Duality Invariance Research Articles

Casimir energy with perfect electromagnetic boundary conditions and duality: A field-theoretic approach

Using functional integral methods, we study the Casimir effect for the case of two infinite parallel plates in the QED vacuum, with (different) perfect electromagnetic boundary conditions applied to both plates. To enforce these boundary conditions, we add two Lagrange multiplier fields to the action. We subsequently recover the known Casimir energy in two ways: once directly from the path integral and once as the vacuum expectation value of the 00 component of the energy-momentum tensor. Comparing both methods, we show that the energy-momentum tensor must be modified and that it picks up boundary contributions as a consequence. We also discuss electromagnetic duality invariance of the theory and its interplay with the boundaries by generalizing the Deser-Teitelboim implementation of the duality transformation. Published by the American Physical Society 2024

Nonlinearly charging the conformally dressed black holes preserving duality and conformal invariance

We start this paper by concisely rederiving ModMax, which is nothing but the unique nonlinear extension of Maxwell’s equations preserving conformal and duality invariance. The merit of this new derivation is its transparency and simplicity since it is based on an approach where the elusive duality invariance is manifest. In the second part, we couple the ModMax electrodynamics to Einstein gravity with a cosmological constant together with a standard conformal scalar field, and new stationary spacetimes with dyonic charges are found. These solutions are later used as seed configurations to generate nonlinearly charged (super-)renormalizably dressed spacetimes by means of a known generating method that we extend to include any nonlinear conformal electrodynamics. We end by addressing the issue of how to generalize some of these results to include the recently studied non-Noetherian conformal scalar fields, whose equation of motion still enjoys conformal symmetry even though its action does not. It turns out that the static non-Noetherian conformally dressed black holes also become amenable to being charged by ModMax. Published by the American Physical Society 2024

Decoupled Unbiased Teacher for Source-Free Domain Adaptive Medical Object Detection.

Source-free domain adaptation (SFDA) aims to adapt a lightweight pretrained source model to unlabeled new domains without the original labeled source data. Due to the privacy of patients and storage consumption concerns, SFDA is a more practical setting for building a generalized model in medical object detection. Existing methods usually apply the vanilla pseudo-labeling technique, while neglecting the bias issues in SFDA, leading to limited adaptation performance. To this end, we systematically analyze the biases in SFDA medical object detection by constructing a structural causal model (SCM) and propose an unbiased SFDA framework dubbed decoupled unbiased teacher (DUT). Based on the SCM, we derive that the confounding effect causes biases in the SFDA medical object detection task at the sample level, feature level, and prediction level. To prevent the model from emphasizing easy object patterns in the biased dataset, a dual invariance assessment (DIA) strategy is devised to generate counterfactual synthetics. The synthetics are based on unbiased invariant samples in both discrimination and semantic perspectives. To alleviate overfitting to domain-specific features in SFDA, we design a cross-domain feature intervention (CFI) module to explicitly deconfound the domain-specific prior with feature intervention and obtain unbiased features. Besides, we establish a correspondence supervision prioritization (CSP) strategy for addressing the prediction bias caused by coarse pseudo-labels by sample prioritizing and robust box supervision. Through extensive experiments on multiple SFDA medical object detection scenarios, DUT yields superior performance over previous state-of-the-art unsupervised domain adaptation (UDA) and SFDA counterparts, demonstrating the significance of addressing the bias issues in this challenging task. The code is available at https://github.com/CUHK-AIM-Group/Decoupled-Unbiased-Teacher.

N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 3 conformal superspace in four dimensions

We develop a superspace formulation for N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 3 conformal supergravity in four spacetime dimensions as a gauge theory of the superconformal group SU(2, 2|3). Upon imposing certain covariant constraints, the algebra of conformally covariant derivatives ∇A=∇a∇αi∇iα⋅\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\ abla}_A=\\left({\ abla}_a,{\ abla}_{\\alpha}^i,{\ abla}_i^{\\overset{\\cdot }{\\alpha }}\\right) $$\\end{document} is shown to be determined in terms of a single primary chiral spinor superfield, the super-Weyl spinor Wα of dimension +1/2 and its conjugate. Associated with Wα is its primary descendant Bij of dimension +2, the super-Bach tensor, which determines the equation of motion for conformal supergravity. As an application of this construction, we present two different but equivalent action principles for N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 3 conformal supergravity. We describe the model for linearised N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 3 conformal supergravity in an arbitrary conformally flat background and demonstrate that it possesses U(1) duality invariance. Additionally, upon degauging certain local symmetries, our superspace geometry is shown to reduce to the U(3) superspace constructed by Howe more than four decades ago. Further degauging proves to lead to a new superspace formalism, called SU(3) superspace, which can also be used to describe N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 3 conformal supergravity. Our conformal superspace setting opens up the possibility to formulate the dynamics of the off-shell N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 3 super Yang-Mills theory coupled to conformal supergravity.

