168 research outputs found
Four curious supergravities
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 vanishing on-shell trace anomaly.Comment: 16 pages late
Black hole entropy and quantum information
We review some recently established connections between the mathematics of
black hole entropy in string theory and that of multipartite entanglement in
quantum information theory. In the case of N=2 black holes and the entanglement
of three qubits, the quartic [SL(2)]^3 invariant, Cayley's hyperdeterminant,
provides both the black hole entropy and the measure of tripartite
entanglement. In the case of N=8 black holes and the entanglement of seven
qubits, the quartic E_7 invariant of Cartan provides both the black hole
entropy and the measure of a particular tripartite entanglement encoded in the
Fano plane.Comment: Minor Improvements. 22 pages late
Generalized mirror symmetry and trace anomalies
We consider compactification of M-theory on X7 with betti numbers (b_0, b_1,
b_2, b_3, b_3, b_2, b_1, b_0) and define a generalized mirror symmetry (b_0,
b_1, b_2, b_3) goes to (b_0, b_1, b_2 -rho/2, b_3+rho/2)$ under which rho =
7b_0-5b_1+3b_2 -b_3 changes sign. Generalized self-mirror theories with rho=0
have massless sectors with vanishing trace anomaly (before dualization).
Examples include pure supergravity with N \geq 4 and supergravity plus matter
with N \leq 4.Comment: 19 pages late
Freudenthal Dual Lagrangians
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 versio
E_7 and the tripartite entanglement of seven qubits
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 E_7(C)
and that the entanglement measure is given by Cartan's quartic E_7 invariant.Comment: Minor improvements. 15 page late
Supersymmetry Enhancement of D-p-branes and M-branes
We examine the supersymmetry of classical D-brane and M-brane configurations
and explain the dependence of Killing spinors on coordinates. We find that one
half supersymmetry is broken in the bulk and that supersymmetry near the
D-brane horizon is restored for , for solutions in the stringy frame,
but only for in the10d canonical frame. We study the enhancement for the
case of four intersecting D-3-branes in 10 dimensions and the implication of
this for the size of the infinite throat of the near horizon geometry in
non-compactified theory. We found some indications of universality of near
horizon geometries of various intersecting brane configurations.Comment: 18 pages, late
On Invariant Structures of Black Hole Charges
We study "minimal degree" complete bases of duality- and "horizontal"-
invariant homogeneous polynomials in the flux representation of two-centered
black hole solutions in two classes of D=4 Einstein supergravity models with
symmetric vector multiplets' scalar manifolds. Both classes exhibit an SL(2,R)
"horizontal" symmetry. The first class encompasses N=2 and N=4 matter-coupled
theories, with semi-simple U-duality given by SL(2,R) x SO(m,n); the analysis
is carried out in the so-called Calabi-Vesentini symplectic frame (exhibiting
maximal manifest covariance) and until order six in the fluxes included. The
second class, exhibiting a non-trivial "horizontal" stabilizer SO(2), includes
N=2 minimally coupled and N=3 matter coupled theories, with U-duality given by
the pseudo-unitary group U(r,s) (related to complex flux representations).
Finally, we comment on the formulation of special Kaehler geometry in terms of
"generalized" groups of type E7.Comment: 1+24 pages; 1 Table. v2 : Eqs. (1.2) and (1.3) added; Eq. (2.87)
change
Observations on Integral and Continuous U-duality Orbits in N=8 Supergravity
One would often like to know when two a priori distinct extremal black
p-brane solutions are in fact U-duality related. In the classical supergravity
limit the answer for a large class of theories has been known for some time.
However, in the full quantum theory the U-duality group is broken to a discrete
subgroup and 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 N=8 supergravity in
four, five and six dimensions. The purpose of this note is to present and
clarify what is currently known about these discrete orbits while at the same
time filling in some of the details not yet appearing in the literature. To
this end we exploit the mathematical framework of integral Jordan algebras and
Freudenthal triple systems. The charge vector of the dyonic black string in D=6
is SO(5,5;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)}(Z) equivalent to a three-charge
canonical form, again uniquely fixed by a set of three arithmetic U-duality
invariants. The situation in four dimensions is less clear: while black holes
preserving more than 1/8 of the supersymmetries may be fully classified by
known arithmetic E_{7(7)}(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 a complete
classification is known. All projective black holes are E_{7(7)}(Z) related to
a four or five charge canonical form determined uniquely by the set of known
arithmetic U-duality invariants. Moreover, E_{7(7)}(Z) acts transitively on the
charge vectors of black holes with a given leading-order entropy.Comment: 43 pages, 8 tables; minor corrections, references added; version to
appear in Class. Quantum Gra
Microscopic Entropy of N=2 Extremal Black Holes
String theory is used to compute the microscopic entropy for several examples
of black holes in compactifications with supersymmetry. Agreement with
the Bekenstein-Hawking entropy and the moduli-independent area formula is
found in all cases.Comment: 9 pages, no figures, uses harvma
Small Orbits
We study both the "large" and "small" U-duality charge orbits of extremal
black holes appearing in D = 5 and D = 4 Maxwell-Einstein supergravity theories
with symmetric scalar manifolds. We exploit a formalism based on cubic Jordan
algebras and their associated Freudenthal triple systems, in order to derive
the minimal charge representatives, their stabilizers and the associated
"moduli spaces". After recalling N = 8 maximal supergravity, we consider N = 2
and N = 4 theories coupled to an arbitrary number of vector multiplets, as well
as N = 2 magic, STU, ST^2 and T^3 models. While the STU model may be considered
as part of the general N = 2 sequence, albeit with an additional triality
symmetry, the ST^2 and T^3 models demand a separate treatment, since their
representative Jordan algebras are Euclidean or only admit non-zero elements of
rank 3, respectively. Finally, we also consider minimally coupled N = 2, matter
coupled N = 3, and "pure" N = 5 theories.Comment: 40 pages, 9 tables. References added. Expanded comments added to
sections III. C. 1. and III. F.
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