Publications
221 results found
Duff MJ, 2013, Black holes and qubits, Proceedings of the International School of Subnuclear Physics, Publisher: World Scientific Publ Co, Pages: 57-66
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.
Duff MJ, 2013, String and M-Theory: Answering the Critics (vol 43, pg 182, 2013), FOUNDATIONS OF PHYSICS, Vol: 43, Pages: 284-284, ISSN: 0015-9018
Duff MJ, 2013, String and M-Theory: Answering the critics, Foundations of Physics, Vol: 43, Pages: 182-200, ISSN: 0015-9018
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.
Duff MJ, 2013, The black hole/qubit correspondence, 6th International Symposium on Quantum Theory and Symmetries (QTS), Publisher: IOP PUBLISHING LTD, ISSN: 1742-6588
- Author Web Link
- Cite
- Citations: 3
Borsten L, Duff MJ, Levay P, 2012, The black-hole/qubit correspondence: an up-to-date review, CLASSICAL AND QUANTUM GRAVITY, Vol: 29, ISSN: 0264-9381
- Author Web Link
- Cite
- Citations: 54
Borsten L, Duff MJ, Ferrara S, et al., 2012, Small orbits, PHYSICAL REVIEW D, Vol: 85, ISSN: 1550-7998
- Author Web Link
- Cite
- Citations: 39
Borsten L, Duff MJ, Rubens W, 2012, Black holes and qubits, Summer School on Decoherence, Entanglement and Entropy / Workshop on Matrix Product State Formulation and Density Matrix Renormalization Group Simulations, Publisher: World Scientific Publ Co, Pages: 3-107, ISSN: 1793-7299
These notes have been compiled to accompany a series of four lectures given at the Kinki University Quantum Computing Series Summer School on Decoherence, Entanglement and Entropy, August 2009 at the Oxford Kobe Institute (Kobe, Japan).Each of the four lectures focuses on a particular topic falling under the broad umbrella of the "black-hole/qubit correspondence". Lecture I introduces the first instance of the black-hole/qubit correspondence, the relationship between the entanglement of three qubits and the entropy of STU black holes. Lecture II develops this correspondence to the case of black holes and the tripartite entanglement of seven qubits. Lecture III examines the use of Jordan algebras and the Freudenthal triple system, which capture the U-duality symmetries of these black hole systems, in entanglement classification. Lecture IV introduces the superqubit, a natural candidate to represent supersymmetric quantum information.These lectures draw on work done with D. Dahanayake, H. Ebrahim, S. Ferrara and A. Marrani whose efforts are most gratefully acknowledged.
Duff MJ, 2011, M-theory on manifolds of G2 holonomy: the first twenty years
Borsten L, Duff MJ, Marrani A, et al., 2011, On the black-hole/qubit correspondence, EUROPEAN PHYSICAL JOURNAL PLUS, Vol: 126, ISSN: 2190-5444
- Author Web Link
- Cite
- Citations: 34
Duff MJ, Ferrara S, 2011, Generalized mirror symmetry and trace anomalies, Classical and Quantum Gravity, Vol: 28, ISSN: 0264-9381
We consider the compactification of M-theory on X7 with Betti numbers (b0, b1, b2, b3, b3, b2, b1, b0) and define a generalized mirror symmetry (b0, b1, b2, b3) → (b0, b1, b2 − ρ/2, b3 + ρ/2) under which ρ ≡ 7b0 − 5b1 + 3b2 − b3 changes sign. Generalized self-mirror theories with ρ = 0 have massless sectors with vanishing trace anomaly (before dualization). Examples include pure supergravity with {\mathcal N} \ge 4 and supergravity plus matter with {\mathcal N} \le 4.
