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Arguably, the simplest chiral gauge theories are SO(10) with 𝑁 𝑓 fermion fields in the spinor representation 𝟏𝟔. We study their dynamics using their supersymmetric limits perturbed by an infinitesimal anomaly mediated supersymmetry breaking as a guide. We predict the theory is gapped for 𝑁 𝑓 = 1, 2, while the SU(𝑁 𝑓 ) global symmetry is broken to SO(N 𝑓 ) for moderately large 𝑁 𝑓 ≥ 3.
We show how to construct Hamiltonian lattice theories with one exact supersymmetry on arbitrary triangulations of curved space in any number of dimensions. Both bosons and fermions satisfy discrete Kähler-Dirac equations. The quantization of the fermions proceeds by imposing conventional anticommutation relations while the bosons require a modification of the usual canonical commutator. On regular lattices we construct parity, time reversal and translation-by-one (shift) symmetries. We argue that the latter are generically noninvertible symmetries. We also show how to couple these degrees of freedom to background gauge fields which leads to a theory with enhanced supersymmetry.
In this paper, we present PyCDFT, a Python package to compute diabatic states using constrained density functional theory (CDFT). PyCDFT provides an object-oriented, customizable implementation of CDFT, and allows for both single-point self-consistent-field calculations and geometry optimizations. PyCDFT is designed to interface with existing density functional theory (DFT) codes to perform CDFT calculations where constraint potentials are added to the Kohn–Sham Hamiltonian. Here, we demonstrate the use of PyCDFT by performing calculations with a massively parallel first-principles molecular dynamics code, Qbox, and we benchmark its accuracy by computing the electronic coupling between diabatic states for a set of organic molecules. We show that PyCDFT yields results in agreement with existing implementations and is a robust and flexible package for performing CDFT calculations. The program is available at https://dx.doi.org/10.5281/zenodo.3821097.
Abstract The filtered lifting line theory is an analytical approach used to solve the equations of flow subjected to body forces with a Gaussian distribution, such as used in the actuator line model. In the original formulation, the changes in chord length along the blade were assumed to be small. This assumption can lead to errors in the induced velocities predicted by the theory compared to full solutions of the equations. In this work, we revisit the original derivation and provide a more general formulation that can account for significant changes in chord along the blade. The revised formulation can be applied to wings with significant changes in chord along the span, such as wind turbine blades.
We present a complete model of a dark QCD sector with light dark pions, broadly motivated by hidden naturalness arguments. The dark quarks couple to the Standard Model via irrelevant Z- and Higgs-portal operators, which encode the low-energy effects of TeV-scale fermions interacting through Yukawa couplings with the Higgs field. The dark pions, depending on their CP properties, behave as either composite axion-like particles (ALPs) mixing with the Z or scalars mixing with the Higgs. The dark pion lifetimes fall naturally in the most interesting region for present and proposed searches for long-lived particles, at the LHC and beyond. This is demonstrated by studying in detail three benchmark scenarios for the symmetries and structure of the theory. Within a coherent framework, we analyze and compare the GeV-scale signatures of flavor-changing meson decays to dark pions, the weak-scale decays of Z and Higgs bosons to hidden hadrons, and the TeV-scale signals of the ultraviolet theory. New constraints are derived from B decays at CMS and from Z-initiated dark showers at LHCb, focusing on the displaced dimuon signature. We also emphasize the strong potential sensitivity of ATLAS and CMS to dark shower signals with large multiplicities and long lifetimes of the dark pions. As a key part of our phenomenological study, we perform a new data-driven calculation of the decays of a light ALP to exclusive hadronic Standard Model final states. The results are provided in a general form, applicable to any model with arbitrary flavor-diagonal couplings of the ALP to fermions.
We compute the stress-tensor two-point function in three-dimensional Yang-Mills theory to three-loops in perturbation theory. Using its calculable shape at high momenta, we test the notion that its Borel transform is saturated at low energies by the lowest glueball state(s). This assumption provides relatively stable estimates for the mass of the lightest glueball that we compare with lattice simulations. We also provide estimates for the coupling of the lightest glueball to the stress tensor. Along the way, we comment on the extent that such estimates are non-rigorous. Lastly, we discuss the possibility of applying the sum-rule analysis to two-point functions of higher-spin operators and obtain a crude approximation for the glueball couplings to these operators.
