MIT Center for Theoretical Physics – a Leinweber Institute

In his 1976 paper “More about the massive Schwinger model”, Coleman introduced $1+1$-dimensional Quantum Electrodynamics coupled to two charged massive fermions. By applying Abelian bosonization, he elucidated much of the physics of this two-flavor Schwinger model, but he listed three puzzles at the end of his paper. We present new analytical and numerical calculations to solve Coleman’s three puzzles and thereby deepen our understanding of this model. These puzzles pertain to the theory with equal fermion masses at $θ= 0$ and at $θ= π$, as well as the size of isospin-breaking effects when the fermion masses are unequal. For the puzzle at $θ= π$, the solution is related to the structure of the zero-temperature phase diagram arXiv:2305.04437: for equal fermion masses $m$, the model exhibits spontaneous breaking of charge conjugation symmetry and absence of confinement for any value of the gauge coupling $g$, so that there is a smooth interpolation from weak to strong coupling. Using two-loop Renormalization Group and integrability methods, we show that the mass gap behaves as $\sim m e^{-0.111 g^2/m^2}$ in the strong coupling regime $m\ll g$. Our numerical results using the lattice Hamiltonian are in good agreement with this behavior. For the puzzle at $θ= 0$, the solution is related to a level crossing between two isosinglet particles with different discrete quantum numbers; we demonstrate the necessity of such a crossing by comparing integrability and weak coupling calculations, and we also exhibit the crossing numerically. Finally, we provide a new estimate for the size of isospin-breaking effects caused by different fermion masses at strong coupling.

Recent developments have shown that some semiclassical spacetimes cannot emerge from a traditional application of the rules of holography, prompting proposals for restoring their emergence with “observer rules”. In this paper, we propose a general semiclassical diagnostic of such failures of emergence, and of the extent to which observer rules can fix them. Our diagnostic is the presence of certain “evanescent” quantum extremal surfaces, which are distinguished by an upper bound on their area rather than their generalized entropy. In particular, the generalized entropy of an evanescent QES may be large: even though its area term must be small, its bulk entanglement term is unconstrained. This feature is explained by an operational distinction between classical and quantum connectivity in semiclassical gravity, or equivalently between the two summands of the generalized entropy.

We prove a singularity theorem in semiclassical gravity without assuming global hyperbolicity or the null energy/curvature condition; the former is replaced by the weaker causality conditions of stable causality and past reflectivity, and the latter is replaced as is standard by the Generalized Second Law. This establishes in particular that the standard models of evaporating black holes are singular – i.e. they are null geodesically incomplete.

The annihilation of self-interacting dark matter with long-range interactions can be significantly enhanced at low velocities through the Sommerfeld effect. At special points in parameter space, where near-zero-energy resonances exist in the spectrum of the theory, the standard calculation of this enhancement appears to violate unitarity. Recently, several approaches have been proposed to regulate this behavior, some introducing explicit ultraviolet (UV) scales and others not, raising the question of whether these prescriptions are consistent. In this paper, we compare these approaches and show that even in nominally cutoff-dependent methods, the regulated Sommerfeld-enhanced cross sections are independent of the UV regulator to a good approximation, and that when the unitarity-preserving corrections are large, the regulation schemes coincide to leading order. We use these insights to write down a regulator-independent prescription for unitarization applicable to multi-state systems, where the modified enhancement can be written solely in terms of the standard enhancement factor, the hard annihilation amplitude, and the $S$-matrix for scattering in the long-range potential.