Duff MJ, Ferrara S, 2011, Four curious supergravities, Physical Review D, Vol: 83, ISSN: 2470-0010
We consider four supergravities with 16+16, 32+32, 64+64, 128+128 degrees of freedom displaying some curious properties: (1) They exhibit minimal supersymmetry (N=1, 2, 2, 1) but maximal rank (r=7, 6, 4, 0) of the scalar coset in D=4, 5, 7, 11. (2) They couple naturally to supermembranes and admit these membranes as solutions. (3) Although the D=4, 5, 7 supergravities follow from truncating the maximally supersymmetric ones, there nevertheless exist M-theory compactifications with G2, SU(3), SU(2) holonomy having these supergravities as their massless sectors. (4) They reduce to N=1, 2, 4, 8 theories all with maximum rank 7 in D=4 which (5) correspond to 0, 1, 3, 7 lines of the Fano plane and hence admit a division algebra (R,C,H,O) interpretation consistent with the black-hole/qubit correspondence, (6) are generalized self-mirror, and hence (7) have a vanishing on-shell trace anomaly.
Borsten L, Dahanayake D, Duff MJ, et al., 2010, Observations on integral and continuous U-duality orbits in N=8 supergravity, Classical and Quantum Gravity, Vol: 27, ISSN: 0264-9381
One would often like to know when two a priori distinct extremal black p-brane solutions are in fact related by U-duality. In the classical supergravity limit the answer for a large class of theories has been known for some time now. However, in the full quantum theory the U-duality group is broken to a discrete subgroup, a consequence of the Dirac–Zwanziger–Schwinger charge quantization conditions. The question of U-duality orbits in this case is a nuanced matter. In the present work we address this issue in the context of \mathcal {N}=8 supergravity in four, five and six dimensions. The purpose of this paper is to present and clarify what is currently known about these orbits while at the same time filling in some of the details not yet appearing in the literature. For the continuous case we present the cascade of relationships existing between the orbits, generated as one descends from six to four dimensions, together with the corresponding implications for the associated moduli spaces. In addressing the discrete case we exploit the mathematical framework of integral Jordan algebras, the integral Freudenthal triple system and, in particular, the work of Krutelevich. The charge vector of the dyonic black string in D = 6 is SO(5,5; \mathds{Z}) related to a two-charge reduced canonical form uniquely specified by a set of two arithmetic U-duality invariants. Similarly, the black hole (string) charge vectors in D = 5 are E_{6(6)}(\mathds{Z}) equivalent to a three-charge canonical form, again uniquely fixed by a set of three arithmetic U-duality invariants. However, the situation in four dimensions is, perhaps predictably, less clear. While black holes preserving more than 1/8 of the supersymmetries may be fully classified by the known arithmetic E_{7(7)}(\mathds{Z}) invariants, 1/8-BPS and non-BPS black holes yield increasingly subtle orbit structures, which remain to be properly understood. However, for the very special subclass of projective black holes
Borsten L, Dahanayake D, Duff MJ, et al., 2010, Four-Qubit Entanglement Classification from String Theory, PHYSICAL REVIEW LETTERS, Vol: 105, ISSN: 0031-9007
- Author Web Link
- Cite
- Citations: 98
Borsten L, Dahanayake D, Duff MJ, et al., 2010, Superqubits, Physical Review D, Vol: 81, ISSN: 2470-0010
We provide a supersymmetric generalization of n quantum bits by extending the local operations and classical communication entanglement equivalence group [SU(2)]n to the supergroup [uOSp(1|2)]n and the stochastic local operations and classical communication equivalence group [SL(2,C)]n to the supergroup [OSp(1|2)]n. We introduce the appropriate supersymmetric generalizations of the conventional entanglement measures for the cases of n=2 and n=3. In particular, super-Greenberger-Horne-Zeilinger states are characterized by a nonvanishing superhyperdeterminant.
Borsten L, Dahanayake D, Duff MJ, et al., 2009, Freudenthal triple classification of three-qubit entanglement, Physical Review A, Vol: 80, ISSN: 1050-2947
We show that the three-qubit entanglement classes, (0) null, (1) separable A−B−C, (2a) biseparable A−BC, (2b) biseparable B−CA, (2c) biseparable C−AB, (3) W, and (4) Greenberger-Horne-Zeilinger, correspond respectively to ranks 0, 1, 2a, 2b, 2c, 3, and 4 of a Freudenthal triple system defined over the Jordan algebra C⊕C⊕C. We also compute the corresponding stochastic local operations and classical communication orbits.