In perturbative string theory, one is generally interested in asymptotic observables, such as the S-matrix in flat spacetime, and boundary correlation functions in anti-de Sitter spacetime. However, there are backgrounds in which such observables do not exist. We study examples of such backgrounds in 1 + 1 dimensional string theory. In these examples, the Liouville wall accelerates and can become spacelike in the past and/or future. When that happens, the corresponding null infinity, at which the standard scattering states are defined, is shielded by the Liouville wall. We compute scattering and particle production amplitudes in these backgrounds in the region in parameter space where the wall remains timelike, and discuss the continuation of this picture to the spacelike regime. We also discuss the physics from the point of view of the dynamics of free fermions in backgrounds with a time-dependent Fermi surface.
Electronic excitations in atomic, molecular, and crystal targets are at the forefront of the ongoing search for light, sub-GeV dark matter (DM). In many light DM-electron interactions the energy and momentum deposited is much smaller than the electron mass, motivating a non-relativistic (NR) description of the electron. Thus, for any target, light DM-electron phenomenology relies on understanding the interactions between the DM and electron in the NR limit. In this work we derive the NR effective field theory (EFT) of general DM-electron interactions from a top-down perspective, starting from general high-energy DM-electron interaction Lagrangians. This provides an explicit connection between high-energy theories and their low-energy phenomenology in electron excitation based experiments. Furthermore, we derive Feynman rules for the DM-electron NR EFT, allowing observables to be computed diagrammatically, which can systematically explain the presence of in-medium screening effects in general DM models. We use these Feynman rules to compute absorption, scattering, and dark Thomson scattering rates for a wide variety of high-energy DM models.
We develop an effective field theory (EFT) framework for superfluid 4 He to model the interactions among quasiparticles, helium atoms and probe particles. Our effective field theory approach brings together symmetry arguments and power-counting and matches to classical fluid dynamics. We then present the decay and scattering rates for the relevant processes involving quasiparticles and helium atoms. The presented EFT framework and results can be used to understand the dynamics of thermalization in the superfluid, and can be further applied to sub-GeV dark matter direct detection with superfluid 4 He.
We introduce and study generalized Rényi entropies defined through the traces of products of Tr B (| Ψ i $\rangle$$\langle$Ψ j | ) where |Ψ i $\rangle$ are eigenstates of a two-dimensional conformal field theory (CFT). When |Ψ i $\rangle$ = |Ψ j $\rangle$ these objects reduce to the standard Rényi entropies of the eigenstates of the CFT. Exploiting the path integral formalism, we show that the second generalized Rényi entropies are equivalent to four point correlators. We then focus on a free bosonic theory for which the mode expansion of the fields allows us to develop an efficient strategy to compute the second generalized Rényi entropy for all eigenstates. As a byproduct, our approach also leads to new results for the standard Rényi and relative entropies involving arbitrary descendent states of the bosonic CFT.
A large class of Λ < 0 cosmologies have big-bang/big crunch spacetimes with time-symmetric backgrounds and asymptotically AdS Euclidean continuations suggesting a possible holographic realization. We argue that these models generically have time-dependent scalar fields, and these can lead to realistic cosmologies at the level of the homogeneous background geometry, with an accelerating phase prior to the turnaround and crunch. We first demonstrate via explicit effective field theory examples that models with an asymptotically AdS Euclidean continuation can also exhibit a period of accelerated expansion without fine tuning. We then show that certain significantly more tuned examples can give predictions arbitrarily close to a ΛCDM model. Finally, we demonstrate via an explicit construction that the potentials of interest can arise from a superpotential, thus suggesting that these solutions may be compatible with an underlying supersymmetric theory.
We establish the existence of an infinite-dimensional fermionic symmetry in four-dimensional supersymmetric gauge theories by analyzing semiclassical photino dynamics in abelian $\mathscr{N}$ = 1 theories with charged matter. The symmetry is parametrized by a spinor-valued function on an asymptotic S2 at null infinity. It is not manifest at the level of the Lagrangian, but acts non-trivially on physical states, and its Ward identity is the soft photino theorem. The infinite-dimensional fermionic symmetry resides in the same $\mathscr{N}$ = 1 supermultiplet as the physically non-trivial large gauge symmetries associated with the soft photon theorem.
We review recent theoretical developments concerning the definition and the renormalization of equal-time correlators that can be computed on the lattice and related to Parton Distribution Functions (PDFs) through a factorization formula. We show how these objects can be studied and analyzed within the framework of a nongauge theory, gaining insight through a one-loop computation. We use scalar field theory as a playground to revise, analyze and present the main features of these ideas, to explore their potential, and to understand their limitations for extracting PDFs. We then propose a framework that would allow to include the available lattice QCD data in a global analysis to extract PDFs.
