Gravity as Gauge Theory Squared: A Ghost Story.

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.

Yang-Mills origin of gravitational symmetries.

By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the biadjoint representation, we derive in linearized 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-Poincaré symmetry. 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).

Tsirelson's bound and supersymmetric entangled states.

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 non-local than ordinary qubits, we construct a class of two-superqubit entangled states as a non-local 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 and (3) Modified Rogers. In cases (1) and (2), the winning probability reaches the Tsirelson bound [Formula: see text] of standard quantum mechanics. Case (3) crosses Tsirelson's bound with pwin≃0.9265. 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.

Magic square from Yang-Mills squared.

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.

Four-qubit entanglement classification 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.

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 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.