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We present 50-fs, single-shot measurements of the x-ray thermal diffuse scattering (TDS) from copper foils that have been shocked via nanosecond laser-ablation up to pressures above 135~GPa. We hence deduce the x-ray Debye-Waller (DW) factor, providing a temperature measurement. The targets were laser-shocked with the DiPOLE 100-X laser at the High Energy Density (HED) endstation of the European X-ray Free-Electron Laser (EuXFEL). Single x-ray pulses, with a photon energy of 18 keV, were scattered from the samples and recorded on Varex detectors. Despite the targets being highly textured (as evinced by large variations in the elastic scattering), and with such texture changing upon compression, the absolute intensity of the azimuthally averaged inelastic TDS between the Bragg peaks is largely insensitive to these changes, and, allowing for both Compton scattering and the low-level scattering from a sacrificial ablator layer, provides a reliable measurement of $T/\Theta_D^2$, where $\Theta_D$ is the Debye temperature. We compare our results with the predictions of the SESAME 3336 and LEOS 290 equations of state for copper, and find good agreement within experimental errors. We thus demonstrate that single-shot temperature measurements of dynamically compressed materials can be made via thermal diffuse scattering of XFEL radation., Comment: 17 pages, 9 figures in main article; 10 pages, 5 figures in supplementary material

The vanishing of the SO(N) beta-function of gauged N>4 supergravity has long seemed like an answer looking for a question. Here we conjecture that it is a consequence of a Montonon-Olive style electric/magnetic duality., Comment: Dedicated to the memory of Stanley Deser

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 AdS_5 x S^5 and the M5-brane with OSp(8^*|4) on AdS_7 x S^4, in addition to the known M2-brane with OSp(8|4) on AdS_4 x S^7. 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., Comment: 14 pages, minor corrections, added references

Celebrating fifty years of collaboration and friendship with Chris Isham., Comment: 9 pages, 3 figures. Minor corrections

When compact manifolds $X$ and $Y$ are both even dimensional, their Euler characteristics obey the K\"unneth formula $\chi(X\times Y)=\chi(X) \chi(Y)$. In terms of the Betti numbers $b_p(X)$, $\chi(X)=\sum_{p}(-1)^p b_p(X)$, implying that $\chi(X)=0$ when $X$ is odd dimensional. We seek a linear combination of Betti numbers, called $\rho$, that obeys an analogous formula $\rho(X\times Y)=\chi(X) \rho(Y)$ when $Y$ is odd dimensional. The unique solution is $\rho(Y)=-\sum_{p}(-1)^p p b_p(Y)$. Physical applications include: (1) $\rho \rightarrow (-1)^m \rho $ under a generalized mirror map in $d=2m+1$ dimensions, in analogy with $\chi \rightarrow (-1)^m \chi $ in $d=2m$; (2) $\rho$ appears naturally in compactifications of M-theory. For example, the 4-dimensional Weyl anomaly for M-theory on $X^4 \times Y^7$ is given by $\chi(X^4)\rho(Y^7)=\rho(X^4 \times Y^7) $ and hence vanishes when $Y^7$ is self-mirror. Since, in particular, $\rho(Y\times S^1)=\chi(Y)$, this is consistent with the corresponding anomaly for Type IIA on $X^4 \times Y^6$, given by $\chi(X^4)\chi(Y^6)=\chi(X^4 \times Y^6)$, which vanishes when $Y^6$ is self-mirror; (3) In the partition function of $p$-form gauge fields, $\rho$ appears in odd dimensions as $\chi$ does in even., Comment: 29 pg

Professor Tom Kibble was an internationally-renowned theoretical physicist whose contributions to theoretical physics range from the theory of elementary particles to modern early-universe cosmology. The unifying theme behind all his work is the theory of non-abelian gauge theories, the Yang-Mills extension of electromagnetism. One of Kibble's most important pieces of work in this area was his study of the symmetry-breaking mechanism whereby the force-carrying vector particles in the theory can acquire a mass accompanied by the appearance of a massive scalar boson. This idea, put forward independently by Brout and Englert, by Higgs and by Guralnik, Hagen and Kibble in 1964, and generalised by Kibble in 1967, lies at the heart of the Standard Model and all modern unified theories of fundamental particles. It was vindicated in 2012 by the discovery of the Higgs boson at CERN. According to Nobel Laureate Steven Weinberg, "Tom Kibble showed us why light is massless"; this is the fundamental basis of electromagnetism., Comment: 15 pages, latex, corrections to citations; published in the Biographical Memoirs of Fellows of the Royal Society

