## Publications

221 results found

Duff MJ, 2022, The conformal brane-scan: an update, *JOURNAL OF HIGH ENERGY PHYSICS*, Vol: 2022, ISSN: 1029-8479

Generalizing the The Membrane at the End of the Universe, a 1987 paper Supersingletons by Blencowe and the author conjectured the existence of BPS p-brane configurations (p = 2, 3, 4, 5) and corresponding CFTs on the boundary of anti-de Sitter space with symmetries appearing in Nahm’s classification of superconformal algebras: OSp(N|4) N = 8, 4, 2, 1; SU(2, 2|N) N = 4, 2, 1; F 2(4); OSp(8∗|N), N = 4, 2. This correctly predicted the D3-brane with SU(2, 2|4) on AdS5 × S5 and the M5-brane with OSp(8∗|4) on AdS7 × S4, in addition to the known M2-brane with OSp(8|4) on AdS4 × S7. However, finding non-singular AdS solutions matching the other symmetries was less straightforward. Here we perform a literature search and confirm that all of the empty slots have now been filled, thanks to a number of extra ingredients including warped products and massive Type IIA. Orbifolds, orientifolds and S-folds also play a part providing examples not predicted: SU(2, 2|3), OSp(3|4), OSp(5|4) and OSp(6|4) but not OSp(7|4). We also examine the status of p = (0, 1) configurations.

Borsten L, Duff MJ, Nagy S, 2021, Odd dimensional analogue of the Euler characteristic, *The Journal of High Energy Physics*, Vol: 2021, ISSN: 1029-8479

When compact manifolds X and Y are both even dimensional, their Euler characteristics obey the Künneth formula χ(X × Y) = χ(X)χ(Y). In terms of the Betti numbers bp(X), χ(X) = Σp(−1)pbp(X), implying that χ(X) = 0 when X is odd dimensional. We seek a linear combination of Betti numbers, called ρ, that obeys an analogous formula ρ(X × Y) = χ(X)ρ(Y) when Y is odd dimensional. The unique solution is ρ(Y) = − Σp(−1)ppbp(Y). Physical applications include: (1) ρ → (−1)mρ under a generalized mirror map in d = 2m + 1 dimensions, in analogy with χ → (−1)mχ in d = 2m; (2) ρ appears naturally in compactifications of M-theory. For example, the 4-dimensional Weyl anomaly for M-theory on X4 × Y7 is given by χ(X4)ρ(Y7) = ρ(X4 × Y7) and hence vanishes when Y7 is self-mirror. Since, in particular, ρ(Y × S1) = χ(Y), this is consistent with the corresponding anomaly for Type IIA on X4 × Y6, given by χ(X4)χ(Y6) = χ(X4 × Y6), which vanishes when Y6 is self-mirror; (3) In the partition function of p-form gauge fields, ρ appears in odd dimensions as χ does in even.

Duff MJ, Stelle KS, 2020, Sir Thomas Walter Bannerman Kibble CBE, Publisher: arXiv

Professor Tom Kibble was an internationally-renowned theoretical physicistwhose contributions to theoretical physics range from the theory of elementaryparticles to modern early-universe cosmology. The unifying theme behind all hiswork is the theory of non-abelian gauge theories, the Yang-Mills extension ofelectromagnetism. One of Kibble's most important pieces of work in this areawas his study of the symmetry-breaking mechanism whereby the force-carryingvector particles in the theory can acquire a mass accompanied by the appearanceof a massive scalar boson. This idea, put forward independently by Brout andEnglert, by Higgs and by Guralnik, Hagen and Kibble in 1964, and generalised byKibble in 1967, lies at the heart of the Standard Model and all modern unifiedtheories of fundamental particles. It was vindicated in 2012 by the discoveryof the Higgs boson at CERN. According to Nobel Laureate Steven Weinberg, "TomKibble showed us why light is massless"; this is the fundamental basis ofelectromagnetism.

