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DOE OSTI2021

Duality defect of the monster CFT

Abstract We show that the fermionization of the Monster CFT with respect to Z 2 A is the tensor product of a free fermion and the Baby Monster CFT. The chiral fermion parity of the free fermion implies that the Monster CFT is self-dual under the Z 2 A orbifold, i.e. it enjoys the Kramers–Wannier duality. The Kramers–Wannier duality defect extends the Monster group to a larger category of topological defect lines that contains an Ising subcategory. We introduce the defect McKay – Thompson series defined as the Monster partition function twisted by the duality defect, and find that the coefficients can be decomposed into the dimensions of the (projective) irreducible representations of the Baby Monster group. We further prove that the defect McKay–Thompson series is invariant under the genus-zero congruence subgroup 16 D 0 of P S L ( 2 , Z ) .

Physics↗

DOE OSTI2024

The duality between color and kinematics and its applications

Abstract This review describes the duality between color and kinematics and its applications, with the aim of gaining a deeper understanding of the perturbative structure of gauge and gravity theories. We emphasize, in particular, applications to loop-level calculations, the broad web of theories linked by the duality and the associated double-copy structure, and the issue of extending the duality and double copy beyond scattering amplitudes. The review is aimed at doctoral students and junior researchers both inside and outside the field of amplitudes and is accompanied by various exercises.

Physics↗

DOE OSTI2026

Entire four-graviton EFT from the duality between color and kinematics

The Bern-Carrasco-Johansson (BCJ) double-copy construction reveals a fundamental structural connection between gauge and gravity theories. At its core, the BCJ double copy is directly due to a duality between the algebraic relations of a color root and those of a kinematic root. We generalize this principle beyond the conventional Lie algebra structure of tree-level Yang-Mills theory. By demanding color-kinematics duality for the complete basis of four-point color structures—including those involving the symmetric 𝑑 𝑎⁢𝑏⁢𝑐 constants—we define the universal double copy. We systematically classify the bases of all such parity-even generalized gauge-theory numerators and, independently, the space of all parity-even four-graviton higher-derivative operators. We demonstrate that our universal double-copy construction precisely spans the entire tower of parity-even four-graviton amplitudes in any dimension, except for the Lovelock 𝑅 3 contribution in 𝐷 > 6 which we can express in terms of a particularly simple universal triple-copy involving gauge theories coupled to scalars. Explicit machine-readable expressions for the complete basis of gauge-theory numerators and fundamental gravitational building blocks are provided in the Supplemental Material. This establishes that all possible four-point gravitational interactions can be factorized into products of gauge-theory building blocks governed by this universal notion of color-kinematics duality.

Carrasco, John Joseph M. [Northwestern Univ., Evan↗

DOE OSTI2025

T Duality and T T ¯ -like Deformations of Sigma Models

We initiate the study of the interplay between T duality and classical stress tensor deformations in two-dimensional sigma models. We first show that a general Abelian T duality commutes with the T T ¯ deformation, which can be engineered by a gravitational dressing. Then, by using an auxiliary field formulation of stress tensor deformations of the principal chiral model (PCM), we prove that non-Abelian T duality and arbitrary T T ¯ -like flows also commute for theories in this class. We argue that all such auxiliary field deformations of both the PCM and its T dual are classically integrable. Published by the American Physical Society 2025

Bielli, Daniele (ORCID:0009000640034768)↗

DOE OSTI2018

Global Symmetries, Counterterms, and Duality in Chern-Simons Matter Theories with Orthogonal Gauge Groups

We study three-dimensional gauge theories based on orthogonal groups. Depending on the global form of the group these theories admit discrete \theta θ -parameters, which control the weights in the sum over topologically distinct gauge bundles. We derive level-rank duality for these topological field theories. Our results may also be viewed as level-rank duality for SO(N)_{K} S O ( N ) K Chern-Simons theory in the presence of background fields for discrete global symmetries. In particular, we include the required counterterms and analysis of the anomalies. We couple our theories to charged matter and determine how these counterterms are shifted by integrating out massive fermions. By gauging discrete global symmetries we derive new boson-fermion dualities for vector matter, and present the phase diagram of theories with two-index tensor fermions, thus extending previous results for SO(N) S O ( N ) to other global forms of the gauge group.

Cordova, Clay↗

DOE OSTI2018

Deconstructing S-Duality

We use the technique of deconstruction to lift dualities from 2+1 to 3+1 dimensions. In this work we demonstrate the basic idea by deriving S-duality of maximally supersymmetric electromagnetism in 3+1 dimensions from mirror symmetry in 2+1. We also study the deconstruction of a non-supersymmetric duality in 3+1 dimensions using Abelian bosonization in 2+1.