We describe various relations between Bhargava's higher composition laws, which generalise Gauss's original composition law on integral binary quadratic forms, and extremal black hole solutions appearing in string/M-theory and related models. The cornerstone of these correspondences is the identification of the charge cube of the STU black hole with Bhargava's cube of integers, which underpins the related higher composition laws., Comment: 25 pages. References and further note added. Minor typos corrected

In a September 1976 PRL Eguchi and Freund considered two topological invariants: the Pontryagin number $P \sim \int d^4x \sqrt{g}R^* R$ and the Euler number $\chi \sim \int d^4x \sqrt{g}R^* R^*$ 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 $\chi$. 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: \[ g^{\mu\nu}\langle T_{\mu\nu}\rangle=\frac{1}{(4\pi)^2}(cF-aG)\] where $F$ is the square of the Weyl tensor and $\int d^4x\sqrt{g} G/(4\pi)^2$ is the Euler number. For free CFTs with $N_s$massless fields of spin $s$ \[ 720c=6N_0 + 18N_{1/2} + 72 N_1~~~~ 720a=2N_0 + 11N_{1/2} + 124N_1 \], Comment: Published version, minor corrections and improvements, added references

When 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., Comment: In honor of Julian Schwinger 27 pages, 10 figures

We study General Freudenthal Transformations (GFT) on black hole solutions in Einstein-Maxwell-Scalar (super)gravity theories with global symmetry of type $E_7$. GFT can be considered as a 2-parameter, $a, b\in {\mathbb R}$, generalisation of Freudenthal duality: $x\mapsto x_F= a x+b\tilde{x}$, where $x$ is the vector of the electromagnetic charges, an element of a Freudenthal triple system (FTS), carried by a large black hole and $ \tilde{x}$ is its Freudenthal dual. These transformations leave the Bekenstein-Hawking entropy invariant up to a scalar factor given by $a^2\pm b^2$. For any $x$ there exists a one parameter subset of GFT that leave the entropy invariant, $a^2\pm b^2=1$, defining the subgroup of Freudenthal rotations. The Freudenthal plane defined by span$_\mathbb{R}\{x, \tilde{x}\}$ 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 sysmmetries or U-dualites 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., Comment: 65 pages

After initially meeting with fierce resistance, "branes", p-dimensional extended objects which go beyond particles (p=0) and strings (p=1), now occupy centre stage in theoretical physics as microscopic components of M-theory, as the 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 this early opposition, Nino Zichichi invited me to to talk about supermembranes and eleven dimensions at the 1987 School on Subnuclear Physics and has continued to keep Erice on the brane ever since. Here I provide a distillation of my Erice brane lectures and some personal recollections., Comment: Published Version 2024. Based on lectures at the International Schools of Subnuclear Physics 1987-2017 and the International Symposium "60 Years of Subnuclear Physics at Bologna", University of Bologna, November 2018. arXiv admin note: text overlap with arXiv:hep-th/9611203

Supersymmetric theories with the same bosonic content but different fermions, aka \emph{twins}, were thought to exist only for supergravity. Here we show that pairs of super conformal field theories, for example exotic $\mathcal{N}=3$ and $\mathcal{N}=1$ theories in $D=4$ spacetime 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., Comment: 28 pages. Updated to match published version. References and brief comments added

We present a conformal isometry for static extremal black hole solutions in all four-dimensional Einstein-Maxwell-scalar theories with electromagnetic duality groups `of type $E_7$'. This includes, but is not limited to, all supergravity theories with $\mathcal{N}>2$ supersymmetry and all $\mathcal{N}=2$ supergravity theories with symmetric scalar manifolds. The conformal isometry is valid for arbitrary electromagnetic charge configurations and relies crucially on the notion of Freudenthal duality.