Even-point multi-loop unitarity and its applications: exponentiation, anomalies and evanescence

We identify novel structure in newly computed multi-loop amplitudes and quantum actions for even-point effective field theories, including both the nonlinear sigma model (NLSM) and double-copy gauge theories such as Born-Infeld and its supersymmetric generalizations. We exploit special properties of all even-point theories towards establishing an efficient unitarity based amplitude construction. In doing so, we find evidence that the leading IR divergence of NLSM amplitudes exponentiates when the target space is CP\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathbbm{CP} $$\\end{document}1 ≅ SU(2)/U(1). We then systematically compute the two-loop anomalous behavior of Born-Infeld, and find that the counterterms needed to restore U(1) invariant behavior at loop-level can be constructed via a symmetric-structure double-copy. We also demonstrate that the divergent part of the one-minus (−+++) two-loop anomaly vanishes upon introducing an evanescent operator. In addition to these purely photonic counterterms, we verify through explicit calculation that the anomalous matrix elements that violate U(1) duality invariance can be alternatively cancelled by summing over internal N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 DBIVA superfields. Finally we find that N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 Dirac-Born-Infeld-Volkov-Akulov (DBIVA) amplitudes admit double-copy construction through two-loop order by reproducing our unitarity based result with a double copy between color-dual N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{N} $$\\end{document} = 4 super-Yang-Mills and our two-loop NLSM amplitudes. This result supports the possibility of color-dual representations for NLSM beyond one-loop. We conclude with an overview of how D-dimensional four-photon counterterms can be constructed in generality with the symmetric-structure double-copy, and outline a convenient way of counting evanescent operators using Hilbert series as generating functions.

Off-Shell Duality Invariance of Schwarzschild Perturbation Theory

We explore the duality invariance of the Maxwell and linearized Einstein–Hilbert actions on a non-rotating black hole background. On-shell, these symmetries are electric–magnetic duality and Chandrasekhar duality, respectively. Off-shell, they lead to conserved quantities; we demonstrate that one of the consequences of these conservation laws is that even- and odd-parity metric perturbations have equal Love numbers. Along the way, we derive an action principle for the Fackerell–Ipser equation and Teukolsky–Starobinsky identities in electromagnetism.

Effective observables for electromagnetic duality from novel amplitude decomposition

We introduce a decomposition of $D$-dimensional vector amplitudes in terms of building blocks that preserve all partial amplitude relations of the parent gauge theory. Using this decomposition, we derive a new set of amplitude relations between nonlinear sigma model pions and the pure-scalar sector of Yang-Mills scalar theory. These new relations indicate an equivalence between Born-Infeld duality invariance and that of Einstein-Maxwell theory, considering their known double-copy construction from the two scalar theories with Yang-Mills. This observation motivates a general framework for constructing duality-invariant effective field theory observables at any multiplicity using the building blocks in our amplitude decomposition. Finally, we conjecture a subtle relationship between these duality-invariant building blocks and the bosonic sector of $\mathcal{N}=4$ super Yang-Mills.

