Field Theoretic Descriptions Research Articles

Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model

We consider supersymmetric surface defects in compactifications of the 6d6d minimal (D_{N+3},D_{N+3})(DN+3,DN+3) conformal matter theories on a punctured Riemann surface. For the case of N=1N=1 such defects are introduced into the supersymmetric index computations by an action of the BC_1\,(\sim A_1\sim C_1)BC1(∼A1∼C1) van Diejen model. We (re)derive this fact using three different field theoretic descriptions of the four dimensional models. The three field theoretic descriptions are naturally associated with algebras A_{N=1}AN=1, C_{N=1}CN=1, and (A_1)^{N=1}(A1)N=1. The indices of these 4d4d theories give rise to three different Kernel functions for the BC_1BC1 van Diejen model. We then consider the generalizations with N>1N>1. The operators introducing defects into the index computations are certain A_{N}AN, C_NCN, and (A_1)^{N}(A1)N generalizations of the van Diejen model. The three different generalizations are directly related to three different effective gauge theory descriptions one can obtain by compactifying the minimal (D_{N+3},D_{N+3})(DN+3,DN+3) conformal matter theories on a circle to five dimensions. We explicitly compute the operators for the A_NAN case, and derive various properties these operators have to satisfy as a consequence of 4d4d dualities following from the geometric setup. In some cases we are able to verify these properties which in turn serve as checks of said dualities. As a by-product of our constructions we also discuss a simple Lagrangian description of a theory corresponding to compactification on a sphere with three maximal punctures of the minimal (D_5,D_5)(D5,D5) conformal matter and as consequence give explicit Lagrangian constructions of compactifications of this 6d SCFT on arbitrary Riemann surfaces.

Non-Abelian anomalies in multi-Weyl semimetals

We construct the effective field theory for time-reversal symmetry breaking multi-Weyl semimetals (mWSMs), composed of a single pair of Weyl nodes of (anti-)monopole charge $n$, with $n=1,2,3$ in crystalline environment. From both the continuum and lattice models, we show that a mWSM with $n>1$ can be constructed by placing $n$ flavors of linearly dispersing simple Weyl fermions (with $n=1$) in a bath of an $SU(2)$ non-Abelian static background gauge field. Such an $SU(2)$ field preserves certain crystalline symmetry (four-fold rotational or $C_4$ in our construction), but breaks the Lorentz symmetry, resulting in nonlinear band spectra (namely, $E \sim (p^2_x + p^2_y)^{n/2}$, but $E \sim |p_z|$, for example, where momenta ${\bf p}$ is measured from the Weyl nodes). Consequently, the effective field theory displays $U(1) \times SU(2)$ non-Abelian anomaly, yielding anomalous Hall effect, its non-Abelian generalization, and various chiral conductivities. The anomalous violation of conservation laws is determined by the monopole charge $n$ and a specific algebraic property of the $SU(2)$ Lie group, which we further substantiate by numerically computing the regular and "isospin" densities from the lattice models of mWSMs. These predictions are also supported from a strongly coupled (holographic) description of mWSMs. Altogether our findings unify the field theoretic descriptions of mWSMs of arbitrary monopole charge $n$ (featuring $n$ copies of the Fermi arc surface states), predict signatures of non-Abelian anomaly in table-top experiments, and pave the route to explore anomaly structures for multi-fold fermions, transforming under arbitrary half-integer or integer spin representations.

Quantum spin quadrumer

A fundamental motif in frustrated magnetism is the fully mutually coupled cluster of $N$ spins, with each spin coupled to every other spin. Clusters with $N=2$ and $3$ have been extensively studied as building blocks of square and triangular lattice antiferromagnets. In both cases, large-$S$ semiclassical descriptions have been fruitfully constructed, providing insights into the physics of macroscopic magnetic systems. Here, we develop a semiclassical theory for the $N=4$ cluster. This problem has rich mathematical structure with a ground state space that has non-trivial topology. We show that the ground states are appropriately parametrized by a unit vector order parameter and a rotation matrix. Remarkably, in the low energy description, the physics of the cluster reduces to that of an emergent free spin-$S$ spin and a rigid rotor. This successfully explains the spectrum of the quadrumer and its associated degeneracies. However, this mapping does not hold in the vicinity of collinear ground states due to a subtle effect that arises from the non-manifold nature of the ground state space. We demonstrate this by an analysis of soft fluctuations, showing that collinear states have a larger number of soft modes. Nevertheless, as these singularities only occur on a subset of measure zero, the mapping to a spin and a rotor provides a good description of the quadrumer. We interpret thermodynamic properties of the quadrumer that are accessible in molecular magnets, in terms of the rotor and spin degrees of freedom. Our study paves the way for field theoretic descriptions of systems such as pyrochlore magnets.