Duff MJ, 2020, Weyl, Pontryagin, Euler, Eguchi and Freund, *Journal of Physics A: Mathematical and Theoretical*, Vol: 53, ISSN: 1751-8113

In a September 1976 PRL Eguchi and Freund considered two topological invariants: the Pontryagin number $P\sim \int {\mathrm{d}}^{4}x\sqrt{g}{R}^{{\ast}}R$ and the Euler number $\chi \sim \int {\mathrm{d}}^{4}x\sqrt{g}{R}^{{\ast}}{R}^{{\ast}}$ and posed the question: to what anomalies do they contribute? They found that P appears in the integrated divergence of the axial fermion number current, thus providing a novel topological interpretation of the anomaly found by Kimura in 1969 and Delbourgo and Salam in 1972. However, they found no analogous role for χ. This provoked my interest and, drawing on my April 1976 paper with Deser and Isham on gravitational Weyl anomalies, I was able to show that for conformal field theories the trace of the stress tensor depends on just two constants: ${g}^{\mu \nu }\langle {T}_{\mu \nu }\rangle =\frac{1}{{\left(4\pi \right)}^{2}}\left(cF-aG\right)$ where F is the square of the Weyl tensor and $\int {\mathrm{d}}^{4}x\sqrt{g}G/{\left(4\pi \right)}^{2}$ is the Euler number. For free CFTs with N s massless fields of spin s $720c=6{N}_{0}+18{N}_{1/2}+72{N}_{1}720a=2{N}_{0}+11{N}_{1/2}+124{N}_{1}$.

Ben-Benjamin JS, Scully MO, Fulling SA,
et al., 2019, Unruh acceleration radiation revisited, *International Journal of Modern Physics A: particles and fields; gravitation; cosmology; nuclear physics*, Vol: 34, ISSN: 0217-751X

Tools ShareAbstractWhen ground-state atoms are accelerated and the field with which they interact is in its normal vacuum state, the atoms detect Unruh radiation. We show that atoms falling into a black hole emit acceleration radiation which, under appropriate initial conditions (Boulware vacuum), has an energy spectrum which looks much like Hawking radiation. This analysis also provides insight into the Einstein principle of equivalence between acceleration and gravity. The Unruh temperature can also be obtained by using the Kubo–Martin–Schwinger (KMS) periodicity of the two-point thermal correlation function, for a system undergoing uniform acceleration; as with much of the material in this paper, this known result is obtained with a twist.

Borsten L, Duff MJ, Fernandez-Melgarejo JJ,
et al., 2019, Black holes and general Freudenthal transformations, *Journal of High Energy Physics*, Vol: 2019, ISSN: 1029-8479

We study General Freudenthal Transformations (GFT) on black hole solutions in Einstein-Maxwell-Scalar (super)gravity theories with global symmetry of type E7. GFT can be considered as a 2-parameter, a, b ∈ ℝ, generalisation of Freudenthal duality: x→xF=ax+bx~ , where x is the vector of the electromagnetic charges, an element of a Freudenthal triple system (FTS), carried by a large black hole and x~ is its Freudenthal dual. These transformations leave the Bekenstein-Hawking entropy invariant up to a scalar factor given by a2 ± b2. For any x there exists a one parameter subset of GFT that leave the entropy invariant, a2 ± b2 = 1, defining the subgroup of Freudenthal rotations. The Freudenthal plane defined by spanℝ{x, x~ } is closed under GFT and is foliated by the orbits of the Freudenthal rotations. Having introduced the basic definitions and presented their properties in detail, we consider the relation of GFT to the global symmetries or U-dualities in the context of supergravity. We consider explicit examples in pure supergravity, axion-dilaton theories and N = 2, D = 4 supergravities obtained from D = 5 by dimensional reductions associated to (non-degenerate) reduced FTS’s descending from cubic Jordan Algebras.

Borsten L, Duff MJ, Marrani A, 2019, Twin conformal field theories, *The Journal of High Energy Physics*, Vol: 2019, ISSN: 1029-8479

Supersymmetric theories with the same bosonic content but different fermions, aka twins, were thought to exist only for supergravity. Here we show that pairs of super conformal field theories, for example exotic N = 3 and N = 1 theories in D = 4 space-time dimensions, can also be twin. We provide evidence from three different perspectives: (i) a twin S-fold construction, (ii) a double-copy argument and (iii) by identifying candidate twin holographically dual gauged supergravity theories. Furthermore, twin W-supergravity theories then follow by applying the double-copy prescription to exotic super conformal field theories.

