Mathematical Physics
We provide a systematic and rigorous geometric framework that relates three structures naturally associated to BPS central charges in $\mathcal{N}=2$ supersymmetric gauge theories: the split attractor flow (SAF) of $|Z|$, the Hessian flow…
We propose a cohomological approach to computing the conformal anomaly. Using the example of current-current deformations of two-dimensional conformal field theories, we reproduce the well-known Cardy formula for the leading contribution to…
We solve large-$N$ Yang--Mills theory on $\mathbb{Z}^d$, for every $d\geq2$, at strong coupling, for structure group $\mathrm{U}(N)$ and for the heat-kernel action. More precisely, we prove that normalized Wilson loop expectations have…
This paper provides an isomorphism between the space of twisted gauge fields on a principal bundle $\mathcal{P}$ and the space of standard gauge fields on a different principal bundle $\mathcal{Q}$ associated to $\mathcal{P}$. This…
We study metric representations in finite-dimensional non-Hermitian quantum mechanics. The main purpose of this work is to emphasize that the physical description of a non-Hermitian system may be formulated in different, but isomorphic,…
In this note, we prove that the two-dimensional Blume-Emery-Griffiths model at the triple point Ferromagnetic-Antiquadrupolar-Disordered (FAD) has a unique Gibbs measure at any temperature, thereby establishing the absence of phase…
In this paper, we introduce and demonstrate a simple geometric algorithm to determine which critical points, both complex as well as real, contribute to the asymptotic evaluation of multiple integrals with exponential integrands of the form…
We compute the transitive realizations for the low dimensional cases of real Lie algebras up to dimension four using Shirokov's method. First, the generic realizations are given, then, making use of the known list of subalgebras, nongeneric…
A Gibbs point process models particles interacting in the continuum through a potential. Among the most classical examples is the hard-sphere model, where given an activity parameter $\lambda$, a radius $r$, and a bounded set $\Lambda…
We prove explicit upper bounds on the propagation velocity of one-dimensional quantum walks with periodic coins of arbitrary period. We treat two complementary settings. First, in a perturbative regime where one transmission parameter is…
Octonions and split-octonions have been used to express the Dirac equation in physics in several conceptually distinct ways. This review sorts them into four groups: the 2-factor (direct-product), 3-factor, and projection representations,…
We construct the causal fermion system for globally hyperbolic spacetimes starting in the framework of algebraic quantum field theory. The fermionic projector is identified with the one-particle density operator of a quasi-free Hadamard…
We study the Dirac equation in the Reissner-Nordstr\"om geometry in horizon-penetrating coordinates up to the Cauchy horizon. A mass decomposition theorem is proved, which gives a covariant representation of the spacetime inner product that…
This note studies the quantized corner structure of four-dimensional $BF$ theory, classifies the associated free and physical corner algebras and constructs possible representations. In the abelian case, for arbitrary closed oriented…
We study a determinantal Coulomb gas in the complex plane associated with the external potential $$ Q(z)=\frac{1}{1-\tau^2}\big(|z|^2-\tau \text{Re } z^2\big)-2c\log|z-a|, $$ where $\tau\in[0,1)$, $c\ge0$, and $a\ge0$. In the regimes where…
It is well known that band inversion across a straight interface in a periodic medium gives rise to interface modes that are localized near the interface and propagate along it inside the bulk spectral gap. This phenomenon constitutes the…
We investigate constrained quantum motion on curves and surfaces using connection factorization methods. We show that Laplace operators admit an exact half-connection factorization generated by connection one-forms. The first-order part of…
Timelike Liouville field theory is a candidate model for positive curvature two-dimensional quantum gravity, but a mathematically controlled Lorentzian formulation has remained elusive. In this paper we construct the theory on the cylinder…
In the Bohr model of the hydrogen atom, the energy levels are a negative constant divided by the square of the level number. It is well known that special pairs of transitions exist that have the same energy difference, and a systematic…
We consider a certain first-order linear system of ordinary differential equations, and we analyze the direct and inverse scattering problems for that linear system. The linear system involves two potentials in the Schwartz class, and those…