Superqubits

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.Comment: 16 pages, 4 figures, 4 tables, revtex; minor corrections, version appearing in Phys. Rev.

Wrapped branes as qubits

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 T^6 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.Comment: Version appearing in Phys. Rev. Lett, includes Type IIA description as well as Type II

Vacuum interpolation in supergravity via super p-branes

We show that many of the recently proposed supersymmetric p-brane solutions of d=10 and d=11 supergravity have the property that they interpolate between Minkowski spacetime and a compactified spacetime, both being supersymmetric supergravity vacua. Our results imply that the effective worldvolume action for small fluctuations of the super p-brane is a supersingleton field theory for $(adS)_{p+2}$, as has been often conjectured in the past.Comment: 8p

Four-qubit entanglement from string theory

We invoke the black hole/qubit correspondence to derive the classification of four-qubit entanglement. The U-duality orbits resulting from timelike reduction of string theory from D=4 to D=3 yield 31 entanglement families, which reduce to nine up to permutation of the four qubits.Comment: 4 pages, 1 figure, 2 tables, revtex; minor corrections, references adde

Black Holes, Qubits and Octonions

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, known as the 3-tangle, and the entropy of the 8-charge STU black hole of N=2 supergravity, both of which are given by the [SL(2)]^3 invariant hyperdeterminant, a quantity first introduced by Cayley in 1845. There are further relationships between the attractor mechanism and local distillation protocols. At the microscopic level, the black holes are described by intersecting D3-branes whose wrapping around the six compact dimensions T^6 provides the string-theoretic interpretation of the charges and we associate the three-qubit basis vectors, |ABC> (A,B,C=0 or 1), with the corresponding 8 wrapping cycles. The black hole/qubit correspondence extends to the 56 charge N=8 black holes and the tripartite entanglement of seven qubits where the measure is provided by Cartan's E_7 supset [SL(2)]^7 invariant. The qubits are naturally described by the seven vertices ABCDEFG of the Fano plane, which provides the multiplication table of the seven imaginary octonions, reflecting the fact that E_7 has a natural structure of an O-graded algebra. This in turn provides a novel imaginary octonionic interpretation of the 56=7 x 8 charges of N=8: the 24=3 x 8 NS-NS charges correspond to the three imaginary quaternions and the 32=4 x 8 R-R to the four complementary imaginary octonions. N=8 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 E_6 supset [SL(3)]^3 invariant.Comment: Version to appear in Physics Reports, including previously omitted new results on small STU black hole charge orbits and expanded bibliography. 145 pages, 15 figures, 41 table

Legal coercion, respect & reason-responsive agency

Legal coercion seems morally problematic because it is susceptible to the Hegelian objection that it fails to respect individuals in a way that is ‘due to them as men’. But in what sense does legal coercion fail to do so? And what are the grounds for this requirement to respect? This paper is an attempt to answer these questions. It argues that (a) legal coercion fails to respect individuals as reason-responsive agents; and (b) individuals ought to be respected as such in virtue of the fact that they are human beings. Thus it is in this sense that legal coercion fails to treat individuals with the kind of respect ‘due to them as men’.The Leverhulme Trust (ECF-2012-032); AHRC (AH/H015655/1

Generating branes via sigma-models

Starting with the D-dimensional Einstein-dilaton-antisymmetric form equations and assuming a block-diagonal form of a metric we derive a $(D-d)$-dimensional $\sigma$-model with the target space $SL(d,R)/SO(d) \times SL(2,R)/SO(2) \times R$ or its non-compact form. Various solution-generating techniques are developed and applied to construct some known and some new $p$-brane solutions. It is shown that the Harrison transformation belonging to the $SL(2,R)$ subgroup generates black $p$-branes from the seed Schwarzschild solution. A fluxbrane generalizing the Bonnor-Melvin-Gibbons-Maeda solution is constructed as well as a non-linear superposition of the fluxbrane and a spherical black hole. A new simple way to endow branes with additional internal structure such as plane waves is suggested. Applying the harmonic maps technique we generate new solutions with a non-trivial shell structure in the transverse space (`matrioshka' $p$-branes). It is shown that the $p$-brane intersection rules have a simple geometric interpretation as conditions ensuring the symmetric space property of the target space. Finally, a Bonnor-type symmetry is used to construct a new magnetic 6-brane with a dipole moment in the ten-dimensional IIA theory.Comment: 21 pages Late

Twenty Years of the Weyl Anomaly

In 1973 two Salam prot\'{e}g\'{e}s (Derek Capper and the author) discovered that the conformal invariance under Weyl rescalings of the metric tensor $g_{\mu\nu}(x)\rightarrow\Omega^2(x)g_{\mu\nu}(x)$ displayed by classical massless field systems in interaction with gravity no longer survives in the quantum theory. Since then these Weyl anomalies have found a variety of applications in black hole physics, cosmology, string theory and statistical mechanics. We give a nostalgic review. (Talk given at the {\it Salamfest}, ICTP, Trieste, March 1993.)Comment: 43 page

Pilgrim’s Progress: Lessons in Shared Governance

In the Spring of 2006, Southern Illinois University Edwardsville (SIUE) initiated a conversation to define a “Teacher-Scholar” Philosophy appropriate for the campus. In an experience similar to John Bunyan’s protagonist, Christian, in the classic 1678 allegory Pilgrim’s Progress, the SIUE faculty and administrators set off on a 21st century journey of discovery.[2] Our journey, however, was toward shared governance, rather than down the path to salvation. Like Bunyan’s Christian, we traveled metaphorically through the Town of Vanity, the Valley of Humiliation, the Slough of Despond, the Hill of Difficulty, and the Castle of Doubt. Unlike Christian, however, our journey of discovery ended before we crossed the River of Death and entered the Celestial City

Higher Structures in M-Theory

The key open problem of string theory remains its non-perturbative completion to M-theory. A decisive hint to its inner workings comes from numerous appearances of higher structures in the limits of M-theory that are already understood, such as higher degree flux fields and their dualities, or the higher algebraic structures governing closed string field theory. These are all controlled by the higher homotopy theory of derived categories, generalised cohomology theories, and $L_\infty$-algebras. This is the introductory chapter to the proceedings of the LMS/EPSRC Durham Symposium on Higher Structures in M-Theory. We first review higher structures as well as their motivation in string theory and beyond. Then we list the contributions in this volume, putting them into context.Comment: 22 pages, Introductory Article to Proceedings of LMS/EPSRC Durham Symposium Higher Structures in M-Theory, August 2018, references update