Philine van Vliet

We investigate the one-dimensional Ising model with long-range interactions decaying as 1/r^{1+s} 1 / r 1 + s . In the critical regime, for 1/2 ≤ s ≤ 1 1 / 2 ≤ s ≤ 1 , this system realizes a family of nontrivial one-dimensional conformal field theories (CFTs), whose data vary continuously with s s . For s;gt1 s > 1 the model has instead no phase transition at finite temperature, as in the short-range case. In the standard field-theoretic description, involving a generalized free field with quartic interactions, the critical model is weakly coupled near s=1/2 s = 1 / 2 but strongly coupled in the vicinity of the short-range crossover at s=1 s = 1 . We introduce a dual formulation that becomes weakly coupled as s \to 1 s → 1 . Precisely at s=1 s = 1 , the dual description becomes an exactly solvable conformal boundary condition of the two-dimensional free scalar. We present a detailed study of the dual model and demonstrate its effectiveness by computing perturbatively the CFT data near s=1 s = 1 , up to next-to-next-to-leading order in 1-s 1 − s , by two independent approaches: (i) standard renormalization of our dual field-theoretic description and (ii) the analytic conformal bootstrap. The two methods yield complete agreement.

We study the 1D Ising model with long-range interactions decaying as 1 / r 1 + s . The critical model corresponds to a family of 1D conformal field theories whose data depend nontrivially on s in the range 1 / 2 ≤ s ≤ 1 . The model is known to be described by a generalized free field with quartic interaction, which is weakly coupled near s = 1 / 2 but strongly coupled near the short-range crossover at s = 1 . We propose a dual description that becomes weakly coupled at s = 1 . At s = 1 , our model becomes an exactly solvable conformal boundary condition for the 2D free scalar. We perform a number of consistency checks of our proposal and calculate the perturbative conformal field theory data around s = 1 analytically using both (1) our proposed field theory and (2) the analytic conformal bootstrap. Our results show complete agreement between the two methods. Published by the American Physical Society 2025

Scalar-fermion models, such as the Gross-Neveu-Yukawa model, admit natural 1d defects given by the exponential of a scalar field integrated along a straight line. In 4 − ε dimensions the defect coupling is weakly relevant and the setup defines a non-trivial interacting defect CFT. In this work we study correlation functions on these defect CFTs to order ε. We focus on 1d correlators constrained to the line, which include canonical operators like the displacement and the one-dimensional analog of the spin field. These results give access to perturbative CFT data that can be used as input in the numerical bootstrap. We also consider local operators outside the line, in particular two-point functions of scalars whose dynamics are non-trivial due to the presence of the defect.

We explore a supersymmetric (SUSY) theory that arises in the Landau level problem with disorder. Charged particles in a strong magnetic field and a local potential are described by small excitations around the ground state, the lowest Landau level (LLL). Around forty years ago Brézin, Gross and Itzykson showed that for a disorder potential certain observables in the LLL limit are described by a chiral SUSY theory. As a consequence, the problem undergoes a dimensional reduction by two dimensions, simplifying the computations. We generalize their findings by identifying the chiral SUSY as a special limit of a `magnetic Parisi-Sourlas (PS)' theory. The latter is a modification of the theories associated to fixed points of random field models. We show that the SUSY features extend to a much larger class of observables and to higher Landau levels. Finally we identify a set of new super-Ward identities and show how observables in the disordered theory must satisfy them.

We combine perturbation theory with analytic and numerical bootstrap techniques to study the critical point of the long-range Ising (LRI) model in two and three dimensions. This model interpolates between short-range Ising (SRI) and mean-field behaviour. We use the Lorentzian inversion formula to compute infinitely many three-loop corrections in the two-dimensional LRI near the mean-field end. We further exploit the exact OPE relations that follow from bulk locality of the LRI to compute infinitely many two-loop corrections near the mean-field end, as well as some one-loop corrections near SRI. By including such exact OPE relations in the crossing equations for LRI we set up a very constrained bootstrap problem, which we solve numerically using SDPB. We find a family of sharp kinks for two- and three-dimensional theories which compare favourably to perturbative predictions, as well as some Monte Carlo simulations for the two-dimensional LRI.

The phenomenon of B⁰ _q – B ¯ q 0 mixing (q = d, s) provides a sensitive probe for physics beyond the Standard Model (SM). We explore the corresponding space for New Physics left through the current data, having a careful look at analyses of the Unitarity Triangle that are needed for the SM predictions of the B _q mixing parameters. In particular, we explore the impact of tensions between inclusive and exclusive determinations of the CKM matrix elements ∣V _ub ∣ and ∣V _cb ∣. Moreover, we focus on the angle γ of the Unitarity Triangle, comparing measurements from B → DK and B → π π, ρ π, ρ ρ decays, where the latter are typically interpreted in terms of the angle α. We discuss various scenarios and present the corresponding state-of-the-art constraints on the New Physics parameters of B _q ⁰– B ¯ q 0 mixing. We point out that these results have an interesting application in the analysis of rare B q 0 → μ + μ − decays, allowing us to minimise the impact of CKM parameters in the search for New Physics. In view of the high-precision era, we make future projections. Interestingly, we find that for the extraction of the New Physics parameters in the B _d system the determination of the apex of the Unitarity Triangle results in a key limiting factor. By contrast, the corresponding impact is negligible for the B _s system, making it a promising candidate to reveal sources of New Physics.

We use the numerical bootstrap to study conformal line defects with O(2) global symmetry. Our results are very general and capture in particular conformal line defects originating from bulk CFTs with a continuous global symmetry, which can either be preserved or partially broken by the presence of the defect. We begin with an agnostic approach and perform a systematic bootstrap study of correlation functions between two canonical operators on the defect: the displacement and the tilt. We then focus on two interesting theories: a monodromy line defect and a localized magnetic field line defect. To this end, we combine the numerical bootstrap with the ε-expansion, where we complement existing results in the literature with additional calculations. For the monodromy defect our numerical results are consistent with expectations, with known analytic solutions sitting inside our numerical bounds. For the localized magnetic field line defect our plots show a series of intriguing cusps which we explore.