Aitken, Kyle↗

DOE OSTI2016

Quark Hadron Duality - Recent Jefferson Lab Results

The duality between the partonic and hadronic descriptions of electron--nucleon scattering is a remarkable feature of nuclear interactions. When averaged over appropriate energy intervals the cross section at low energy which is dominated by nucleon resonances resembles the smooth behavior expected from perturbative QCD. Recent Jefferson Lab results indicate that quark-hadron duality is present in a variety of observables, not just the proton F2 structure function. An overview of recent results, especially local quark-hadron duality on the neutron, are presented here.

Niculescu, Maria Ioana↗

DOE OSTI2017

New dualities and misleading anomaly matchings from outer-automorphism twists

We study four-dimensional N=1, 2 superconformal theories in class S obtained by compactifying the 6d N=(2, 0) theory on a Riemann surface C with outer-automorphism twist lines. From the pair-of-pants decompositions of C, we find various dual descriptions for the same theory having distinct gauge groups. We show that the various configurations of the twist line give rise to dual descriptions for the identical theory. We compute the ’t Hooft anomaly coefficients and the superconformal indices to test dualities. Surprisingly, we find that the class S theories with twist lines wrapping 1-cycles of C have the identical ’t Hooft anomalies as the ones without the twist line, whereas the superconformal indices differ. As a result, this provides a large set of examples where the anomaly matching is insufficient to test dualities.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Argyres-Douglas matter and S-duality. Part II

We study S-duality of Argyres-Douglas theories obtained by compactification of 6d (2,0) theories of ADE type on a sphere with irregular punctures. Here, the weakly coupled descriptions are given by the degeneration limit of auxiliary Riemann sphere with marked points, among which three punctured sphere represents isolated superconformal theories. We also discuss twisted irregular punctures and their S-duality.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2017

Discrete symmetries in Heterotic/F-theory duality and mirror symmetry

We study aspects of Heterotic/F-theory duality for compacti cations with Abelian discrete gauge symmetries. We consider F-theory compacti cations on genus-one bered Calabi-Yau manifolds with n-sections, associated with the Tate-Shafarevich group Z n . Such models are obtained by studying rst a speci c toric set-up whose associated Heterotic vector bundle has structure group Z n . By employing a conjectured Heterotic/Ftheory mirror symmetry we construct dual geometries of these original toric models, where in the stable degeneration limit we obtain a discrete gauge symmetry of order two and three, for compacti cations to six dimensions. We provide explicit constructions of mirrorpairs for symmetric examples with Z 2 and Z 3 , in six dimensions. The Heterotic models with symmetric discrete symmetries are related in eld theory to a Higgsing of Heterotic models with two symmetric abelian U(1) gauge factors, where due to the Stuckelberg mechanism only a diagonal U(1) factor remains massless, and thus after Higgsing only a diagonal discrete symmetry of order n is present in the Heterotic models and detected via Heterotic/F-theory duality. These constructions also provide further evidence for the conjectured mirror symmetry in Heterotic/F-theory at the level of brations with torsional sections and those with multi-sections.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Dualities among massive, partially massless and shift symmetric fields on (A)dS

We catalog all the electromagnetic-like dualities that exist between free dynamical bosonic fields of arbitrary symmetry type and mass on (anti-) de Sitter space in all dimensions, including dualities among the partially massless and shift symmetric fields. This generalizes to all these field types the well known fact that a massless p-form is dual to a massless (D − p − 2)-form in D spacetime dimensions. In the process, we describe the structure of the Weyl modules (the spaces of local operators linear in the fields and their derivative relations) for all the massive, partially massless and shift symmetric fields.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2018

Dark monopoles and SL(2,$\mathbb{Z}$) duality

We explore kinetic mixing between two Abelian gauge theories that have both electric and magnetic charges. When one of the photons becomes massive, novel effects arise in the low-energy effective theory, including the failure of Dirac charge quantization as particles from one sector obtain parametrically small couplings to the photon of the other. We maintain a manifest SL(2, $\mathbb{Z}$) duality throughout our analysis, which is the diagonal subgroup of the dualities of the two un-mixed gauge theories.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Quantitative Boltzmann–Gibbs Principles via Orthogonal Polynomial Duality