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 anti commute as a direct consequence of the formalism., Comment: Updated to match published version. Minor clarifications/corrections made

Using a unified formulation of $\mathcal{N} = 1, 2, 4, 8$, super Yang-Mills theories in $D = 3$ spacetime dimensions with fields valued respectively in $\mathbb{R, C, H, O}$, it was shown that tensoring left and right multiplets yields a Freudenthal magic square of $D = 3$ supergravities. When tied in with the more familiar $\mathbb{R, C, H, O}$ description of super Yang-Mills in $D = 3, 4, 6, 10$ this results in a magic pyramid of supergravities: the known $4 \times 4$ magic square at the base in $D=3$, a $3\times 3$ square in $D=4$, a $2 \times 2$ square in $D=6$ and Type II supergravity at the apex in $D=10$., Comment: Contribution to the proceedings of the 4th Mile High Conference on Nonassociative Mathematics University of Denver, Denver, Colorado, USA, July 29-August 5, 2017

The description of the dynamics of an electron in an external electromagnetic field of arbitrary intensity is one of the most fundamental outstanding problems in electrodynamics. Remarkably, to date there is no unanimously accepted theoretical solution for ultra-high intensities and little or no experimental data. The basic challenge is the inclusion of the self-interaction of the electron with the field emitted by the electron itself - the so-called radiation reaction force. We report here on the experimental evidence of strong radiation reaction, in an all-optical experiment, during the propagation of highly relativistic electrons (maximum energy exceeding 2 GeV) through the field of an ultra-intense laser (peak intensity of $4\times10^{20}$ W/cm$^2$). In their own rest frame, the highest energy electrons experience an electric field as high as one quarter of the critical field of quantum electrodynamics and are seen to lose up to 30% of their kinetic energy during the propagation through the laser field. The experimental data show signatures of quantum effects in the electron dynamics in the external laser field, potentially showing departures from the constant cross field approximation.

The dynamics of energetic particles in strong electromagnetic fields can be heavily influenced by the energy loss arising from the emission of radiation during acceleration, known as radiation reaction. When interacting with a high-energy electron beam, today's lasers are sufficiently intense to explore the transition between the classical and quantum radiation reaction regimes. We report on the observation of radiation reaction in the collision of an ultra-relativistic electron beam generated by laser wakefield acceleration ($\varepsilon > 500$ MeV) with an intense laser pulse ($a_0 > 10$). We measure an energy loss in the post-collision electron spectrum that is correlated with the detected signal of hard photons ($\gamma$-rays), consistent with a quantum (stochastic) description of radiation reaction. The generated $\gamma$-rays have the highest energies yet reported from an all-optical inverse Compton scattering scheme, with critical energy $\varepsilon_{\rm crit} > $ 30 MeV., Comment: 11 pages, 9 figures, accepted for publication in PRX

Using simple symmetry arguments we classify the ungauged $D=4$, $\mathcal{N}=2$ supergravity theories, coupled to both vector and hyper multiplets through homogeneous scalar manifolds, that can be built as the product of $\mathcal{N}=2$ and $\mathcal{N}=0$ matter-coupled Yang-Mills gauge theories. This includes all such supergravities with two isolated exceptions: pure supergravity and the $T^3$ model., Comment: 22 pages

The radiation pressure of next generation ultra-high intensity ($>10^{23}$ W/cm$^{2}$) lasers could efficiently accelerate ions to GeV energies. However, nonlinear quantum-electrodynamic effects play an important role in the interaction of these laser pulses with matter. Here we show that these effects may lead to the production of an extremely dense ($\sim10^{24}$ cm$^{-3}$) pair-plasma which absorbs the laser pulse consequently reducing the accelerated ion energy and energy conversion efficiency by up to 30-50\% \& 50-65\%, respectively. Thus we identify the regimes of laser-matter interaction where either ions are efficiently accelerated or dense pair-plasmas are produced as a guide for future experiments.