The Editorial Meeting at a Little Magazine: An Ethnography of Group Judgment

Judgment and distinction have been topics of persistent interest for cultural sociologists. Recent theory has particularly emphasized social interaction and cognition as key sites for understanding judgment, and a number of studies examine gatekeeping practices as a means of understanding the interactive and perceptual determinants of judgment. This article builds upon previous work by presenting the results of an eighteen-month ethnography at a long-running little magazine based in a large American city. In addition to providing an empirical description of an important but understudied domain of cultural production, this article has two findings of theoretical interest. First, without strong external constraints on processes of group evaluation, editors’ judgments became markedly negative, and their deliberations were often inconclusive. Second, negative and positive evaluations were not symmetric, but were produced by two differing sets of evaluative practices. These findings are broadly consistent with developing field theoretic descriptions of social life, but also raise many empirical and theoretical questions.

An estimate of Λ in resummed quantum gravity in the context of asymptotic safety

We show that, by using recently developed exact resummation techniques based on the extension of the methods of Yennie, Frautschi and Suura to Feynman's formulation of Einstein's theory, we get quantum field theoretic descriptions for the UV fixed-point behaviors of the dimensionless gravitational and cosmological constants postulated by Weinberg. Connecting our work to the attendant phenomenological asymptotic safety analysis of Planck scale cosmology by Bonanno and Reuter, we estimate the value of the cosmological constant \Lambda. We find the encouraging estimate \rho_\Lambda\equiv \frac{\Lambda}{8\pi G_N} \simeq (2.4\times 10^{-3}eV)^4. While this numerical value is close to recent experimental observations, we caution the reader that the estimate involves a number of model parameters that still possess significant levels of uncertainty, such as the value of the transition time between the Planck scale cosmology era and the Friedmann-Robertson-Walker radiation dominated era, where our current understanding allows for at least two orders of magnitude in its uncertainty and this would change our estimate of \rho_\Lambda by at least four orders of magnitude. We discuss such theoretical uncertainties as well. We show why GUT and EW scale vacuum energies from spontaneous symmetry breaking are suppressed in our approach to the estimation of \rho_\Lambda. As a bonus, we show how our estimate constrains susy GUTS.

Phases and phase transitions in aU(1)×U(1)system withθ=2π/3mutual statistics

We study a $U(1)\ifmmode\times\else\texttimes\fi{}U(1)$ system with short-range interactions and mutual $\ensuremath{\theta}=2\ensuremath{\pi}/3$ statistics in (2+1) dimensions. We are able to reformulate the model to eliminate the sign problem and perform a Monte Carlo study. We find a phase diagram containing a phase with only small loops and two phases with one species of proliferated loop. We also find a phase where both species of loop condense, but without any gapless modes. Lastly, when the energy cost of loops becomes small, we find a phase that is a condensate of bound states, each made up of three particles of one species and a vortex of the other. We define several exact reformulations of the model that allow us to precisely describe each phase in terms of gapped excitations. We propose field-theoretic descriptions of the phases and phase transitions, which are particularly interesting on the ``self-dual'' line where both species have identical interactions. We also define irreducible responses useful for describing the phases.

