topological recursion can be described in terms of twisted representations of the Virasoro algebra. In this talk, I will first give an introductory overview of topological recursion as well as Airy structures. Then, I will present how one can generalise the current formalism of topological recursion, e.g. by upgrading the Virasoro algebra to the super Virasoro algebra or the q-Virasoro algebra. If time permits, I will also discuss expected applications of such generalisations. This is in part joint with Vincent Bouchard and also in part joint with Nitin Chidambaram. Notice the unusual day!

I will discuss how to setup renormalization of bulk loops in AdS and the implications for the AdS/CFT correspondence.

The epsilon-expansion was invented more than 50 years ago and has been used extensively ever since to study aspects of renormalization group flows and critical phenomena. Its most famous applications are found in theories involving scalar fields in (4-epsilon) dimensions. In this talk, we will discuss the structure of the epsilon-expansion and the fixed points that can be obtained within it. We will mostly focus on scalar theories, but we will also discuss theories with fermions as well as line defects. Our motivation is based on the goal of classifying conformal field theories in d=3 dimensions. We will describe recently discovered universal constraints obtained within the framework of the epsilon-expansion and show that a 'heavy handed' quest for fixed points yields a plethora of new ones. These fixed points reveal aspects of the structure of the epsilon-expansion and suggest that a classification of conformal field theories in d=3 is likely to be highly non-trivial.

We will discuss a connection between OPE algebras appearing in celestial holography for various theories and the `colour-kinematics duality' in the bulk spacetime description of those theories. Both the celestial algebras and the colour-kinematics duality take a particularly simple form for self-dual Yang-Mills and gravity. In particular, we show that the $Lw_{1+\infty}$ celestial algebra recently unveiled in self-dual gravity arises from the soft expansion of an area-preserving diffeomorphism algebra, which plays the role of the kinematic algebra in the colour-kinematics duality. We also present deformations of the celestial algebras resulting from Moyal deformations of the self-dual theories, e.g. the deformation of $Lw_{1+\infty}$ into $LW_{1+\infty}$ in the case of self-dual gravity. In addition, we discuss the relation of these deformations to higher-spin theories of massless particles that can be thought of as extensions of self-dual Yang-Mills and gravity. Finally, we present a proof that tree-level scattering amplitudes in the theories we focus on vanish, signalling their classical integrability, which is an S-matrix version of the Ward conjecture for integrable systems.

I will describe a method for approximately solving the crossing equations in a general CFT, using Reinforcement Learning as a stochastic optimiser. I will then present an application of this approach in the context of the 6D (2,0) theory.

We determine the full 1/sqrt(lambda) correction to the flat-space Wilson coefficients which enter the AdS Virasoro-Shapiro amplitude in N=4 SYM theory at strong coupling. The assumption that the Wilson coefficients are in the ring of single-valued multiple zeta values, as expected for closed string amplitudes, is surprisingly powerful and leads to a unique solution to the dispersive sum rules relating Wilson coefficients and OPE data. The corresponding OPE data fully agrees with and extends the results from integrability.

The problem of time is often discussed as an obstacle in canonical quantisation of gravity: general covariance means there is no preferred time parameter with respect to which evolution could be defined. We can instead characterise dynamics in relational terms by defining one degree of freedom to play the role of an internal clock for the other variables; this leads to a "multiple choice problem". I will review recent results obtained in a quantum cosmological model with three dynamical degrees of freedom: a volume or scale factor variable for the geometry, a massless scalar matter field, and a perfect fluid. Each of these variables can be used as a clock for the other two. We obtain three different theories which, if we require them to have unitary time evolution with respect to the given clock, make very different statements about the fate of the Universe. Only one resolves the classical singularity, and only one leads to a quantum recollapse of the Universe at large volume. Nonclassical behaviour arises whenever a classical solution terminates in finite time so that reflecting boundary conditions are needed to make the theory unitary.

In this talk, I will discuss the construction of 2d (0,2) supersymmetric gauge theories corresponding to the 18 smooth Fano 3-folds and the families of Y^(p,k)(CP1xCP1) and Y^(p,k)(CP2) Sasaki-Einstein 7-manifolds. These 2d (0,2) gauge theories can be considered as the worldvolume theories of D1-branes probing toric Calabi-Yau 4-folds. The talk will illustrate how the map between gauge theory and the corresponding geometry is considerably simplified by a Type IIA brane configuration called brane brick models.

I will discuss positivity bounds on EFT coefficients in theories where Lorentz boosts are spontaneously broken. The well-known S-matrix argument from the Lorentz-invariant scenario does not straightforwardly generalize to this case. Instead the analytic properties of the retarded Green’s function of conserved currents (or of the stress-energy tensor) will be used, and the theory will be assumed to become conformal in the UV. The method is general and applicable to both cosmology and condensed matter systems. As a concrete example we will consider the EFT of conformal superfluids, which describes the universal low-energy dynamics of CFTs at large U(1) charge, and we will derive inequalities on the coefficients of the operators, in three spacetime dimensions, at NLO and NNLO.

