Stochastic fluctuations of bosonic dark matter

Numerous theories extending beyond the standard model of particle physics predict the existence of bosons that could constitute dark matter. In the standard halo model of galactic dark matter, the velocity distribution of the bosonic dark matter field defines a characteristic coherence time τc. Until recently, laboratory experiments searching for bosonic dark matter fields have been in the regime where the measurement time T significantly exceeds τc, so null results have been interpreted by assuming a bosonic field amplitude Φ0 fixed by the average local dark matter density. Here we show that experiments operating in the T ≪ τc regime do not sample the full distribution of bosonic dark matter field amplitudes and therefore it is incorrect to assume a fixed value of Φ0 when inferring constraints. Instead, in order to interpret laboratory measurements (even in the event of a discovery), it is necessary to account for the stochastic nature of such a virialized ultralight field. The constraints inferred from several previous null experiments searching for ultralight bosonic dark matter were overestimated by factors ranging from 3 to 10 depending on experimental details, model assumptions, and choice of inference framework.

Excited state Rényi entropy and subsystem distance in two-dimensional non-compact bosonic theory. Part II. Multi-particle states

We study the excited state Rényi entropy and subsystem Schatten distance in the two-dimensional free massless non-compact bosonic field theory, which is a conformal field theory. The discretization of the free non-compact bosonic theory gives the harmonic chain with local couplings. We consider the field theory excited states that correspond to the harmonic chain states with excitations of more than one quasiparticle, which we call multi-particle states. This extends the previous work by the same authors to more general excited states. In the field theory we obtain the exact Rényi entropy and subsystem Schatten distance for several low-lying states. We obtain short interval expansion of the Rényi entropy and subsystem Schatten distance for general excited states, which display different universal scaling behaviors in the gapless and extremely gapped limits of the non-compact bosonic theory. In the locally coupled harmonic chain we calculate numerically the excited state Rényi entropy and subsystem Schatten distance using the wave function method. We find excellent matches of the analytical results in the field theory and numerical results in the gapless limit of the harmonic chain. We also make some preliminary investigations of the Rényi entropy and the subsystem Schatten distance in the extremely gapped limit of the harmonic chain.

Mass generation in the large N Gross-Neveu model: a constructive proof without intermediate field

We give a new constructive proof of the infrared behavior of the Euclidean Gross-Neveu model in two dimensions with small coupling and large component number N. Our argument does not rely on the use of an intermediate (auxiliary bosonic) field. Instead bubble series are resummed by hand, and determinant bounds replaced by a control of local factorials relying on combinatorial arguments and Pauli's principle. The discrete symmetry-breaking is ensured by considering the model directly with a mass counterterm chosen in such a way as to cancel tadpole diagrams. Then the fermion two-point function is shown to decay (quasi-)exponentially as in [12]/

Thermal Ionization for Short-Range Potentials

We study a concrete model of a confined particle in form of a Schrödinger operator with a compactly supported smooth potential coupled to a bosonic field at positive temperature. We show, that the model exhibits thermal ionization for any positive temperature, provided the coupling is sufficiently small. Mathematically, one has to rule out that zero is an eigenvalue of the self-adjoint generator of time evolution—the Liouvillian. This will be done by using positive commutator methods with dilations in the space of scattering functions. Our proof relies on a spatial cutoff in the coupling but does otherwise not require any unnatural restrictions.

An exact mapping between loop-erased random walks and an interacting field theory with two fermions and one boson

We give a simplified proof for the equivalence of loop-erased random walks to a lattice model containing two complex fermions, and one complex boson. This equivalence works on an arbitrary directed graph. Specifying to the dd-dimensional hypercubic lattice, at large scales this theory reduces to a scalar \phi^4ϕ4-type theory with two complex fermions, and one complex boson. While the path integral for the fermions is the Berezin integral, for the bosonic field we can either use a complex field \phi(x)\in \mathbb Cϕ(x)∈ℂ (standard formulation) or a nilpotent one satisfying \phi(x)^2 =0ϕ(x)2=0. We discuss basic properties of the latter formulation, which has distinct advantages in the lattice model.

Symmetry-enriched quantum spin liquids in (3 + 1)d

We use the intrinsic one-form and two-form global symmetries of (3+1)d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the 0-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in (2 + 1)d. We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative ’t Hooft anomaly for different couplings. We discuss several examples including the gapless pure U(1) gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in (3 + 1)d for SU(2) gauge theory with two adjoint Weyl fermions.

Conformal Field Theory of Free Bosonic and Fermionic Fields

Free theories are usually regarded as trivial examples of quantum systems. This chapter proves that this is not the case of the conformal field theories associated to the free bosonic and fermionic fields. The subject is not only full of beautiful mathematical identities but is also the source of deep physical concepts with far reaching applications. Chapter 12 also covers quantization of the bosonic field, vertex operators, the free bosonic field on a torus, modular transformations, the quantization of the free Majorana fermion, the Neveu–Schwarz and Ramond sectors, fermions on a torus, calculus for anti-commuting quantities and partition functions.