Competing orders, nonlinear sigma models, and topological terms in quantum magnets

A number of examples have demonstrated the failure of the Landau-Ginzburg-Wilson(LGW) paradigm in describing the competing phases and phase transitions of two dimensional quantum magnets. In this paper we argue that such magnets possess field theoretic descriptions in terms of their slow fluctuating orders provided certain topological terms are included in the action. These topological terms may thus be viewed as what goes wrong within the conventional LGW thinking. The field theoretic descriptions we develop are possible alternates to the popular gauge theories of such non-LGW behavior. Examples that are studied include weakly coupled quasi-one dimensional spin chains, deconfined critical points in fully two dimensional magnets, and two component massless $QED_3$. A prominent role is played by an anisotropic O(4) non-linear sigma model in three space-time dimensions with a topological theta term. Some properties of this model are discussed. We suggest that similar sigma model descriptions might exist for fermionic algebraic spin liquid phases.

Microscopic models for fractionalized phases in strongly correlated systems

We construct explicit examples of microscopic models that stabilize a variety of fractionalized phases of strongly correlated systems in spatial dimension bigger than one, and in zero external magnetic field. These include models of charge fractionalization in boson-only systems, and various kinds of spin-charge separation in electronic systems. We determine the excitation spectrum and show the consistency with that expected from field theoretic descriptions of fractionalization. Our results are further substantiated by direct numerical calculation of the phase diagram of one of the models.

On the applicability of the classical nucleation theory in an Ising system

Large-scale dynamic Monte Carlo simulations of a lattice gas on a 2000×2000 square lattice with a Glauber-type spin flip dynamics were performed. The results are discussed in the light of classical nucleation theory (CNT) which can be fully specified for the problem due to the availability of exact values for the interfacial energy of a large nucleus, known from the Onsager solution. Several alternative (field-theoretic or nonclassical) descriptions were also considered. Special attention was paid to the pre-exponential in the cluster distribution function and to the finite-size corrections to the interfacial energies which are required in order to comply with observations. If taken literally, the CNT produces large errors when predicting either the cluster distribution function or the nucleation rate. However, at intermediate temperatures (up to 0.7 Tc) the correspondence can be substantially improved by considering the low-temperature properties of small clusters and adjusting the pre-exponential. At higher temperatures the CNT is in qualitative disagreement with the simulations. Several explanations for this, including coagulation between clusters, are proposed.

The D2–D6 system and a fibered AdS geometry

The system of D2-branes localized on or near D6-branes is considered. The world-volume theory on the D2-branes is investigated, using its conjectured relation to the near-horizon geometry. The results are in agreement with known facts and expectations for the corresponding field theory and a rich phase structure is obtained as a function of the energy scale and the number of branes. In particular, for an intermediate range of the number of D6-branes, the IR geometry is that of an AdS 4 space fibered over a compact space. This D2–D6 system is compared to other systems, related to it by compactification and duality and it is shown that the qualitative differences have compatible explanations in the geometric and field-theoretic descriptions. Another system — that of NS5 branes located at D6-branes — is also briefly studied, leading to a similar phase structure.

On Quantum Descriptions of (Non-)Abelian Anyons

We elaborate on both field-theoretic and quantum mechanical descriptions of (non-)Abelian anyons, emphasizing the role of contact interaction terms. Field theoretic contact terms, required for the sake of renormalizability in general, implement the self-adjoint extension of the quantum mechanical Hamiltonian.

Zero Temperature Phase Transitions in Quantum Heisenberg Ferromagnets

The purpose of this work is to understand the zero temperature phases and the phase transitions of Heisenberg spin systems which can have an extensive, spontaneous magnetic moment; this entails a study of quantum transitions with an order parameter which is also a non-abelian conserved charge. To this end, we introduce and study a new class of lattice models of quantum rotors. We compute their mean-field phase diagrams and present continuum, quantum field-theoretic descriptions of their low energy properties in different regimes. We argue that, in spatial dimensiond=1, the phase transitions in itinerant Fermi systems are in the same universality class as the corresponding transitions in certain rotor models. We discuss implications of our results for itinerant fermions systems in higherdand for other physical systems.

Scalar field theories for Z N symmetric conformal models

We study scalar field theories for two-dimensional Z N symmetric conformal models realized by the GKO coset construction with an SU( N) Kac-Moody algebra. For N = 2 we also discuss field theoretic descriptions of the A-D-E discrete series.