This review is based on lectures given by M. J. Duff summarising the far reaching contributions of Ettore Majorana to fundamental physics, with special focus on Majorana fermions in all their guises. The theoretical discovery of the eponymous fermion in 1937 has since had profound implications for particle physics, solid state and quantum computation. The breadth of these disciplines is testimony to Majorana's genius, which continues to permeate physics today. These lectures offer a whistle-stop tour through some limited subset of the key ideas. In addition to touching on these various applications, we will draw out some fascinating relations connecting the normed division algebras $\mathbb{R}, \mathbb{C}, \mathbb{H}, \mathbb{O}$ to spinors, trialities, $K$-theory and the classification of stable topological states of symmetry-protected gapped free-fermion systems., Comment: Contribution to the Proceedings of the Erice International School of Subnuclear Physics, 53rd Course: "The Future of Our Physics Including New Frontiers", and Celebration of the Triumph of Ettore Majorana, Erice, 24 June-3 July 2015

We consider the dimensional reduction to D = 3 of four maximal-rank supergravities 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 alpha-attractors, which are based on the disk geometry with possible restrictions on the parameter alpha. 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., Comment: 1+7 pages; v2 : minor refinements, one Ref. added, matches published version

We consider `twin supergravities' - pairs of supergravities with $\mathcal{N}_+$ and $\mathcal{N}_-$ supersymmetries, $\mathcal{N}_+>\mathcal{N}_-$, 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. In particular, the matter coupled $\mathcal{N}_-$ twins in $D=3,5,6$ and the $\mathcal{N}_-=1$ 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 bi-fundamental scalar that couples to the well-known bi-adjoint scalar field. It is also shown that certain matter coupled supergravities admit more than one factorisation into left and right super Yang-Mills-matter theories., Comment: v2 reference added, 29 pages, 4 figs

In these lectures we review how the symmetries of gravitational theories may be regarded as originating from those of "Yang-Mills squared". We begin by motivating the idea that certain aspects of gravitational theories can be captured by the product, in some sense, of two distinct Yang-Mills theories, particularly in the context of scattering amplitudes. We then introduce a concrete dictionary for the covariant fields of (super)gravity in terms of the product of two (super) Yang-Mills theories. The dictionary implies that the symmetries of each (super) Yang-Mills factor generate the symmetries of the corresponding (super)gravity theory: general covariance, $p$-form gauge invariance, local Lorentz invariance, local supersymmetry, R-symmetry and U-duality., Comment: Typos fixed. 26 pages, 6 figs. Based on lectures delivered by M. J. Duff at the Richard Arnowitt Symposium. Published in the Focus Issue on gravity, supergravity and fundamental physics: the Richard Arnowitt Symposium. Chosen as Physica Scripta's Paper of the Week 01/12/2015

Just as string T-duality originates from transforming field equations into Bianchi identities on the string worldsheet, so it has been suggested that M-theory U-dualities originate from transforming field equations into Bianchi identities on the membrane worldvolume. However, this encounters a problem unless the target space has dimension $D = p + 1$. We identify the problem to be the nonintegrability of the U-duality transformation assigned to the pull-back map. Just as a double geometry renders manifest the $O(D,D)$ string T-duality, here we show in the case of the M2-brane in $D = 3$ that a generalised geometry renders manifest the $SL(3) \times SL(2)$ U-duality. In the case of M2-brane in $D=4$, with and without extra target space coordinates, we show that only the ${\rm GL}(4,R)\ltimes R^4$ subgroup of the expected $SL(5,R)$ U-duality symmetry is realised., Comment: 26 pages

A review of the book "A Brief History of String Theory: From Dual Models to M-Theory" by Dean Rickles, Comment: 6 pages latex. Book review commissioned by Contemporary Physics

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, alpha. 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, scales... they use to measure them. Dimensional constants, on the other hand, such as h, c, G, e, 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., Comment: Note added. 30 pages latex. 7 figures. arXiv admin note: text overlap with arXiv:hep-th/0208093 (unpublished)

Superqubits provide a supersymmetric generalisation of the conventional qubit in quantum information theory. After a review of their current status, we address the problem of generating entangled states. We introduce the global unitary supergroup $\text{UOSp}((3^n+1)/2 | (3^n-1)/2)$ for an $n$-superqubit system, which contains as a subgroup the local unitary supergroup $[\text{UOSp}(2|1)]^n$. While for $4>n>1$ the bosonic subgroup in $\text{UOSp}((3^n+1)/2 | (3^n-1)/2)$ does not contain the standard global unitary group $\text{SU}(2^n)$, it does have an $\text{USp}(2^n)\subset\text{SU}(2^n)$ subgroup which acts transitively on the $n$-qubit subspace, as required for consistency with the conventional multi-qubit framework. For two superqubits the $\text{UOSp}(5|4)$ action is used to generate entangled states from the "bosonic" separable state $|00\rangle$., Comment: 12 pages, updated to match published version. RIVISTA DEL NUOVO CIMENTO, 38, 2015, Imperial/TP/2014/mjd/04