Anastasiou A, Borsten L, Duff MJ, et al., 2019, The mile high magic pyramid, 4th Mile High Conference on Nonassociative Mathematics, Publisher: AMER MATHEMATICAL SOC, Pages: 1-27, ISSN: 0271-4132

Duff MJ, 2018, Thirty years of Erice on the brane

After initially meeting with fierce resistance, "branes", p-dimensionalextended objects which go beyond particles (p=0) and strings (p=1), now occupycentre stage in theoretical physics as microscopic components of M-theory, asthe seeds of the AdS/CFT correspondence, as a branch of particle phenomenology,as the higher-dimensional progenitors of black holes and, via the"brane-world", as entire universes in their own right. Notwithstanding thisearly opposition, Nino Zichichi invited me to to talk about supermembranes andeleven dimensions at the 1987 School on Subnuclear Physics and has continued tokeep Erice on the brane ever since. Here I provide a distillation of my Ericebrane lectures and some personal recollections.

Anastasiou A, Borsten L, Duff MJ,
et al., 2018, Gravity as gauge theory squared: a ghost story, *Physical Review Letters*, Vol: 121, Pages: 1-6, ISSN: 0031-9007

The Becchi-Rouet-Stora-Tyutin (BRST) transformations and equations of motion of a gravity–two-form–dilaton system are derived from the product of two Yang-Mills theories in a BRST covariant form, to linear approximation. The inclusion of ghost fields facilitates the separation of the graviton and dilaton. The gravitational gauge fixing term is uniquely determined by those of the Yang-Mills factors which can be freely chosen. Moreover, the resulting gravity–two-form–dilaton Lagrangian is anti-BRST invariant and the BRST and anti-BRST charges anticommute as a direct consequence of the formalism.

Anastasiou A, Borsten L, Duff MJ,
et al., 2018, Are all supergravity theories Yang-Mills squared?, *Nuclear Physics B*, Vol: 934, Pages: 606-633, ISSN: 0550-3213

Using simple symmetry arguments we classify the ungauged D =4, N = 2, supergravity theories, coupled to both vector and hyper multiplets through homogeneous scalar manifolds, that can be built as the product of N = 2 andN = 0 matter-coupled Yang–Mills gauge theories. This includes all such supergravities with two isolated exceptions: pure supergravity and the T3 model.

Anastasiou A, Borsten L, Duff MJ,
et al., 2017, Twin supergravities from Yang-Mills theory squared, *PHYSICAL REVIEW D*, Vol: 96, ISSN: 2470-0010

We consider “twin supergravities”—pairs of supergravities with N+ and N− supersymmetries, N+>N−, with identical bosonic sectors—in the context of tensoring super Yang-Mills multiplets. It is demonstrated that the pairs of twin supergravity theories are related through their left and right super Yang-Mills factors. This procedure generates new theories from old ones. In particular, the matter coupled N− twins in D=3, 5, 6 and the N−=1 twins in D=4 have not, as far as we are aware, been obtained previously using the double-copy construction, adding to the growing list of double-copy constructible theories. The use of fundamental matter multiplets in the double-copy construction leads us to introduce a bifundamental scalar that couples to the well-known biadjoint scalar field. It is also shown that certain matter coupled supergravities admit more than one factorization into left and right super Yang-Mills-matter theories.

Duff MJ, 2017, Abdus Salam at Imperial College, *INTERNATIONAL JOURNAL OF MODERN PHYSICS A*, Vol: 32, ISSN: 0217-751X

Duff MJ, Ferrara S, Marrani A, 2017, D=3 unification of curious supergravities, *Journal of High Energy Physics*, Vol: 2017, ISSN: 1029-8479

We consider the dimensional reduction to D = 3 of four maximal-rank super-gravities which preserve minimal supersymmetry in D = 11, 7, 5 and 4. Such “curious” theories were investigated some time ago, and the four-dimensional one corresponds to an N=1 supergravity with 7 chiral multiplets spanning the seven-disk manifold. Recently, this latter theory provided cosmological models for α-attractors, which are based on the disk geometry with possible restrictions on the parameter α. A unified picture emerges in D = 3, where the Ehlers group of General Relativity merges with the S-, T- and U-dualities of the D = 4 parent theories.

