15,080 research outputs found
On almost duality for Frobenius manifolds
We present a universal construction of almost duality for Frobenius
manifolds. The analytic setup of this construction is described in details for
the case of semisimple Frobenius manifolds. We illustrate the general
considerations by examples from the singularity theory, mirror symmetry, the
theory of Coxeter groups and Shephard groups, from the Seiberg - Witten
duality.Comment: 62 pages, a reference adde
Reflection positivity and invertible topological phases
We implement an extended version of reflection positivity (Wick-rotated
unitarity) for invertible topological quantum field theories and compute the
abelian group of deformation classes using stable homotopy theory. We apply
these field theory considerations to lattice systems, assuming the existence
and validity of low energy effective field theory approximations, and thereby
produce a general formula for the group of Symmetry Protected Topological (SPT)
phases in terms of Thom's bordism spectra; the only input is the dimension and
symmetry group. We provide computations for fermionic systems in physically
relevant dimensions. Other topics include symmetry in quantum field theories, a
relativistic 10-fold way, the homotopy theory of relativistic free fermions,
and a topological spin-statistics theorem.Comment: 136 pages, 16 figures; minor changes/corrections in version 2; v3
major revision; v4 minor revision: corrected proof of Lemma 9.55, many small
changes throughout; v5 version for publication in Geometry & Topolog
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
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