Borsten L, Dahanayake D, Duff MJ, et al., 2009, Black holes admitting a Freudenthal dual, Physical Review D, Vol: 80, ISSN: 2470-0010
The quantized charges x of four-dimensional stringy black holes may be assigned to elements of an integral Freudenthal triple system whose automorphism group is the corresponding U duality and whose U-invariant quartic norm Δ(x) determines the lowest-order entropy. Here, we introduce a Freudenthal duality x→˜x, for which ˜˜x=−x. Although distinct from U duality, it nevertheless leaves Δ(x) invariant. However, the requirement that ˜x be an integer restricts us to the subset of black holes for which Δ(x) is necessarily a perfect square. The issue of higher-order corrections remains open as some, but not all, of the discrete U-duality invariants are Freudenthal invariant. Similarly, the quantized charges A of five-dimensional black holes and strings may be assigned to elements of an integral Jordan algebra, whose cubic norm N(A) determines the lowest-order entropy. We introduce an analogous Jordan dual A⋆, with N(A) necessarily a perfect cube, for which A⋆⋆=A and which leaves N(A) invariant. The two dualities are related by a 4D/5D lift.
Duff MJ, 2009, Near-horizon brane-scan revived, Nuclear Physics B, Vol: 810, Pages: 193-209, ISSN: 0550-3213
In 1987 two versions of the brane-scan of D-dimensional super p-branes were put forward. The first pinpointed those slots consistent with kappa-symmetric Green–Schwarz type actions; the second generalized the membrane at the end of the universe idea to all those superconformal groups describing p-branes on the boundary of . Although the second version predicted D3- and M5-branes in addition to those of the first, it came unstuck because the 1/2 BPS solitonic branes failed to exhibit the required symmetry enhancement in the near-horizon limit, except in the non-dilatonic cases , and . Just recently, however, it has been argued that the fundamental heterotic string does indeed display a near-horizon enhancement to as predicted by the brane-scan, provided corrections are taken into account. If this logic could be extended to the other strings and branes, it would resolve this 21-year-old paradox and provide a wealth of new AdS/CFT dualities, which we tabulate.
Borsten L, Dahanayake D, Duff MJ, et al., 2009, Black holes, qubits and octonions, Physics Reports, Vol: 471, Pages: 113-219, ISSN: 0370-1573
We review the recently established relationships between black hole entropy in string theory and the quantum entanglement of qubits and qutrits in quantum information theory. The first example is provided by the measure of the tripartite entanglement of three qubits (Alice, Bob and Charlie), known as the 3-tangle, and the entropy of the 8-charge black hole of supergravity, both of which are given by the invariant hyperdeterminant, a quantity first introduced by Cayley in 1845. Moreover the classification of three-qubit entanglements is related to the classification of supersymmetric black holes. There are further relationships between the attractor mechanism and local distillation protocols and between supersymmetry and the suppression of bit flip errors. At the microscopic level, the black holes are described by intersecting -branes whose wrapping around the six compact dimensions provides the string-theoretic interpretation of the charges and we associate the three-qubit basis vectors, , with the corresponding 8 wrapping cycles. The black hole/qubit correspondence extends to the 56 charge black holes and the tripartite entanglement of seven qubits where the measure is provided by Cartan’s invariant. The qubits are naturally described by the seven vertices of the Fano plane, which provides the multiplication table of the seven imaginary octonions, reflecting the fact that has a natural structure of an -graded algebra. This in turn provides a novel imaginary octonionic interpretation of the charges of : the NS–NS charges correspond to the three imaginary quaternions and the R–R to the four complementary imaginary octonions. We contrast this approach with that based on Jordan algebras and the Freudenthal triple system. black holes (or black strings) in five dimensions are also related to the bipartite entanglement of three qutrits (3-state systems), where the analogous measure is Cartan’s invariant. Similar analogies exist for magic supergravi
Duff M, 2008, SPECIAL ISSUE: Proceedings of the SALAM+50 Conference, Imperial College London, UK, 7 July 2007 PREFACE, INTERNATIONAL JOURNAL OF MODERN PHYSICS A, Vol: 23, Pages: V-VI, ISSN: 0217-751X
Duff MJ, Ferrara S, 2008, Black hole entropy and quantum information, Supersymmetric Mechanics - Vol. 3 Attractors and Black Holes in Supersymmetric Gravity, Editors: Bellucci, Publisher: Springer, Pages: 93-114, ISBN: 978-3-540-79523-0
We review some recently established connections between the mathematics ofblack hole entropy in string theory and that of multipartite entanglement inquantum information theory. In the case of N=2 black holes and the entanglementof three qubits, the quartic [SL(2)]^3 invariant, Cayley's hyperdeterminant,provides both the black hole entropy and the measure of tripartiteentanglement. In the case of N=8 black holes and the entanglement of sevenqubits, the quartic E_7 invariant of Cartan provides both the black holeentropy and the measure of a particular tripartite entanglement encoded in theFano plane.