Borsten L, Duff MJ, 2017, Majorana Fermions in Particle Physics, Solid State and Quantum Information, 53rd Course of the International-School-of-Subnuclear-Physics (ISSP), Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD

Borsten L, Duff MJ, 2017, Gravity as the square of Yang-Mills?, 53rd Course of the International-School-of-Subnuclear-Physics (ISSP), Publisher: WORLD SCIENTIFIC PUBL CO PTE LTD

Duff MJ, 2016, Comment on time-variation of fundamental constants, Publisher: arXiv

The possible time variation of dimensionless fundamental constants of nature, such as the fine-structure constant α, is a legitimate subject of physical enquiry. By contrast, the time variation of dimensional constants, such as ℏ, c, G, e, k,... which are merely human constructs whose number and values differ from one choice of units to the next, has no operational meaning. To illustrate this, we refute a recent claim of Davies et al that black holes can discriminate between two contending theories of varying α, one with varying c and the other with varying e. In Appendix A we respond to criticisms by P. Davies and two Nature referees. In Appendix B we respond to remarks by Magueijo and by T. Davis. In Appendix C we critique recent claims by Copi, A. Davis and Krauss to have placed constraints on ΔG/G.} In Appendix D we provide extracts of a lecture by Dirac, of which we have only recently become aware, which includes the comment "Talking about whether a thing is constant or not does not have any absolute meaning unless that quantity is dimensionless".

Duff MJ, Lu JX, Percacci R,
et al., 2015, Membrane duality revisited, *Nuclear Physics B*, Vol: 901, Pages: 1-21, ISSN: 0550-3213

Borsten L, Duff MJ, 2015, Gravity as the square of Yang-Mills?, *PHYSICA SCRIPTA*, Vol: 90, ISSN: 0031-8949

Borsten L, Bradler K, Duff MJ, 2015, The structure of superqubit states, *Rivista del Nuovo Cimento*, Vol: 38, Pages: 371-386, ISSN: 0393-697X

Duff MJ, 2015, M-history without the M, *Contemporary Physics*, Vol: 57, Pages: 83-85, ISSN: 0010-7514

Duff MJ, 2015, How fundamental are fundamental constants?, *Contemporary Physics*, Vol: 56, Pages: 35-47, ISSN: 0010-7514

I argue that the laws of physics should be independent of one’s choice of units or measuring apparatus. This is the case if they are framed in terms of dimensionless numbers such as the fine structure constant, α. For example, the standard model of particle physics has 19 such dimensionless parameters whose values all observers can agree on, irrespective of what clock, rulers or scales… they use to measure them. Dimensional constants, on the other hand, such as ħ, c, G, e and k …, are merely human constructs whose number and values differ from one choice of units to the next. In this sense, only dimensionless constants are ‘fundamental’. Similarly, the possible time variation of dimensionless fundamental ‘constants’ of nature is operationally well defined and a legitimate subject of physical enquiry. By contrast, the time variation of dimensional constants such as c or G on which a good many (in my opinion, confusing) papers have been written, is a unit-dependent phenomenon on which different observers might disagree depending on their apparatus. All these confusions disappear if one asks only unit-independent questions. We provide a selection of opposing opinions in the literature and respond accordingly.

Anastasiou A, Borsten L, Duff MJ,
et al., 2014, Yang-Mills Origin of Gravitational Symmetries, *PHYSICAL REVIEW LETTERS*, Vol: 113, ISSN: 0031-9007

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- Citations: 92

Anastasiou A, Borsten L, Duff MJ,
et al., 2014, An octonionic formulation of the M-theory algebra, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 13

Borsten L, Bradler K, Duff MJ, 2014, Tsirelson's bound and supersymmetric entangled states, *PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES*, Vol: 470, ISSN: 1364-5021

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- Citations: 3

Anastasiou A, Borsten L, Duff MJ,
et al., 2014, Super Yang-Mills, division algebras and triality, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 20

Anastasiou A, Borsten L, Duff MJ,
et al., 2014, A magic pyramid of supergravities, *JOURNAL OF HIGH ENERGY PHYSICS*, ISSN: 1029-8479

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- Citations: 42

Borsten L, Duff MJ, Hughes LJ,
et al., 2014, Magic Square from Yang-Mills Squared, *PHYSICAL REVIEW LETTERS*, Vol: 112, ISSN: 0031-9007

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- Citations: 44

Borsten L, Duff MJ, Ferrara S,
et al., 2014, Explicit Orbit Classification of Reducible Jordan Algebras and Freudenthal Triple Systems, *COMMUNICATIONS IN MATHEMATICAL PHYSICS*, Vol: 325, Pages: 17-39, ISSN: 0010-3616

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- Citations: 10

Borsten L, Duff MJ, Ferrara S,
et al., 2013, Freudenthal dual Lagrangians, *CLASSICAL AND QUANTUM GRAVITY*, Vol: 30, ISSN: 0264-9381

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- Citations: 13

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