Convergence of sewing conformal blocks

In a recent work [On factorization and vector bundles of conformal blocks from vertex algebras, preprint (2019), arXiv:1909.04683], Damiolini et al. showed that for a [Formula: see text]-cofinite rational vertex operator algebra [Formula: see text], sheaves of conformal blocks are locally free and satisfy the factorization property. In this paper, we prove that if [Formula: see text] is [Formula: see text]-cofinite, the sewing of conformal blocks is convergent. This proves a conjecture proposed by Zhu [Global vertex operators on Riemann surfaces, Commun. Math. Phys. 165(3) (1994) 485–531] and Huang [Some open problems in mathematical two-dimensional conformal field theory, preprint (2016), arXiv:1606.04493], generalizing previous results on the convergence of products, iterates, and traces (but not pseudo-traces) of vertex operators and intertwining operators in [Y. Zhu, Modular invariance of characters of vertex operator algebras, J. Amer. Math. Soc. 9(1) (1996) 237–302; Y. Z. Huang, A theory of tensor products for module categories for a vertex operator algebra, IV, J. Pure Appl. Algebra 100(1–3) (1995) 173–216; Y. Z. Huang, Differential equations, duality and modular invariance, Commun. Contemp. Math. 7(05) (2005) 649–706; Y. Z. Huang, J. Lepowsky and L. Zhang, Logarithmic tensor category theory, VII: Convergence and extension properties and applications to expansion for intertwining maps, preprint (2011), arXiv:1110.1929] and on the convergence of projective factors related to the central charge of the Virasoro algebra in [Y. Z. Huang, Two-Dimensional Conformal Geometry and Vertex Operator Algebras, Vol. 148 (Springer Science & Business Media, 1997)].

Polarisability and magnetisation of electrically K-mouflaged objects: the Born-Infeld ModMax case study

We consider a family of non-linear theories of electromagnetism that interpolate between Born-Infeld at small distances and the recently introduced ModMax at large distances. These models are duality invariant and feature a K-mouflage screening in the Born-Infeld regime. We focus on computing the static perturbations around a point-like screened charge in terms of two decoupled scalar potentials describing the polar and the axial sectors respectively. Duality invariance imposes that the propagation speed of the odd perturbations goes to zero as fast as the effective screened charge of the object, potentially leading to strong coupling and an obstruction to the viability of the EFT below the screened radius. We then consider the linear response to external fields and compute the electric polarisability and the magnetic susceptibility. Imposing regularity of the perturbations at the position of the particle, we find that the polarisability for the odd multipoles vanishes whilst for the magnetisation Born-Infeld emerges as the only theory with vanishing susceptibility for even multipoles. The perturbation equations factorise in terms of ladder operators connecting different multipoles. There are two such ladder structures for the even sector: one that acts as an automorphism between the first four multipoles and another one that connects multipoles separated by four units. When requiring a similar ladder structure for the odd sector, Born-Infeld arises again as the unique theory. We use this ladder structure to relate the vanishing of the polarisability and the susceptibility to the values of conserved charges. Finally the perturbation equations correspond to a supersymmetric quantum mechanical system such that the polar sector can be described in terms of Schrödinger’s equations with four generalised hyperbolic Pösch-Teller potentials whose eigenfunctions are in correspondence with the multipoles.

Maximally symmetric nonlinear extension of electrodynamics with Galilean conformal symmetries

A maximally symmetric nonlinear extension of Maxwell's theory in four dimensions called ModMax has been recently introduced in the literature. This theory preserves both electromagnetic duality and conformal invariance of the linear theory. In this short paper, we introduce a Galilean cousin of the ModMax theory, written in a covariant formalism, that is explicitly shown to be invariant under Galilean conformal symmetries. We discuss the construction of such a theory involving Galilean electromagnetic invariants and show how the classical structure of the theory is invariant under the action of Galilean conformal algebra.

Coupling the precursor of the most general theory of electromagnetism invariant under duality and conformal invariance with scalars, and BIon-type solutions

Recently, the most general theory of electromagnetism invariant under duality and conformal invariance was written, and dubbed ModMax. It arises from a generalization of Born-Infeld (BI) theory by taking the infinite tension limit, $T\ensuremath{\rightarrow}\ensuremath{\infty}$. In this paper we show that this generalization can be obtained from a branelike construction, just like BI, and can thus be coupled to scalars in the same way to obtain a Dirac-Born-Infeld (DBI)-like action. All the BIon and catenoid solutions, and their interpolations, are still solutions of the generalized DBI-like action, suggesting that an interpretation within string theory could be possible. We also show that Ra\~nada's knotted solutions (with nonzero helicities) are still valid, both in the ModMax theory, and in its precursor.

Democratic Lagrangians for Nonlinear Electrodynamics.