Borsten L, Dahanayake D, Duff MJ, et al., 2008, Wrapped branes as qubits, Physical Review Letters, Vol: 100, ISSN: 0031-9007
Recent work has established a correspondence between the tripartite entanglement measure of three qubits and the macroscopic entropy of the four-dimensional 8-charge STU black hole of supergravity. Here we consider the configurations of intersecting D3-branes, whose wrapping around the six compact dimensions T6 provides the microscopic string-theoretic interpretation of the charges, and associate the three-qubit basis vectors |ABC⟩, (A, B, C=0 or 1) with the corresponding 8 wrapping cycles. In particular, we relate a well-known fact of quantum information theory, that the most general real three-qubit state can be parameterized by four real numbers and an angle, to a well-known fact of string theory, that the most general STU black hole can be described by four D3-branes intersecting at an angle.
Duff MJ, Ferrara S, 2008, Black Hole Entropy and Quantum Information, SUPERSYMMETRIC MECHANICS, VOL 3, Editors: Bellucci, Publisher: SPRINGER-VERLAG BERLIN, Pages: 93-114, ISBN: 978-3-540-79522-3
- Author Web Link
- Cite
- Citations: 16
Duff MJ, Ferrara S, 2007, E-6 and the bipartite entanglement of three qutrits, Physical Review D, Vol: 76, ISSN: 2470-0010
Recent investigations have established an analogy between the entropy of four-dimensional supersymmetric black holes in string theory and entanglement in quantum information theory. Examples include: (1) N=2 STU black holes and the tripartite entanglement of three qubits (2-state systems), where the common symmetry is [SL(2)]3 and (2) N=8 black holes and the tripartite entanglement of seven qubits where the common symmetry is E7⊃[SL(2)]7. Here we present another example: N=8 black holes (or black strings) in five dimensions and the bipartite entanglement of three qutrits (3-state systems), where the common symmetry is E6⊃[SL(3)]3. Both the black hole (or black string) entropy and the entanglement measure are provided by the Cartan cubic E6 invariant. Similar analogies exist for magic N=2 supergravity black holes in both four and five dimensions.
Duff M, 2007, String triality, black hole entropy and Cayley's hyperdeterminant, Physical Review D, Vol: 76, ISSN: 2470-0010
The four-dimensional N=2 STU model of string compactification is invariant under an SL(2,Z)S×SL(2,Z)T×SL(2,Z)U duality acting on the dilaton/axion S, complex Kahler form T, and the complex structure fields U, and also under a string/string/string triality S↔T↔U. The model admits an extremal black hole solution with four electric and four magnetic charges whose entropy must respect these symmetries. It is given by the square root of the hyperdeterminant introduced by Cayley in 1845. This also features three-qubit quantum entanglement.
Duff MJ, Ferrara S, 2007, E-7 and the tripartite entanglement of seven qubits, Physical Review D, Vol: 76, ISSN: 2470-0010
In quantum information theory, it is well known that the tripartite entanglement of three qubits is described by the group [SL(2,C)]3 and that the entanglement measure is given by Cayley’s hyperdeterminant. This has provided an analogy with certain N=2 supersymmetric black holes in string theory, whose entropy is also given by the hyperdeterminant. In this paper, we extend the analogy to N=8. We propose that a particular tripartite entanglement of seven qubits, encoded in the Fano plane, is described by the exceptional group E7(C) and that the entanglement measure is given by Cartan’s quartic E7 invariant.
