817 research outputs found
The elliptic genus from split flows and Donaldson-Thomas invariants
We analyze a mixed ensemble of low charge D4-D2-D0 brane states on the
quintic and show that these can be successfully enumerated using attractor flow
tree techniques and Donaldson-Thomas invariants. In this low charge regime one
needs to take into account worldsheet instanton corrections to the central
charges, which is accomplished by making use of mirror symmetry. All the
charges considered can be realized as fluxed D6-D2-D0 and anti-D6-D2-D0 pairs
which we enumerate using DT invariants. Our procedure uses the low charge
counterpart of the picture developed Denef and Moore. By establishing the
existence of flow trees numerically and refining the index factorization
scheme, we reproduce and improve some results obtained by Gaiotto, Strominger
and Yin. Our results provide appealing evidence that the strong split flow tree
conjecture holds and allows to compute exact results for an important sector of
the theory. Our refined scheme for computing indices might shed some light on
how to improve index computations for systems with larger charges.Comment: 37 pages, 12 figure
Examples of M5-Brane Elliptic Genera
We determine the modified elliptic genus of an M5-brane wrapped on various
one modulus Calabi-Yau spaces, using modular invariance together with some
known Gopakumar-Vafa invariants of small degrees. As a bonus, we find
nontrivial relations among Gopakumar-Vafa invariants of different degrees and
genera from modular invariance.Comment: 13 page
Black Hole Deconstruction
A D4-D0 black hole can be deconstructed into a bound state of D0 branes with
a D6-anti-D6 pair containing worldvolume fluxes. The exact spacetime solution
is known and resembles a D0 accretion disk surrounding a D6-anti-D6 core. We
find a scaling limit in which the disk and core drop inside an AdS_2 throat.
Crossing this AdS_2 throat and the D0 accretion disk into the core, we find a
second scaling region describing the D6-anti-D6 pair. It is shown that the
M-theory lift of this region is AdS_3 x S^2. Surprisingly, time translations in
the far asymptotic region reduce to global, rather than Poincare, time
translations in this core AdS_3. We further find that the quantum mechanical
ground state degeneracy reproduces the Bekenstein-Hawking entropy-area law.Comment: 11 page
The M5-Brane Elliptic Genus: Modularity and BPS States
The modified elliptic genus for an M5-brane wrapped on a four-cycle of a
Calabi-Yau threefold encodes the degeneracies of an infinite set of BPS states
in four dimensions. By holomorphy and modular invariance, it can be determined
completely from the knowledge of a finite set of such BPS states. We show the
feasibility of such a computation and determine the exact modified elliptic
genus for an M5-brane wrapping a hyperplane section of the quintic threefold.Comment: 21 page
Exceptional Indices
Recently a prescription to compute the superconformal index for all theories
of class S was proposed. In this paper we discuss some of the physical
information which can be extracted from this index. We derive a simple
criterion for the given theory of class S to have a decoupled free component
and for it to have enhanced flavor symmetry. Furthermore, we establish a
criterion for the "good", the "bad", and the "ugly" trichotomy of the theories.
After interpreting the prescription to compute the index with non-maximal
flavor symmetry as a residue calculus we address the computation of the index
of the bad theories. In particular we suggest explicit expressions for the
superconformal index of higher rank theories with E_n flavor symmetry, i.e. for
the Hilbert series of the multi-instanton moduli space of E_n.Comment: 33 pages, 11 figures, v2: minor correction
CHL Dyons and Statistical Entropy Function from D1-D5 System
We give a proof of the recently proposed formula for the dyon spectrum in CHL
string theories by mapping it to a configuration of D1 and D5-branes and
Kaluza-Klein monopole. We also give a prescription for computing the degeneracy
as a systematic expansion in inverse powers of charges. The computation can be
formulated as a problem of extremizing a duality invariant statistical entropy
function whose value at the extremum gives the logarithm of the degeneracy.
