The rapid advance in gravitational wave detectors has spurred renewed interest in the two-body problem in general relativity. Two perturbative approaches based on quantum field theory have emerged, one based on scattering amplitudes and the other based on worldlines. We argue that the two approaches are equivalent at an intimate level. By systematic algebraic manipulations through the Schwinger parametrization, the loop integrand in the Kosower-Maybe-O'Connell formalism based on wavepacket scattering becomes identical to the counterpart in the worldline QFT formalism of Mogull et al., as shown explicitly for a simple scalar model as well as electrodynamics at two loops. This makes manifest the cancellations of superclassical divergences and exhibits the emergence of the worldline picture including the classical causality flow.

Physics beyond relativistic invariance and without Lorentz (or Poincare) symmetry and the geometry underlying these non-Lorentzian structures have become very fashionable of late. This is primarily due to the discovery of uses of non-Lorentzian structures in various branches of physics, including condensed matter physics, classical and quantum gravity, fluid dynamics, cosmology, etc. In this talk, I will be talking about one such theory - Carrollian theory, where the Carroll group replaces the Poincare group as the symmetry group of interest. Interestingly, any null hypersurface is a Carroll manifold and the Killing vectors on the null manifold generate Carroll algebra. Historically, Carroll group was first obtained from the Poincare group via a contraction by taking the speed of light going to zero limit as a "degenerate cousin of the Poincare group". I will shed some light on Carrollian fermions, i.e. fermions defined on generic null surfaces. Due to the degenerate nature of the Carroll manifold, there exist two distinct Carroll Clifford algebras and, correspondingly, two different Carroll fermionic theories. I will discuss them in detail. Then, I will show some examples; when the dispersion relation becomes trivial, i.e. energy bands flatten out, there can be a possibility of the emergence of Carroll symmetry.

Four-point correlation functions are observables of significant interest in holographic quantum field theories. In this talk I will describe the computation of a family of four-point correlation functions of operators in short multiplets of 4D N=4 super Yang-Mills theory, by studying the quadratic fluctuations around non-trivial supergravity backgrounds. The supergravity backgrounds are supersymmetric smooth geometries in the family derived by Lin, Lunin and Maldacena. For generic parameters, the supergravity backgrounds are dual to heavy CFT states. However I will also discuss the limit in which the dual CFT states become light single-particle states. The resulting all-light four-point correlators are related by superconformal Ward identities to previously known four-point correlators of half-BPS chiral primary operators. By verifying that the Ward identities are satisfied, we confirm the validity of the supergravity method.

For small values of k and N, this theory describes various experimentally relevant systems in condensed matter, and is also conjectured to be part of a web of non-supersymmetric dualities. We compute the scaling dimensions of monopole operators in a large N and k expansion, which appears to be extremely accurate even down to the smallest values of N and k, and allows us to find dynamical evidence for these dualities and make predictions about the phase transitions. For instance, we combine these estimates with the conformal bootstrap to predict that the notorious Neel-VBS transition (QED3 with 2 scalars) is tricritical, which was recently confirmed by independent lattice simulations. Lastly, we propose a novel phase diagram for QED3 with 2 fermions, including duality with the O(4) Wilson-Fisher fixed point.

Amongst the most fascinating behaviours to arise from Einstein's equations is the onset of chaotic dynamics in the approach to certain cosmological singularities. This was analysed in detail in seminal work by Belinskii, Khalatnikov, Lifshitz (BKL) and others some fifty years ago. A consequence of these results is that the Schwarzschild interior solution near the singularity appears very fine-tuned and should give way for BKL-like dynamics in more generic black holes. In arxiv:2312.11622, we construct a setup that realises the so-called "mixmaster" chaotic dynamics in the interior of an AdS black hole. After reviewing the work of BKL, I will describe our holographic setup and discuss the peculiar symmetries appearing in this problem.

In this talk, I will discuss a novel strategy to fit experimental data using an amplitude ansatz satisfying the constraints of Analyticity, Crossing, Unitarity, and UV completeness. The fit strategy requires both the use of S-matrix Bootstrap methods and non-convex Particle Swarm Optimization (PSO) techniques. As a proof of principle, I will focus on $\pi\pi$ scattering. Using this procedure, I will show how to construct numerically a full-fledged scattering amplitude that fits the available experimental and lattice data, and that features all the known QCD spectrum with quantum numbers $I^G=0^+,1^+$ below 1.4 GeV, plus an additional surprise.