Batrachenko A, Duff MJ, Lu JX, 2007, The membrane at the end of the (de Sitter) universe, Nuclear Physics B, Vol: 762, Pages: 95-111, ISSN: 0550-3213
The original membrane at the end of the universe corresponds to a probe M2-brane of signature occupying the boundary of the spacetime , and is described by an SCFT. However, it was subsequently generalized to other worldvolume signatures and other spacetime signatures . An interesting special case is provided by the brane at the end of the de Sitter universe which has recently featured in the dS/CFT correspondence. The resulting CFT contains the one recently proposed as the holographic dual of a four-dimensional de Sitter cosmology. Supersymmetry restricts S, T, s, t by requiring that the corresponding bosonic symmetry be a subgroup of a superconformal group. The case of is ‘doubly holographic’ and may be regarded as the near horizon geometry of M2-branes or equivalently, under interchange of conformal and R-symmetry, of M5-branes, provided . The same correspondence holds in the pp-wave limit of conventional M-theory.
Duff MJ, Kalkkinen J, 2007, Metric and coupling reversal in string theory, Nuclear Physics B, Vol: 760, Pages: 64-88, ISSN: 0550-3213
Invariance under reversing the sign of the metric and/or the sign of the string coupling field , where , leads to four possible universes denoted 1, , , according as , , , , respectively. Universe 1 is described by conventional string/M theory and contains all M, D, F and NS branes. Universe contains only , D3 and D7. Universe contains only D1, D5, D9 and Type I. Universe contains only F1 and NS5 of IIB and heterotic SO(32).
Duff MJ, Kalkkinen J, 2006, Signature reversal invariance, Nuclear Physics B, Vol: 758, Pages: 161-184, ISSN: 0550-3213
We consider the signature reversing transformation of the metric tensor induced by the chiral transformation of the curved space gamma matrices in spacetimes with signature , which also induces a spacetime orientation reversal. We conclude: (1) It is a symmetry only for chiral theories with , with k integer. (2) Yang–Mills theories require dimensions with T even for which even rank antisymmetric tensor field strengths and mass terms are also allowed. For example, super-Yang–Mills is ruled out. (3) Gravitational theories require dimensions with T odd, for which the symmetry is preserved by coupling to odd rank field strengths. In , for example, it is a symmetry of and type IIB supergravity but not type IIA. A cosmological term and also mass terms are forbidden but non-minimal coupling is permitted. (4) Spontaneous compactification from leads to interesting but different symmetries in lower dimensions such as , so Yang–Mills terms, Kaluza–Klein masses and a cosmological constant may then appear. As a well-known example, IIB permits .
Duff MJ, 2006, Hidden symmetries of the Nambu-Goto action, Physics Letters B, Vol: 641, Pages: 335-337, ISSN: 0370-2693
We organize the eight variables of the four-dimensional bosonic string into a hypermatrix and show that in signature the Nambu–Goto Lagrangian is given by where Det is Cayley's hyperdeterminant. This is invariant not only under but also under interchange of the indices A, and . This triality reveals hitherto hidden discrete symmetries of the Nambu–Goto action.
Liu JT, Duff MJ, Stelle KS, et al., 2006, Deserfest: A celebration of the life and works of stanley deser: Michigan center for theoretical physics, university of Michigan, Ann Arbor, USA, 3-5 April 2004, ISBN: 9789812560827
This volume comprises the contributions to the proceedings of Deserfest-A festschrift in honor of Stanley Deser. Many of Stanley Deser’s colleagues and longtime collaborators, including Richard Arnowitt and Charles Misner of ‘ADM’ fame, contribute insighted article. Ranging from lower dimensional gravity theories all the way to supergravity in eleven dimensions and M-Theory, the papers highlight the wide impact that Deser has had in the field.
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.