188 research outputs found
Constructive Wall-Crossing and Seiberg-Witten
We outline a comprehensive and first-principle solution to the wall-crossing
problem in D=4 N=2 Seiberg-Witten theories. We start with a brief review of the
multi-centered nature of the typical BPS states and recall how the
wall-crossing problem thus becomes really a bound state formation/dissociation
problem. Low energy dynamics for arbitrary collections of dyons is derived,
from Seiberg-Witten theory, with the proximity to the so-called marginal
stability wall playing the role of the small expansion parameter. We find that,
surprisingly, the low energy dynamics of n+1 BPS dyons cannot
be consistently reduced to the classical moduli space, \CM, yet the index can
be phrased in terms of \CM. We also explain how an equivariant version of
this index computes the protected spin character of the underlying field
theory, where SO(3)_\CJ isometry of \CM turns out to be the diagonal
subgroup of spatial rotation and R-symmetry. The so-called
rational invariants, previously seen in the Kontsevich-Soibelman formalism of
wall-crossing, are shown to emerge naturally from the orbifolding projection
due to Bose/Fermi statistics.Comment: 25 pages, conference proceeding contribution for "Progress of Quantum
Field Theory and String Theory," Osaka, April 201
D3-instantons, Mock Theta Series and Twistors
The D-instanton corrected hypermultiplet moduli space of type II string
theory compactified on a Calabi-Yau threefold is known in the type IIA picture
to be determined in terms of the generalized Donaldson-Thomas invariants,
through a twistorial construction. At the same time, in the mirror type IIB
picture, and in the limit where only D3-D1-D(-1)-instanton corrections are
retained, it should carry an isometric action of the S-duality group SL(2,Z).
We prove that this is the case in the one-instanton approximation, by
constructing a holomorphic action of SL(2,Z) on the linearized twistor space.
Using the modular invariance of the D4-D2-D0 black hole partition function, we
show that the standard Darboux coordinates in twistor space have modular
anomalies controlled by period integrals of a Siegel-Narain theta series, which
can be canceled by a contact transformation generated by a holomorphic mock
theta series.Comment: 42 pages; discussion of isometries is amended; misprints correcte
Evidence for Duality of Conifold from Fundamental String
We study the spectrum of BPS D5-D3-F1 states in type IIB theory, which are
proposed to be dual to D4-D2-D0 states on the resolved conifold in type IIA
theory. We evaluate the BPS partition functions for all values of the moduli
parameter in the type IIB side, and find them completely agree with the results
in the type IIA side which was obtained by using Kontsevich-Soibelman's
wall-crossing formula. Our result is a quite strong evidence for string
dualities on the conifold.Comment: 24 pages, 13 figures, v2: typos corrected, v3: explanations about
wall-crossing improved and figures adde
BPS Spectrum, Indices and Wall Crossing in N=4 Supersymmetric Yang-Mills Theories
BPS states in N=4 supersymmetric SU(N) gauge theories in four dimensions can
be represented as planar string networks with ends lying on D3-branes. We
introduce several protected indices which capture information on the spectrum
and various quantum numbers of these states, give their wall crossing formula
and describe how using the wall crossing formula we can compute all the indices
at all points in the moduli space.Comment: LaTeX file, 33 pages, 15 figure
From Black Holes to Quivers
Middle cohomology states on the Higgs branch of supersymmetric quiver quantum
mechanics - also known as pure Higgs states - have recently emerged as possible
microscopic candidates for single-centered black hole micro-states, as they
carry zero angular momentum and appear to be robust under wall-crossing. Using
the connection between quiver quantum mechanics on the Coulomb branch and the
quantum mechanics of multi-centered black holes, we propose a general algorithm
for reconstructing the full moduli-dependent cohomology of the moduli space of
an arbitrary quiver, in terms of the BPS invariants of the pure Higgs states.
