10,845 research outputs found
Special geometry, black holes and Euclidean supersymmetry
We review recent developments in special geometry and explain its role in the
theory of supersymmetric black holes. To make this article self-contained, a
short introduction to black holes is given, with emphasis on the laws of black
hole mechanics and black hole entropy. We also summarize the existing results
on the para-complex version of special geometry, which occurs in Euclidean
supersymmetry. The role of real coordinates in special geometry is illustrated,
and we briefly indicate how Euclidean supersymmetry can be used to study
stationary black hole solutions via dimensional reduction over time.
This article is an updated and substantially extended version of the previous
review article `New developments in special geometry', hep-th/0602171.Comment: 39 pages, Contribution to the Handbook on Pseudo-Riemannian Geometry
and Supersymmtry, ed. V. Corte
The degree of the eigenvalues of generalized Moore geometries
AbstractUsing elementary methods it is proved that the eigenvalues of generalized Moore geometries of type GMm(s, t, c) are of degree at most 3 with respect to the field of rational numbers, if st > 1
Supersymmetric AdS Backgrounds in String and M-theory
We first present a short review of general supersymmetric compactifications
in string and M-theory using the language of G-structures and intrinsic
torsion. We then summarize recent work on the generic conditions for
supersymmetric AdS_5 backgrounds in M-theory and the construction of classes of
new solutions. Turning to AdS_5 compactifications in type IIB, we summarize the
construction of an infinite class of new Sasaki-Einstein manifolds in dimension
2k+3 given a positive curvature Kahler-Einstein base manifold in dimension 2k.
For k=1 these describe new supergravity duals for N=1 superconformal field
theories with both rational and irrational R-charges and central charge. We
also present a generalization of this construction, that has not appeared
elsewhere in the literature, to the case where the base is a product of
Kahler-Einstein manifolds.Comment: LaTeX, 35 pages, to appear in the proceedings of the 73rd Meeting
between Physicists and Mathematicians "(A)dS/CFT correspondence", Strasbourg,
September 11-13, 200
A Farey Tail for Attractor Black Holes
The microstates of 4d BPS black holes in IIA string theory compactified on a
Calabi-Yau manifold are counted by a (generalized) elliptic genus of a (0,4)
conformal field theory. By exploiting a spectral flow that relates states with
different charges, and using the Rademacher formula, we find that the elliptic
genus has an exact asymptotic expansion in terms of semi-classical
saddle-points of the dual supergravity theory. This generalizes the known
"Black Hole Farey Tail" of [1] to the case of attractor black holes.Comment: 36 pages, 3 figures, note adde
New developments in special geometry
We review recent developments in special geometry, emphasizing the role of
real coordinates. In the first part we discuss the para-complex geometry of
vector and hypermultiplets in rigid Euclidean N=2 supersymmetry. In the second
part we study the variational principle governing the near horizon limit of BPS
black holes in matter-coupled N=2 supergravity and observe that the black hole
entropy is the Legendre transform of the Hesse potential encoding the geometry
of the scalar fields.Comment: 27 pages, contributed to the Handbook on Pseudo-Riemannian Geometry
and Supersymmetr
IIB supergravity on manifolds with SU(4) structure and generalized geometry
We consider N=(2,0) backgrounds of IIB supergravity on eight-manifolds M_8
with strict SU(4) structure. We give the explicit solution to the Killing
spinor equations as a set of algebraic relations between irreducible su(4)
modules of the fluxes and the torsion classes of M_8. One consequence of
supersymmetry is that M_8 must be complex. We show that the conjecture of
arxiv:1010.5789 concerning the correspondence between background supersymmetry
equations in terms of generalized pure spinors and generalized calibrations for
admissible static, magnetic D-branes, does not capture the full set of
supersymmetry equations. We identify the missing constraints and express them
in the form of a single pure-spinor equation which is well defined for generic
SU(4)\times SU(4) backgrounds. This additional equation is given in terms of a
certain analytic continuation of the generalized calibration form for
codimension-2 static, magnetic D-branes.Comment: 23 pages. V2: added references, including to spinorial geometr
Blowup Equations for Refined Topological Strings
G\"{o}ttsche-Nakajima-Yoshioka K-theoretic blowup equations characterize the
Nekrasov partition function of five dimensional supersymmetric
gauge theories compactified on a circle, which via geometric engineering
correspond to the refined topological string theory on geometries. In
this paper, we study the K-theoretic blowup equations for general local
Calabi-Yau threefolds. We find that both vanishing and unity blowup equations
exist for the partition function of refined topological string, and the crucial
ingredients are the fields introduced in our previous paper. These
blowup equations are in fact the functional equations for the partition
function and each of them results in infinite identities among the refined free
energies. Evidences show that they can be used to determine the full refined
BPS invariants of local Calabi-Yau threefolds. This serves an independent and
sometimes more powerful way to compute the partition function other than the
refined topological vertex in the A-model and the refined holomorphic anomaly
equations in the B-model. We study the modular properties of the blowup
equations and provide a procedure to determine all the vanishing and unity fields from the polynomial part of refined topological string at large
radius point. We also find that certain form of blowup equations exist at
generic loci of the moduli space.Comment: 85 pages. v2: Journal versio
Geometric Aspects of Mirror Symmetry (with SYZ for Rigid CY manifolds)
In this article we discuss the geometry of moduli spaces of (1) flat bundles
over special Lagrangian submanifolds and (2) deformed Hermitian-Yang-Mills
bundles over complex submanifolds in Calabi-Yau manifolds.
These moduli spaces reflect the geometry of the Calabi-Yau itself like a
mirror. Strominger, Yau and Zaslow conjecture that the mirror Calabi-Yau
manifold is such a moduli space and they argue that the mirror symmetry duality
is a Fourier-Mukai transformation. We review various aspects of the mirror
symmetry conjecture and discuss a geometric approach in proving it.
The existence of rigid Calabi-Yau manifolds poses a serious challenge to the
conjecture. The proposed mirror partners for them are higher dimensional
generalized Calabi-Yau manifolds. For example, the mirror partner for a certain
K3 surface is a cubic fourfold and its Fano variety of lines is birational to
the Hilbert scheme of two points on the K3. This hyperkahler manifold can be
interpreted as the SYZ mirror of the K3 by considering singular special
Lagrangian tori.
We also compare the geometries between a CY and its associated generalized
CY. In particular we present a new construction of Lagrangian submanifolds.Comment: To appear in the proceedings of International Congress of Chinese
Mathematicians 2001, 47 page
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