By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincar\'e. As a concrete example we focus on the new-minimal (12+12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4+4,N_L =1)and(3+0,N_R =0)., Comment: References added plus minor revisions

We give an octonionic formulation of the N = 1 supersymmetry algebra in D = 11, including all brane charges. We write this in terms of a novel outer product, which takes a pair of elements of the division algebra A and returns a real linear operator on A. More generally, with this product comes the power to rewrite any linear operation on R^n (n = 1,2,4,8) in terms of multiplication in the n-dimensional division algebra A. Finally, we consider the reinterpretation of the D = 11 supersymmetry algebra as an octonionic algebra in D = 4 and the truncation to division subalgebras.

By formulating N = 1, 2, 4, 8, D = 3, Yang-Mills with a single Lagrangian and single set of transformation rules, but with fields valued respectively in R,C,H,O, it was recently shown that tensoring left and right multiplets yields a Freudenthal-Rosenfeld-Tits magic square of D = 3 supergravities. This was subsequently tied in with the more familiar R,C,H,O description of spacetime to give a unified division-algebraic description of extended super Yang-Mills in D = 3, 4, 6, 10. Here, these constructions are brought together resulting in a magic pyramid of supergravities. The base of the pyramid in D = 3 is the known 4x4 magic square, while the higher levels are comprised of a 3x3 square in D = 4, a 2x2 square in D = 6 and Type II supergravity at the apex in D = 10. The corresponding U-duality groups are given by a new algebraic structure, the magic pyramid formula, which may be regarded as being defined over three division algebras, one for spacetime and each of the left/right Yang-Mills multiplets. We also construct a conformal magic pyramid by tensoring conformal supermultiplets in D = 3, 4, 6. The missing entry in D = 10 is suggestive of an exotic theory with G/H duality structure F4(4)/Sp(3) x Sp(1)., Comment: 30 pages, 6 figures. Updated to match published version. References and comments added

We give a unified division algebraic description of (D=3, N=1,2,4,8), (D=4, N=1,2,4), (D=6, N=1,2) and (D=10, N=1) super Yang-Mills theories. A given (D=n+2, N) theory is completely specified by selecting a pair (A_n, A_{nN}) of division algebras, A_n, A_{nN} = R, C, H, O, where the subscripts denote the dimension of the algebras. We present a master Lagrangian, defined over A_{nN}-valued fields, which encapsulates all cases. Each possibility is obtained from the unique (O, O) (D=10, N=1) theory by a combination of Cayley-Dickson halving, which amounts to dimensional reduction, and removing points, lines and quadrangles of the Fano plane, which amounts to consistent truncation. The so-called triality algebras associated with the division algebras allow for a novel formula for the overall (spacetime plus internal) symmetries of the on-shell degrees of freedom of the theories. We use imaginary A_{nN}-valued auxiliary fields to close the non-maximal supersymmetry algebra off-shell. The failure to close for maximally supersymmetric theories is attributed directly to the non-associativity of the octonions., Comment: 24 pages, 2 figures. Updated to match published version. References added

We give a unified description of D = 3 super-Yang-Mills theory with N = 1, 2, 4, and 8 supersymmeties in terms of the four division algebras: reals (R), complexes (C), quaternions (H) and octonions (O). Tensoring left and right super-Yang-Mills multiplets with N = 1, 2, 4, 8 we obtain a magic square RR, CR, CC, HR, HC, HH, OR, OC, OH, OO description of D = 3 supergravity with N = 2, 3, 4, 5, 6, 8, 9, 10, 12, 16., Comment: 4 pages, refs 11 and 12 added, footnote 1 modified. Updated to match published version