We analyze many examples of quivers with loops, including all cyclic Abelian
quivers and several examples with two loops or non-Abelian gauge groups, and
provide supporting evidence for this proposal. We also develop methods to count
pure Higgs states directly.Comment: 56 pages; v2: added Eqs 4.28-30, 5.35-36, 5.55; v3: journal version;
v4: Misprints corrected, improved discussion of Higgs branch for non-Abelian
3-node quiver, see around Eq. (6.22) and (6.37
Black Hole Meiosis
The enumeration of BPS bound states in string theory needs refinement.
Studying partition functions of particles made from D-branes wrapped on
algebraic Calabi-Yau 3-folds, and classifying states using split attractor flow
trees, we extend the method for computing a refined BPS index, arXiv:0810.4301.
For certain D-particles, a finite number of microstates, namely polar states,
exclusively realized as bound states, determine an entire partition function
(elliptic genus). This underlines their crucial importance: one might call them
the `chromosomes' of a D-particle or a black hole. As polar states also can be
affected by our refinement, previous predictions on elliptic genera are
modified. This can be metaphorically interpreted as `crossing-over in the
meiosis of a D-particle'. Our results improve on hep-th/0702012, provide
non-trivial evidence for a strong split attractor flow tree conjecture, and
thus suggest that we indeed exhaust the BPS spectrum. In the D-brane
description of a bound state, the necessity for refinement results from the
fact that tachyonic strings split up constituent states into `generic' and
`special' states. These are enumerated separately by topological invariants,
which turn out to be partitions of Donaldson-Thomas invariants. As modular
predictions provide a check on many of our results, we have compelling evidence
that our computations are correct.Comment: 46 pages, 8 figures. v2: minor changes. v3: minor changes and
reference adde
Multiple D4-D2-D0 on the Conifold and Wall-crossing with the Flop
We study the wall-crossing phenomena of D4-D2-D0 bound states with two units
of D4-brane charge on the resolved conifold. We identify the walls of marginal
stability and evaluate the discrete changes of the BPS indices by using the
Kontsevich-Soibelman wall-crossing formula. In particular, we find that the
field theories on D4-branes in two large radius limits are properly connected
by the wall-crossings involving the flop transition of the conifold. We also
find that in one of the large radius limits there are stable bound states of
two D4-D2-D0 fragments.Comment: 24 pages, 4 figures; v2: typos corrected, minor changes, a reference
adde
Automorphic Instanton Partition Functions on Calabi-Yau Threefolds
We survey recent results on quantum corrections to the hypermultiplet moduli
space M in type IIA/B string theory on a compact Calabi-Yau threefold X, or,
equivalently, the vector multiplet moduli space in type IIB/A on X x S^1. Our
main focus lies on the problem of resumming the infinite series of D-brane and
NS5-brane instantons, using the mathematical machinery of automorphic forms. We
review the proposal that whenever the low-energy theory in D=3 exhibits an
arithmetic "U-duality" symmetry G(Z) the total instanton partition function
arises from a certain unitary automorphic representation of G, whose Fourier
coefficients reproduce the BPS-degeneracies. For D=4, N=2 theories on R^3 x S^1
we argue that the relevant automorphic representation falls in the quaternionic
discrete series of G, and that the partition function can be realized as a
holomorphic section on the twistor space Z over M. We also offer some comments
on the close relation with N=2 wall crossing formulae.Comment: 25 pages, contribution to the proceedings of the workshop "Algebra,
Geometry and Mathematical Physics", Tjarno, Sweden, 25-30 October, 201
BPS dyons and Hesse flow
We revisit BPS solutions to classical N=2 low energy effective gauge
theories. It is shown that the BPS equations can be solved in full generality
by the introduction of a Hesse potential, a symplectic analog of the
holomorphic prepotential. We explain how for non-spherically symmetric,
non-mutually local solutions, the notion of attractor flow generalizes to
gradient flow with respect to the Hesse potential. Furthermore we show that in
general there is a non-trivial magnetic complement to this flow equation that
is sourced by the momentum current in the solution.Comment: 25 pages, references adde
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