The worldsheet theory of string backgrounds is a CFT with zero central charge. This is the definition of on-shell string theory. In off-shell string theory, on the other hand, conformal invariance on the worldsheet is explicitly broken, and the worldsheet theory is therefore a QFT rather than a CFT, with a UV cutoff. In this talk, I will explain Tseytlin's prescriptions for constructing classical (tree-level) off-shell effective actions and provide a general proof, using conformal perturbation theory, that it gives the correct equations of motion, to all orders in perturbation theory and $\alpha'$. I will also show how Tseytlin's prescriptions are equivalent to quotienting out by the gauge orbits of a regulated moduli space with "n" operator insertions. I will also explain how Tseytlin's prescriptions encode the correct prescription for the Lorentzian S-matrix in which case we obtain Feynman's $i\varepsilon$ prescription for the internal poles. Finally, I will explain how the classical off-shell string action was used by Susskind and Uglum to calculate the tree-level black hole entropy on a conical manifold in Rindler background. Time permitting, I will present very recent upcoming work on a closed-form expression for a generalized Tseytlin (GT) operator that eliminates all spurious tadpoles from higher curvature couplings on the worldsheet. This allows us to study its action on correlations functions of scalar primaries and descendants with arbitrary conformal dimensions.

I will review how non-linearities can allow for screening solar-system scales from non-tensorial gravitational polarizations, focusing on the case of scalar-tensor theories with derivative self-interactions (K-essence). I will then present fully relativistic simulations in these theories in 1+1 dimensions (stellar oscillations and collapse) and 3+1 dimensions (binary neutron stars), showing how to avoid breakdowns of the Cauchy problem that have affected similar attempts in the past. I will show that screening tends to suppress the (subdominant) dipole scalar emission in binary neutron star systems, but that it fails to quench monopole scalar emission in gravitational collapse, and quadrupole scalar emission in binaries.

Mixed anomalies and generalized symmetries have proved to be useful in providing non-trivial constraints on the dynamics of quantum field theories (QFTs). A natural question is whether these are related in any way to certain supersymmetric partition functions or indices, which have also been used extensively to study the dynamics of QFTs. In this talk, we address this question in the context of 3d N≥3 gauge theories using the superconformal index. In particular, using the index we are able to detect mixed anomalies involving discrete 0-form global symmetries, and possibly a 1-form symmetry. The effectiveness of this method is demonstrated via several classes of theories, including Chern-Simons-matter theories, the T(SU(N)) theory of Gaiotto-Witten and variants of the Aharony-Bergman-Jafferis (ABJ) theory with the orthosymplectic gauge algebra. Gauging appropriate global symmetries involved in mixed anomalies of some of these models and using constructions available in the literature, we obtain various interesting theories with two-group structures or non-invertible symmetries.

In some ways the ocean acts like a topological insulator. There are chiral edge modes, localised at the coast, that go clockwise in the Northern hemisphere and anti-clockwise in the Southern hemisphere. I’ll describe these features and explain how this can be understood in terms of something more familiar to high energy physicists. I’ll show that the equations that govern the long-time dynamics of the ocean can be recast as a Maxwell-Chern-Simons theory.

Tremendous progress has been achieved during the last years in bootstrapping conformal correlators at strong coupling using analytical bootstrap methods and the AdS/CFT correspondence. In particular, the development of Lorentzian inversion formulae revealed helpful in reconstructing four-point functions. In this talk I will present how this technology can be adapted to defect setups in order to compute scalar two-point functions in the presence of a conformal defect in the strong-coupling regime. We derived a dispersion relation that allows to efficiently generate elegant closed-form expressions for a variety of setups, and in particular we apply this method to two-point functions of single-trace half-BPS operators in the presence of the supersymmetric Wilson line defect in 4d N=4 SYM, using minimal input from holography.

In 1968, D. Atkinson proved in a series of papers the existence of functions satisfying all known constraints of the S-matrix bootstrap for the 2-to-2 S-matrix of gapped theories. To date, this is the only result of this sort, while a contrario no current technology allows to generate, even numerically, fully consistent S-matrices in d>2. Beyond the mathematical results themselves, the proof, based on establishing the existence of a fixed point of a certain map, also suggests a procedure to be implemented numerically and which would produce fully consistent S-matrix functions via iterating dispersion relations, and using as an input a quantity related to the inelasticity of a given scattering process. In this talk, I will report on some work being finalised, done in collaboration with A. Zhiboedov, about analytical and numerical aspects of developing and implementing this scheme. I will review basic concepts of the S-matrix program and show some of our results on non-perturbative scalar, phi^4-like S-matrices in 4, describe their properties and compare to other approaches in the literature. If time allows, I will present some results in 3 dimensions and discuss subtle aspects of the high energy (Regge behaviour) of the S-matrices.

Dynamical Chern-Simons gravity (dCS) is a four-dimensional parity-violating extension of general relativity. Current models predict the effect of this extension to be negligible due to large decay constants f close to the scale of grand unified theories. Here, we present a construction of dCS allowing for much smaller decay constants, ranging from sub-eV to Planck scales. Specifically, we show that if there exists a fermion species with strong self-interactions, the short-wavelength fermion modes form a bound state. This bound state can then undergo dynamical symmetry breaking and the resulting pseudoscalar develops Yukawa interactions with the remaining long-wavelength fermion modes. Due to this new interaction, loop corrections with gravitons then realize a linear coupling between the pseudoscalar and the gravitational Chern-Simons term. The strength of this coupling is set by the Yukawa coupling constant divided by the fermion mass. Therefore, since self-interacting fermions with small masses are ideal, we identify neutrinos as promising candidates. For example, if a neutrino has a mass mν ≲meV and the Yukawa coupling is order unity, the dCS decay constant can be as small as f∼10^3mν ≲eV. We discuss other potential choices for fermions.