The original singularity theorems of Penrose and Hawking have, in their hypotheses, pointwise energy conditions violated by some classical and all quantum fields. If we want to extend their validity to semiclassical gravity, these conditions have to be replaced by weaker ones. In this talk I will first discuss recent results for singularity theorems with weakened energy conditions, some of which are obeyed by quantum fields. Then I will argue for the need of singularity theorems with worldvolume averaged energy conditions both in the timelike and the null case. For each case I will present progress and open questions.

In the first part of the talk I will recap the black hole thermodynamics of a certain non-supersymmetric asymptotically AdS_5 black hole: I will define its asymptotic charges and associated potentials and show some thermodynamic relations between them. Then I will describe the so-called BPS point, where the black hole is extremal (zero temperature) and supersymmetric. Finally, I will show how to approach the vicinity of the BPS point, without exactly landing on it and discuss the significance of this near-BPS limit and its relation to the Schwarzian mode. In the second part of the talk, I will introduce the holographically dual 4d field theory and describe its basic properties. In particular, I will describe how the supersymmetry breaking (which occurred on the gravity side) can be kept under control on the field theory side. Finally, I will present a preliminary calculation providing a match between the classical gravity partition function and the classical field theory partition function in this thermal setting.

We derive a universal inequality on the unitary 2D CFT partition function with general central charge $c\geqslant 0$, using analytical modular bootstrap. We derive an iterative equation for the domain of validity of the bound on the mixed-temperature plane. The infinite iteration of this equation gives the boundary of maximal-validity domain of our inequality. In the $c\to\infty$ limit, with additional assumption of having a sparse spectrum below the scaling dimension $\frac{c}{12}+\varepsilon$ and below the twist $\frac{\alpha c}{12}$ (with $\alpha\in(0,1]$ fixed), our inequality implies that the grand-canonical free energy has universal large-c behavior in the maximal-validity domain, which does not encompass the entire mixed-temperature phase diagram, except in the case of $\alpha = 1$. In particular, we prove the conjecture proposed by Hartman, Keller and Stoica [1405.5137] (the $\alpha=1$ case): the free energy is universal in the large c limit for all $\beta_L\beta_R \neq 4\pi^2$.

Recent developments in the field of integrability include the discovery of higher-dimensional generalised Chern-Simons theories. These theories encode a linear system known as a Lax pair which underpins the integrability of the lower-dimensional theory. We will start with a generous review of these developments before presenting some extensions of this formalism. The applications of these extensions include: integrable deformations (a class of less-symmetric string backgrounds which are nonetheless integrable), stationary axisymmetric general relativity, and gauged WZW models.

Coset symmetry arises in many systems such as Higgs phases of gauge theories and quantum spin liquids. When the coset is quotient by a non-normal subgroup, coset symmetry becomes a non-invertible symmetry. I will discuss properties of coset non-invertible symmetry and its fractionalization using examples in field theories and lattice models, and comment on the dynamical implication. The talk is based on arXiv: 2405.20401 and work in progress with Ryohei Kobayashi and Carolyn Zhang

In recent years, there has been a lot of interest in a generalized notion of symmetry, obtained by relaxing the invertibility constraint and/or allowing symmetry operators to act on submanifolds rather than the full space. The mathematical structure underlying these generalized symmetries is provided by (higher) category theory, but it turns out that in the lattice setting, the abstract categorical formulation can be broken down to concrete tensor network operators that realize these generalized symmetries. In a certain sense, these tensor network operators provide the lattice representation theory of these generalized symmetries. As an application, I will explain how this representation theory provides a systematic, constructive theory for duality transformations on the lattice. Additionally, I will explain how dualities and generalized symmetries can be turned into unitary operators by including an ancillary degree of freedom, turning them into completely positive maps.

It has recently been recognized that various observables in different four-dimensional supersymmetric gauge theories can be computed for an arbitrary 't Hooft coupling as determinants of certain semi-infinite matrices. It turns out that these quantities can be expressed as Fredholm determinants of the so-called Bessel kernel and they are closely related to celebrated Tracy-Widom distribution (more precisely, its finite temperature generalization) describing level-spacing distributions in matrix models. We exploit this relation to determine their dependence on the ’t Hooft coupling constant. Unlike the weak coupling expansion, which has a finite radius of convergence, the strong coupling expansion is factorially divergent, necessitating the inclusion of nonperturbative, exponentially small corrections. We develop a method to systematically compute these corrections and discuss the resurgent properties of the resulting transseries.