The global U-dualities of extended supergravity have played a central role in differentiating the distinct classes of extremal black hole solutions. When the U-duality group satisfies certain algebraic conditions, as is the case for a broad class of supergravities, the extremal black holes enjoy a further symmetry known as Freudenthal duality (F-duality), which although distinct from U-duality preserves the Bekenstein-Hawking entropy. Here it is shown that, by adopting the doubled Lagrangian formalism, F-duality, defined on the doubled field strengths, is not only a symmetry of the black hole solutions, but also of the equations of motion themselves. A further role for F-duality is introduced in the context of world-sheet actions. The Nambu-Goto world-sheet action in any (t, s) signature spacetime can be written in terms of the F-dual. The corresponding field equations and Bianchi identities are then related by F-duality allowing for an F-dual formulation of Gaillard-Zumino duality on the world-sheet. An equivalent polynomial "Polyakov- type" action is introduced using the so-called black hole potential. Such a construction allows for actions invariant under all groups of type E7, including E7 itself, although in this case the stringy interpretation is less clear., Comment: 1+16 pages, 1 Table, updated to match published version

A superqubit, belonging to a $(2|1)$-dimensional super-Hilbert space, constitutes the minimal supersymmetric extension of the conventional qubit. In order to see whether superqubits are more nonlocal than ordinary qubits, we construct a class of two-superqubit entangled states as a nonlocal resource in the CHSH game. Since super Hilbert space amplitudes are Grassmann numbers, the result depends on how we extract real probabilities and we examine three choices of map: (1) DeWitt (2) Trigonometric (3) Modified Rogers. In cases (1) and (2) the winning probability reaches the Tsirelson bound $p_{win}=\cos^2{\pi/8}\simeq0.8536$ of standard quantum mechanics. Case (3) crosses Tsirelson's bound with $p_{win}\simeq0.9265$. Although all states used in the game involve probabilities lying between 0 and 1, case (3) permits other changes of basis inducing negative transition probabilities., Comment: Updated to match published version. Minor modifications. References added

We give a review of the black-hole/qubit correspondence that incorporates not only the earlier results on black hole entropy and entanglement measures, seven qubits and the Fano plane, wrapped branes as qubits and the attractor mechanism as a distillation procedure, but also newer material including error-correcting codes, Mermin squares, Freudenthal triples and 4-qubit entanglement classification., Comment: 66 pages, 11 figures, to appear in Classical and Quantum Gravity special focus issue on relativistic quantum information

Quantum entanglement lies at the heart of quantum information theory, with applications to quantum computing, teleportation, cryptography and communication. In the apparently separate world of quantum gravity, the Hawking effect of radiating black holes has also occupied centre stage. Despite their apparent differences, it turns out that there is a correspondence between the two., Comment: Talk delivered at the Pontifical Academy of Sciences Symposium on Subnuclear Physics, Vatican City, October 2011

Recent calculations have confirmed the belief that the ultraviolet behaviour of N-extended supergravities improves with increasing N. We give a comprehensive review., Comment: In view of the revival of interest in the subject, we are posting these lectures delivered at the 1981 Spring School on Supergravity ICTP, Trieste

Using as a springboard a three-way debate between theoretical physicist Lee Smolin, philosopher of science Nancy Cartwright and myself, I address in layman's terms the issues of why we need a unified theory of the fundamental interactions and why, in my opinion, string and M-theory currently offer the best hope. The focus will be on responding more generally to the various criticisms. I also describe the diverse application of string/M-theory techniques to other branches of physics and mathematics which render the whole enterprise worthwhile whether or not "a theory of everything" is forthcoming., Comment: Update on EPSRC. (Contribution to the Special Issue of Foundations of Physics: "Forty Years Of String Theory: Reflecting On the Foundations", edited by Gerard 't Hooft, Erik Verlinde, Dennis Dieks and Sebastian de Haro. 22 pages latex)

We determine explicit orbit representatives of reducible Jordan algebras and of their corresponding Freudenthal triple systems. This work has direct application to the classification of extremal black hole solutions of N = 2, 4 locally supersymmetric theories of gravity coupled to an arbitrary number of Abelian vector multiplets in D = 4, 5 space-time dimensions., Comment: 18 pages. Updated to match published version