We construct a Lagrangian for general nonlinear electrodynamics that features electric and magnetic potentials on equal footing. In the language of this Lagrangian, discrete and continuous electric-magnetic duality symmetries can be straightforwardly imposed, leading to a simple formulation for theories with the SO(2) duality invariance. When specialized to the conformally invariant case, our construction provides a manifestly duality-symmetric formulation of the recently discovered ModMax theory. We briefly comment on a natural generalization of this approach to p-forms in 2p+2 dimensions.

Exact electromagnetic duality with nonminimal couplings

We study nonminimal extensions of Einstein-Maxwell theory with exact electromagnetic duality invariance. Any such theory involves an infinite tower of higher-derivative terms whose computation and summation usually represents a challenging problem. Despite that, we manage to obtain a closed form of the action for all the theories with a quadratic dependence on the vector field strength. In these theories we find that the Maxwell field couples to gravity through a curvature-dependent susceptibility tensor that takes a peculiar form, reminiscent of that of Born-Infeld Lagrangians. We study the static and spherically symmetric black hole solutions of the simplest of these models, showing that the corresponding equations of motion are invariant under rotations of the electric and magnetic charges. We compute the perturbative corrections to the Reissner-Nordstr\"om solution in this theory, and in the case of extremal black holes we determine exactly the near-horizon geometry as well as the entropy. Remarkably, the entropy only possesses a constant correction despite the action containing an infinite number of terms. In addition, we find there is a lower bound for the charge and the mass of extremal black holes. When the sign of the coupling is such that the weak gravity conjecture is satisfied, the area and the entropy of extremal black holes vanish at the minimal charge.

The dual continuity equations

The ordinary continuity equation relating to the current and density of a system is extended to incorporate systems with dual (longitudinal and transverse) currents. Such a system of equations is found to have the same mathematical structure as that of Maxwell equations. The longitudinal and transverse currents and the densities associated with them are found to be coupled with each other. Each of these quantities is found to obey a wave equation traveling at the velocity of light in a vacuum. London equations of super-conductivity are shown to emerge from some sort of continuity equations. The new London equations are symmetric and are shown to be dual to each other. It is shown that London’s equations are Maxwell’s equations with a massive electromagnetic field (photon). These equations preserve the gauge invariance that is broken in other massive electrodynamics. The duality invariance may allow magnetic monopoles to be present inside superconductors. The new duality is called the comprehensive duality transformation.

ModMax meets Susy

We give a prescription for mathcal{N} = 1 supersymmetrization of any (four-dimensional) nonlinear electrodynamics theory with a Lagrangian density satisfying a convexity condition that we relate to semi-classical unitarity. We apply it to the one-parameter ModMax extension of Maxwell electrodynamics that preserves both electromagnetic duality and conformal invariance, and its Born-Infeld-like generalization, proving that duality invariance is preserved. We also establish superconformal invariance of the superModMax theory by showing that its coupling to supergravity is super-Weyl invariant. The higher-derivative photino-field interactions that appear in any supersymmetric nonlinear electrodynamics theory are removed by an invertible nonlinear superfield redefinition.

The Analysis of Network Models for the Design of Industrial and Fire Safety Systems for Oil Refineries

Tensor network models represent the processes and structure of complex systems, including dangerous technological objects of oil refineries. Complex systems tensor method research based on duality invariance. It is the sum constancy of the metric tensors dual networks whenever there is a change in structure. Dual subspaces closed and unclosed paths are responses to external and internal influences, which do not depend on each other. As an example of a network model is considered the atmospheric column oil-refining plant, which is used to organize the work of training stand. Thermal energy flows are presented in a mesh network, and massive flows of mechanical energy - in a junction network. The amount of mechanical and thermal energy flows allows you to determine the load on the nodes of the unit. The results are applied to predict dangerous situations on refining facilities to assess changes in restructuring processes and the risk of accidents. Calculations, such as heat and mass flow change if you change the control actions, disable installation elements and assess change critical settings.