Predicting the outcome of scattering processes of elementary particles in colliders is the central achievement of relativistic quantum field theory applied to the fundamental (non-gravitational) interactions of nature. While the gravitational interactions are too minuscule to be observed in the microcosm, they dominate the interactions at large scales. As such the inspiral and merger of black holes and neutron stars in our universe are now routinely observed by gravitational wave detectors. The need for high precision theory predictions of the emitted gravitational waveforms has opened a new window for the application of perturbative quantum field theory techniques to the domain of gravity. In this talk I will show how observables in the classical scattering of black holes and neutron stars can be efficiently computed in a perturbative expansion using a world-line quantum field theory; thereby combining state-of-the-art Feynman integration technology with perturbative quantum gravity. Here, the black holes or neutron stars are modelled as point particles in an effective field theory sense. Fascinatingly, the intrinsic spin of the black holes may be captured by a supersymmetric extension of the world-line theory, enabling the computation of the far field wave-form including spin and tidal effects to highest precision. I will review our most recent results at the fifth order in the post-Minkowskian expansion amounting to the computations of tens of thousands of four loop Feynman integrals.

In a physical system with conformal symmetry, observables depend on cross-ratios, measures of distance invariant under global conformal transformations (conformal geometry for short). We identify a quantum information-theoretic mechanism by which the conformal geometry emerges at the gapless edge of a 2+1D quantum many-body system with a bulk energy gap. We introduce a novel pair of information-theoretic quantities (c,n) that can be defined locally on the edge from the wavefunction of the many-body system, without prior knowledge of any distance measure. We posit that, for a topological groundstate, the quantity c is stationary under arbitrary variations of the quantum state, and study the logical consequences. We show that stationarity, modulo an entanglement-based assumption about the bulk, implies (i) c is a non-negative constant that can be interpreted as the total central charge of the edge theory. (ii) n is a cross-ratio, obeying the full set of mathematical consistency rules, which further indicates the existence of a distance measure of the edge with global conformal invariance. Thus, the conformal geometry emerges from a simple assumption on groundstate entanglement. The stationarity of c is equivalent to a vector fixed-point equation involving n, making our assumption locally checkable. If time permits, we discuss a class of modular flow on a disk, which creates only edge excitations. We intuitively explain why Virasoro algebra can be revealed from a single wavefunction by analyzing such modular flows.

I'll discuss the exact non-invertible Kramers-Wannier symmetry of 1+1d lattice models on a tensor product Hilbert space of qubits. This symmetry mixes with lattice translations, and obeys a different algebra compared to the continuum one. The non-invertible symmetry leads to a constraint similar to that of Lieb-Schultz-Mattis, implying that the system cannot have a unique gapped ground state. It is either in a gapless phase or in a gapped phase with three (or a multiple of three) ground states, associated with the spontaneous breaking of the non-invertible symmetry.

In planar N=4 SYM, massless scattering amplitudes are dual to null polygonal Wilson loops (T-duality) or the same as the four-dimensional null limit of stress-tensor correlators. I will present a (conjectured) generalization of this duality which equates correlators of determinant operators, in a special ten-dimensional null limit, with massive scattering amplitudes in the Coulomb branch of N=4. This determinant operator is a generating function of all half-BPS single-traces operators. By taming it on twistor space I will show its correlators have ten dimensional poles which combine 4d space-time and 6d R-charge kinematics.

The discovery of gravitational waves has opened a new experimental window into the Universe. The fact that the relevant dynamics is often out of equilibrium offers a golden opportunity for holography to make a unique impact on cosmology and astrophysics. I will illustrate this with applications to cosmological phase transitions, to neutron star mergers and to the BKL dynamics near a cosmological singularity.

In this talk we use integrability data to bootstrap correlation functions of planar maximally supersymmetric Yang- Mills theory. Focusing on four-point correlation function of stress-tensor, we first introduce a set of sum rules that are only sensitive to single-traces in the OPE expansion (this is advantageous because this data is available from integrability). We then discuss how these sum rules can be employed in numerical bootstrap to nonperturbatively bound planar OPE coefficients. We show rigorous bounds for the OPE coefficient of the Konishi operator at various t’Hooft couplings outside the perturbative regime. The talk is based on an ongoing work and 2207.01615.

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