During this analysis we also determine the locations of the zeroes and poles of
the Siegel modular forms whose inverse give the dyon partition function in the
CHL models.Comment: LaTeX file, 48 pages; v2: typos correcte
Dying Dyons Don't Count
The dyonic 1/4-BPS states in 4D string theory with N=4 spacetime
supersymmetry are counted by a Siegel modular form. The pole structure of the
modular form leads to a contour dependence in the counting formula obscuring
its duality invariance. We exhibit the relation between this ambiguity and the
(dis-)appearance of bound states of 1/2-BPS configurations. Using this insight
we propose a precise moduli-dependent contour prescription for the counting
formula. We then show that the degeneracies are duality-invariant and are
correctly adjusted at the walls of marginal stability to account for the
(dis-)appearance of the two-centered bound states. Especially, for large black
holes none of these bound states exists at the attractor point and none of
these ambiguous poles contributes to the counting formula. Using this fact we
also propose a second, moduli-independent contour which counts the "immortal
dyons" that are stable everywhere.Comment: 27 pages, 2 figures; one minus sign correcte
Quantum Attractor Flows
Motivated by the interpretation of the Ooguri-Strominger-Vafa conjecture as a
holographic correspondence in the mini-superspace approximation, we study the
radial quantization of stationary, spherically symmetric black holes in four
dimensions. A key ingredient is the classical equivalence between the radial
evolution equation and geodesic motion of a fiducial particle on the moduli
space M^*_3 of the three-dimensional theory after reduction along the time
direction. In the case of N=2 supergravity, M^*_3 is a para-quaternionic-Kahler
manifold; in this case, we show that BPS black holes correspond to a particular
class of geodesics which lift holomorphically to the twistor space Z of M^*_3,
and identify Z as the BPS phase space. We give a natural quantization of the
BPS phase space in terms of the sheaf cohomology of Z, and compute the exact
wave function of a BPS black hole with fixed electric and magnetic charges in
this framework. We comment on the relation to the topological string amplitude,
extensions to N>2 supergravity theories, and applications to automorphic black
hole partition functions.Comment: 43 pages, 6 figures; v2: typos and references added; v3: published
version, minor change
Superconformal Quantum Mechanics of Small Black Holes
Recently, Gaiotto, Strominger and Yin have proposed a holographic dual
description for the near-horizon physics of certain N=2 black holes in terms of
the superconformal quantum mechanics on D0-branes in the attractor geometry. We
provide further evidence for their proposal by applying it to the case of
`small' black holes which have vanishing horizon area in the leading
supergravity approximation. We consider 2-charge black holes in type IIA on
, where can be either or , made up out of
D0-branes and D4-branes wrapping . We construct the corresponding
superconformal quantum mechanics and show that the asymptotic growth of chiral
primaries exactly matches with the known entropy of these black holes. The
state-counting problem reduces to counting lowest Landau levels on and
Dolbeault cohomology classes on .Comment: Latex, 16 pages; v2: minor corrections, references added, published
versio
Walls of Marginal Stability and Dyon Spectrum in N=4 Supersymmetric String Theories
The spectrum of quarter BPS dyons in N=4 supersymmetric string theories can
change as the asymptotic moduli cross walls of marginal stability on which the
dyon can break apart into a pair of half BPS states. In this paper we classify
these marginal stability walls and examine this phenomenon in the context of
exact dyon spectrum found in a class of N=4 supersymmetric string theories. We
argue that the dyon partition functions in different domains separated by
marginal stability walls are the same, but the choice of integration contour
needed for extracting the degeneracies from the partition function differ in
these different regions. We also find that in the limit of large charges the
change in the degeneracy is exponentially suppressed compared to the leading
contribution. This is consistent with the fact that in the computation of black
hole entropy we do not encounter any change as the asymptotic moduli fields
move across the walls of marginal stability. Finally we carry out some tests of
S-duality invariance in the theory.Comment: LateX file, 1 figure, 42 pages; v2 more tests of S-duality added with
complete proof for all N<7; v3: minor change
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