If dark matter has strong self-interactions, future astrophysical and cosmological observations, together with a clearer understanding of baryonic feedback effects, might be used to extract the velocity dependence of the dark matter scattering rate. To interpret such data, we should understand what predictions for this quantity are made by various models of the underlying particle nature of dark matter. In this paper, we systematically compute this function for fermionic dark matter with light bosonic mediators of vector, scalar, axial vector, and pseudoscalar type. We do this by matching to the nonrelativistic effective theory of self-interacting dark matter and then computing the spin-averaged viscosity cross section nonperturbatively by solving the Schrödinger equation, thus accounting for any possible Sommerfeld enhancement of the low-velocity cross section. In the pseudoscalar case, this requires a coupled-channel analysis of different angular momentum modes. We find, contrary to some earlier analyses, that nonrelativistic effects only provide a significant enhancement for the cases of light scalar and vector mediators. Scattering from light pseudoscalar and axial vector mediators is well described by tree-level quantum field theory.
We study the N-point Coon amplitude discovered first by Baker and Coon in the 1970s and then again independently by Romans in the 1980s. This Baker-Coon-Romans (BCR) amplitude retains several properties of tree-level string amplitudes, namely duality and factorization, with a q-deformed version of the string spectrum. Although the formula for the N-point BCR amplitude is only valid for q > 1, the four-point case admits a straightforward extension to all q ≥ 0 which reproduces the usual expression for the four-point Coon amplitude. At five points, there are inconsistencies with factorization when pushing q < 1. Despite these issues, we find a new relation between the five-point BCR amplitude and Cheung and Remmen’s four-point basic hypergeometric amplitude, placing the latter within the broader family of Coon amplitudes. Finally, we compute the q → ∞ limit of the N-point BCR amplitudes and discover an exact correspondence between these amplitudes and the field theory amplitudes of a scalar transforming in the adjoint representation of a global symmetry group with an infinite set of non-derivative single-trace interaction terms. This correspondence at q = ∞ is the first definitive realization of the Coon amplitude (in any limit) from a field theory described by an explicit Lagrangian.
Using the second law of local thermodynamics and the first-order Palatini formalism, we formulate relativistic spin hydrodynamics for quantum field theories with Dirac fermions, such as QED and QCD, in a torsionful curved background. We work in a regime where spin density, which is assumed to relax much slower than other non-hydrodynamic modes, is treated as an independent degree of freedom in an extended hydrodynamic description. Spin hydrodynamics in our approach contains only three non-hydrodynamic modes corresponding to a spin vector, whose relaxation time is controlled by a new transport coefficient: the rotational viscosity. We study linear response theory and observe an interesting mode mixing phenomenon between the transverse shear and the spin density modes. We propose several field-theoretical ways to compute the spin relaxation time and the rotational viscosity, via the Green-Kubo formula based on retarded correlation functions.
The geometry of field space governs on-shell scattering amplitudes. We formulate a geometric description of effective field theories which extends previous results for scalars and gauge fields to fermions. The field-space geometry reorganizes and simplifies the computation of quantum loop corrections. Using this geometric framework, we calculate the fermion loop contributions to the renormalization group equations for bosonic operators in the Standard Model Effective Field Theory up to mass dimension eight.
We perform a comprehensive analysis of the symmetry-resolved (SR) entanglement entropy (EE) for one single interval in the ground state of a 1 + 1D conformal field theory (CFT), that is invariant under an arbitrary finite or compact Lie group, G. We utilize the boundary CFT approach to study the total EE, which enables us to find the universal leading order behavior of the SREE and its first correction, which explicitly depends on the irreducible representation under consideration and breaks the equipartition of entanglement. We present two distinct schemes to carry out these computations. The first relies on the evaluation of the charged moments of the reduced density matrix. This involves studying the action of the defect-line, that generates the symmetry, on the boundary states of the theory. This perspective also paves the way for discussing the infeasibility of studying symmetry resolution when an anomalous symmetry is present. The second scheme draws a parallel between the SREE and the partition function of an orbifold CFT. This approach allows for the direct computation of the SREE without the need to use charged moments. From this standpoint, the infeasibility of defining the symmetry-resolved EE for an anomalous symmetry arises from the obstruction to gauging. Finally, we derive the symmetry-resolved entanglement spectra for a CFT invariant under a finite symmetry group. We revisit a similar problem for CFT with compact Lie group, explicitly deriving an improved formula for U(1) resolved entanglement spectra. Using the Tauberian formalism, we can estimate the aforementioned EE spectra rigorously by proving an optimal lower and upper bound on the same. In the abelian case, we perform numerical checks on the bound and find perfect agreement.