Deformed hopfion-Rañada knots in ModMax electrodynamics

Source-free so-called ModMax theories of nonLinear electrodynamics (NLE) in the four dimensional Minkowski spacetime vacuum are the only possible continuous deformations—and as a function of a single real and positive parameter—of source-free Maxwell linear electrodynamics (MLE) in the same vacuum, which preserve all the same Poincaré and conformal spacetime symmetries as well as the continuous duality invariance of Maxwell’s theory. Null field configurations of the latter however, including null electromagnetic knots, are singular for the Lagrangian formulation of any spacetime Poincaré and conformal invariant theory of NLE. In particular null hopfion-Rañada (HR) knots are a distinguished and fascinating class on their own of topologically nontrivial solutions to Maxwell’s equations. This work addresses the fate of these configurations within ModMax theories. A doubled class of ModMax deformed HR knots is thereby identified, each of which coalescing back in a continuous fashion to the original HR knot when the nonlinear deformation parameter is turned off.

Electromagnetic duality and D3-brane scattering amplitudes beyond leading order

We use on-shell methods to study the non-supersymmetric and supersymmetric low-energy S-matrix on a probe D3-brane, including both the 1-loop contributions of massless states as well as the effects of higher-derivative operators. Our results include: (1) A derivation of the duality invariance of Born-Infeld electrodynamics as the dimensional oxidation of the group of spatial rotations transverse to a probe M2-brane; this is done using a novel implementation of subtracted on-shell recursion. (2) The first explicit loop-level BCJ double-copy in a non-gravitational model, namely the calculation of the 4-point self-dual amplitude of non-supersymmetric Born-Infeld. (3) From previous results for n-point self-dual 1-loop BI amplitudes and the conjectured dimension-shifting relations in Yang-Mills, we obtain an explicit all-multiplicity, at all orders in E, expression for the 1-loop integrand of the MHV sector of mathcal{N} = 4 DBI. (4) For all n > 4, the explicitly integrated duality-violating 1-loop amplitudes (self-dual and next-to-self-dual in pure BI as well as MHV in mathcal{N} = 4 DBI) are shown to be removable at mathcal{O}left({upepsilon}^0right) by adding finite local counterterms; we propose that this may be true more generally at 1-loop order. (5) We find that in non-supersymmetric Born-Infeld, not all finite local counterterms needed to restore electromagnetic duality can be constructed using the double-copy with higher-derivative corrections, suggesting a fundamental tension between electromagnetic duality and color-kinematics duality at loop-level. Finally we comment on oxidation of duality symmetries in supergravity and the parallels it has to the M2-brane to D3-brane oxidation demonstrated in this paper.

Nonlinear duality-invariant conformal extension of Maxwell’s equations

All nonlinear extensions of the source-free Maxwell equations preserving both SO(2) electromagnetic duality invariance and conformal invariance are found, and shown to be limits of a one-parameter generalisation of Born-Infeld electrodynamics. The strong-field limit is the same as that found by Bialynicki-Birula from Born-Infeld theory but the weak-field limit is a new one-parameter extension of Maxwell electrodynamics, which is interacting but admits exact light-velocity plane-wave solutions of arbitrary polarisation. Small-amplitude waves on a constant uniform electromagnetic background exhibit birefringence, but one polarisation mode remains lightlike.

Pair production and gravity as the weakest force

The Weak Gravity Conjecture (WGC) is usually formulated in terms of the stability of extremal black-holes or in terms of long distance Coulomb/Newton potentials. However one can think of other physical processes to compare the relative strength of gravity versus other forces. We argue for an alternative formulation in terms of particle pair production at threshold or, equivalently, pair annihilation at rest. Imposing that the production rate by any force mediator (photon or scalar) of pairs of charged particles be larger or equal to graviton production, we recover known conditions for the U(1) WGC and its extensions. Unlike other formulations though, threshold pair production is sensitive to short range couplings present in scalar interactions and gives rise to a Scalar WGC. Application to moduli scalars gives rise to specific conditions on the trilinear and quartic couplings which involve first and second derivatives of the WGC particle mass with respect to the moduli. Some solutions saturating equations correspond to massive states behaving like BPS, KK and winding states which feature duality invariance and are in agreement with the Swampland distance conjecture. Conditions for N = 2 BPS states saturate our bounds and we discuss specific examples of BPS states which become massless at large Kahler moduli in Type IIA N=2, D=4 CY and orbifold compactifications. We study possible implications for potentials depending on moduli only through WGC massive states. For some simple classes of potentials one recovers constraints somewhat similar but not equivalent to a Swampland dS conjecture.