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In this talk I will consider type IIB string theory on $AdS_5\times S^5/\mathbb{Z}_L$ orbifold spaces with arbitrary L. Recent localisation results in the dual 4d $N=2$ circular quiver gauge theories provide us with strong coupling expansions of certain correlators involving twisted half-BPS operators. To leading order, these results have been matched to an effective theory for massless twisted string states, constructed by resolving the orbifold singularity and considering localised supergravity modes on the resolution cycles. Applying this reasoning to subleading order in strong coupling, we observe that for $L\neq 2,3,4,6$, a naive reduction of the 10d $(\alpha^\prime)^3$-correction does not result in the correct coefficients to match the localisation result.  This mismatch may be explained by the appearance of twisted sector resonances in string amplitudes involving external twisted sector states. Indeed, performing the low-energy expansion of a ‘twisted‘ Virasoro-Shapiro amplitude, one recovers the expected coefficients, suggesting that the orbifold resolution and the low-energy expansion cannot be interchanged directly. If time permits, I will also sketch more recent developments in the understanding of the ‘long‘ quiver limit, arising as $L$ is taken to infinity, from the string theory side.

Loop models are statistical mechanical models where the underlying degrees of freedom are loop configurations drawn on an underlying 2d lattice. When these models are tuned to their critical point and a continuum limit is taken, they can be described by a 2d CFT. These 2d CFTs are solvable, however unlike previously solved 2d CFTs they have a discrete, yet infinite, spectrum of primary fields. We will solve these models in the presence of a boundary. The spectrum can be determined analytically by studying annulus partition functions and this data can then be used in the crossing equations for correlators. With a known spectrum, the crossing equations are a set of linear equations for the coefficients in front of the conformal blocks. By combining analytic and numerical tools we can find analytic conjectures for these coefficients. This leads to analytic expressions for the correlators and hence we deem the model solved.

In this talk, we will present a unified Fermi-gas framework for computing BPS observables in ABJM theory on S^3. Supersymmetric localization reduces the problem to an interacting matrix model that can be interpreted as a one-dimensional ideal Fermi gas, whose dynamics is encoded in a set of TBA-like equations. We will show that these equations enable a non-perturbative bootstrap approach that systematically captures the instanton sectors of the free energy and winding Wilson loops. As applications, we will provide an analytic proofs of several previously conjectural formulas and derive closed-form expressions, valid at arbitrary winding number, for the leading membrane- and worldsheet-instanton corrections to the 1/6- and 1/2-BPS  Wilson loops.

We are interested in the problem of understanding the structure of the Bethe roots for the periodic spin-1/2 Heisenberg XXZ chain. To probe this structure it is fruitful to study what happens as one varies the parameters. We start with the (ferromagnetic) Ising limit ∆ → ∞, in which ​the Bethe roots become explicit, and strings of Bethe roots become directly visible on the lattice, already examined by Gaudin. Despite the simplicity of the limiting model, there are some subtleties in the limit. Next we study what happens with the explicit Ising Bethe roots as ∆ is lowered, where bound states may form or unbind. I will present a ‘critical equation’ that determines when Bethe roots switch between real and complex for the sector with M = 2 magnons, generalising Essler–Korepin–Schoutens (1992, ∆ = 1) and Imoto–Sato–Deguchi (2019, ∆ ≥ 1), and discuss some results for M > 2. If time allows, I will outline how a similar game can be played by turning on long-range interactions, going from Heisenberg XXX, via the Inozemtsev chain, to the Haldane-Shasatry chain.

This is based on joint work J.-S. Caux and R. Koch, to appear, and with R. Klabbers (2022).

We study the long-time, large-distance asymptotic behaviour of dynamical two-point correlation functions of the Lieb–Liniger model in the limit of infinite repulsion (the one-dimensional impenetrable Bose gas). Starting with exact representations of correlation functions in terms of Fredholm determinants of an integrable integral operator, we perform the rigorous asymptotic analysis, using Riemann–Hilbert techniques. The integral operator
depends parametrically on time \(t\), distance \(x\) and on the filling fraction — a function that characterizes the thermal or non-thermal equilibrium conditions. We consider a large class of non-thermal equilibrium conditions, extending previous results established for the thermal equilibrium case. The long-time and large-distance asymptotic behaviour is derived for two classes of filling fractions. These classes are characterized by the number of poles on the real axis (a generalization of Fermi points) that, together with the unique saddle point, contribute to the asymptotic expansion. For each class, we derive the long-time, large-distance symptotic behaviour as a series in \(x\)^\(−1/2\) as \(x\) and \(t\) go to infinity for a fixed ratio \(x/t\). We provide explicit closed-form expressions for the leading and sub-leading terms, logarithmic corrections, and overall constants in terms of special functions and simple integrals. For the impenetrable Bose gas in thermal equilibrium, we verify the derived asymptotic expansions by comparing them with the existing results in the literature and with numerical data.
This talk is based on joint work with Frank Göhmann, Karol K. Kozlowski, and Alexander Weiße.

After describing elastic interactions and the discovery of the odderon by the TOTEM and D0 Collaborations, we will discuss new kinematical regimes where the gluon density in the proton or Pb can be very large which leads to new equations in Quantum Chromodynamics.  We will also present the latest expectations on beyond standard model physics and especially the production of axion-like particles using intact protons after the collision.  We will finish by describing briefly the Low Gain Avalanche Detectors and their applications in medicine for cancer treatment and with NASA to measure cosmic rays.