We study fluctuation fields of orthogonal polynomials in the context of particle systems with duality. We thereby obtain a systematic orthogonal decomposition of the fluctuation fields of local functions, where the order of every term can be quantified. This implies a quantitative generalization of the Boltzmann–Gibbs principle. In the context of independent random walkers, we complete this program, including also fluctuation fields in non-stationary context (local equilibrium). For other interacting particle systems with duality such as the symmetric exclusion process, similar results can be obtained, under precise conditions on the n particle dynamics.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2017

Duality between a dark state and a quasi-dark state

We study a physical system coupled with two one-mode Bose fields. The physical system is a two-level system or a harmonic oscillator. We prove that each dark and quasi-dark state appears under a proper condition, and then, we derive a duality between the dark state and the quasi-dark state. This duality induces the switch between the dark state and the quasi-dark state.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Boson–fermion duality in a gravitational background

We study the 2+1 dimensional boson–fermion duality in the presence of background curvature and electromagnetic fields. The main players are, on the one hand, a massive complex |&straightphi;|{sup 4} scalar field coupled to a U(1) Maxwell–Chern–Simons gauge field at level 1, representing a relativistic composite boson with one unit of attached flux, and on the other hand, a massive Dirac fermion. We show that, in a curved background and at the level of the partition function, the relativistic composite boson, in the infinite coupling limit, is dual to a short-range interacting Dirac fermion. The coupling to the gravitational spin connection arises naturally from the spin factors of the Wilson loop in the Chern–Simons theory. A non-minimal coupling to the scalar curvature is included on the bosonic side in order to obtain agreement between partition functions. Although an explicit Lagrangian expression for the fermionic interactions is not obtained, their short-range nature constrains them to be irrelevant, which protects the duality in its strong interpretation as an exact mapping at the IR fixed point between a Wilson–Fisher–Chern–Simons complex scalar and a free Dirac fermion. We also show that, even away from the IR, keeping the |&straightphi;|{sup 4} term is of key importance as it provides the short-range bosonic interactions necessary to prevent intersections of worldlines in the path integral, thus forbidding unknotting of knots and ensuring preservation of the worldline topologies.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2018

Anomalies of duality groups and extended conformal manifolds

A self-duality group $\cal G$ in quantum field theory can have anomalies. In that case, the space of ordinary coupling constants $\cal M$ can be extended to include the space $\cal F$ of coefficients of counterterms in background fields. The extended space $\cal N$ forms a bundle over $\cal M$ with fiber $\cal F$, and the topology of the bundle is determined by the anomaly. For example, the ${\cal G}=SL(2,\mathbb{Z})$ duality of the 4d Maxwell theory has an anomaly, and the space ${\cal F}=S^1$ for the gravitational theta-angle is nontrivially fibered over ${\cal M}=\mathbb{H}/SL(2,\mathbb{Z})$. We will explain a simple method to determine the anomaly when the 4d theory is obtained by compactifying a 6d theory on a Riemann surface in terms of the anomaly polynomial of the parent 6d theory. Our observations resolve an apparent contradiction associated with the global structure of the Kahler potential on the space of exactly marginal couplings of supersymmetric theories.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2017

Symmetry for Flavor-Kinematics Duality from an Action

In this paper, we propose a new representation of the nonlinear sigma model that exhibits a manifest duality between flavor and kinematics. The fields couple exclusively through cubic Feynman vertices which define the structure constants of an underlying kinematic algebra. The action is invariant under a combination of internal and spacetime symmetries whose conservation equations imply flavor-kinematics duality, ensuring that all Feynman diagrams satisfy kinematic Jacobi identities. Substituting flavor for kinematics, we derive a new cubic action for the special Galileon theory. Finally, in this picture, the vanishing soft behavior of amplitudes is a by-product of the Weinberg soft theorem.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Noninvertible chiral symmetry and axions under electromagnetic duality

We study the implications of noninvertible chiral symmetry in a four-dimensional U(1) gauge theory coupled to massless fermions with electromagnetic 𝑆⁢𝐿⁡(2,ℤ) duality. This is done by deriving the Adler-Bell-Jackiw anomaly of massless QED in the dual frame that is used to explicitly construct the symmetry defect operator as well as the conserved two-form symmetry current. As expected, the noninvertible chiral symmetry is covariant under the duality transformation. This has implications for understanding the nature of kinetic and topological terms in the dual frame and for axion electrodynamics. In particular, we show that to generate an axion potential from a dyon loop, the one-form magnetic symmetry must be explicitly broken by a mutually nonlocal charged state with nonzero pairwise helicity.

Anomalies↗