Higher derivative fermionic field theories

Fusion algebras of fermionic rational conformal field theories via a generalized Verlinde formula

We extend to a non-Hermitian fermionic quantum field theory with PT symmetry our previous discussion of second quantization, discrete symmetry transformations, and inner products in a scalar field theory [arXiv:2006.06656]. For illustration, we consider a prototype model containing a single Dirac fermion with a parity-odd, anti-Hermitian mass term. In the phase of unbroken PT symmetry, this Dirac fermion model is equivalent to a Hermitian theory under a similarity transformation, with the non-Hermitian nature of the model residing only in the spinor structure, whereas the algebra of the creation and annihilation operators is just that of a Hermitian theory.

The dimer tiling problem asks in how many ways can the edges of a graph be covered by dimers so that each site is covered once. In the special case of a planar graph, this problem has a solution in terms of a free fermionic field theory. We rediscover and explore an expression for the number of coverings of an arbitrary graph by arbitrary objects in terms of an interacting fermionic field theory first proposed by Samuel. Generalizations of the dimer tiling problem, which we call “dimer piling problems,” demand that each site be covered N times by indistinguishable dimers. Our field theory provides a solution of these problems in the large-N limit. We give a similar path integral representation for certain lattice coloring problems. Published by the American Physical Society 2024

The quantum null energy condition (QNEC) is a quantum generalization of the null energy condition, which gives a lower bound on the null energy in terms of the second derivative of the von Neumann entropy or entanglement entropy of some region with respect to a null direction. The QNEC states that $⟨{T}_{kk}{⟩}_{p}\ensuremath{\ge}{\mathrm{lim}}_{A\ensuremath{\rightarrow}0}(\frac{\ensuremath{\hbar}}{2\ensuremath{\pi}A}{S}_{\mathrm{out}}^{\ensuremath{'}\ensuremath{'}})$, where ${S}_{\mathrm{out}}$ is the entanglement entropy restricted to one side of a codimension-2 surface $\mathrm{\ensuremath{\Sigma}}$, which is deformed in the null direction about a neighborhood of point $p$ with area $A$. A proof of QNEC has been given before, which applies to free and super-renormalizable bosonic field theories, and to any points that lie on a stationary null surface. Using similar assumptions and methods, we prove the QNEC for fermionic field theories.

Studying quantum field theories numerically on the continuum and a new look at perturbation theory

In this paper we provide exact expressions for propagators of noncommutative Bosonic or Fermionic field theories after adding terms of the Grosse-Wulkenhaar type to the usual free action in order to ensure Langmann–Szabo covariance. We emphasize the new Fermionic case and we give in particular all necessary bounds for the multiscale analysis and renormalization of the noncommutative Gross-Neveu model.

Conformal embeddings and hidden symmetries of free fermion theories

We construct Schrödinger-like solutions of the Vasiliev higher spin theory in dimension. Symmetries of such solutions and the linearized equation of motion for the scalar on such backgrounds are analyzed. We further propose Galilean invariant bosonic and fermionic field theories that could be dual to the two parity invariant higher spin theories on the Schrödinger-like background respectively. The discussion is phrased mainly in D = 4 dimension, while similar constructions follow straightforwardly in higher dimensions.

We investigate two measures of quantum correlations and entanglement, namely\nthe violation of the Bell-Mermin-Klyshko inequalities and the quantum discord,\nfor Dirac fermions in the cosmological de Sitter background of dimension four.\nThe BMK violation is focussed on the vacuum for two and four mode squeezed\nstates and it is shown to increase with the number of modes. For the quantum\ndiscord, we investigate a maximally entangled in-vacuum state. Qualitative\nsimilarities as well as differences of our results with that of different\ncoordinatisations of de Sitter in the context of scalar and fermionic field\ntheory is discussed.\n

We numerically analyze the feasibility of a platform-neutral, general strategy to perform quantum simulations of fermionic lattice field theories under open boundary conditions. The digital quantum simulator requires solely one- and two-qubit gates and is scalable since integrating each Hamiltonian term requires a finite (non-scaling) cost. The exact local fermion encoding we adopt relies on auxiliary Z2 lattice gauge fields by adding a pure gauge Hamiltonian term akin to the Toric Code. By numerically emulating the quantum simulator real-time dynamics, we observe a timescale separation for spin- and charge-excitations in a spin-12 Hubbard ladder in the t−J model limit.

For a two-dimensional field theory of bosons and fermions, the author constructs, using Dirac's method, the quantum theory around finite-energy classical solutions with arbitrary bosonic and fermionic parameters. Quantisation around a space-translated and a supertranslated solution of a supersymmetric field theory is a special case of our treatment.

Two-dimensional conformal field theory for disordered systems at criticality

In many quantum quench experiments involving cold atom systems the post-quench phase can be described by a quantum field theory of free scalars or fermions, typically in a box or in an external potential. We will study mass quench of free scalars in arbitrary spatial dimensions d with particular emphasis on the rate of relaxation to equilibrium. Local correlators expectedly equilibrate to GGE; for quench to zero mass, interestingly the rate of approach to equilibrium is exponential or power law depending on whether d is odd or even respectively. For quench to non-zero mass, the correlators relax to equilibrium by a cosine-modulated power law, for all spatial dimensions d, even or odd. We briefly discuss generalization to O(N ) models.

Due to an accidentally large s-wave scattering length, in a relatively wide range of energy, neutrons are approximately described by the nonrelativistic conformal field theory of unitarity fermions, perturbed by one relevant and an infinite number of irrelevant operators. We develop a formalism which provides a nonperturbative definition of local operators in that nonrelativistic conformal field theory. We compute the scattering-length and effective-range corrections to the two-point functions of primary charge-three operators using the technique of conformal perturbation theory. These calculations allow us to find the first corrections to the scale-invariant behavior of the rate of nuclear reactions with three neutrons in the final state in the regime when the neutrons have small relative momenta. Published by the American Physical Society 2024

Using the semiclassical functional method developed by Dashen, Hasslacher, and Neveu, the classical localized solutions for the bound states of massive fermions in two-dimensional field theories are quantized. The mass spectra of the bound states are then obtained. For the massive Gross-Neveu model, the mass spectrum agrees with what has been found by Dashen et al. for the massless Gross-Neveu model where fermions acquire mass through dynamical symmetry breaking. For a theory of massive fermions with scalar as well as pseudoscalar Fermi interactions, the mass spectrum is found to be very similar to that for the doublet in the sine-Gordon equation. In fact, under certain conditions they become identical.