990 research outputs found
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
BKM Lie superalgebras from counting twisted CHL dyons
Following Sen[arXiv:0911.1563], we study the counting of (`twisted') BPS
states that contribute to twisted helicity trace indices in four-dimensional
CHL models with N=4 supersymmetry. The generating functions of half-BPS states,
twisted as well as untwisted, are given in terms of multiplicative eta products
with the Mathieu group, M_{24}, playing an important role. These multiplicative
eta products enable us to construct Siegel modular forms that count twisted
quarter-BPS states. The square-roots of these Siegel modular forms turn out be
precisely a special class of Siegel modular forms, the dd-modular forms, that
have been classified by Clery and Gritsenko[arXiv:0812.3962]. We show that each
one of these dd-modular forms arise as the Weyl-Kac-Borcherds denominator
formula of a rank-three Borcherds-Kac-Moody Lie superalgebra. The walls of the
Weyl chamber are in one-to-one correspondence with the walls of marginal
stability in the corresponding CHL model for twisted dyons as well as untwisted
ones. This leads to a periodic table of BKM Lie superalgebras with properties
that are consistent with physical expectations.Comment: LaTeX, 32 pages; (v2) matches published versio
Negative discriminant states in N=4 supersymmetric string theories
Single centered BPS black hole solutions exist only when the charge carried
by the black hole has positive discriminant. On the other hand the exact dyon
spectrum in heterotic string theory compactified on T^6 is known to contain
states with negative discriminant. We show that all of these negative
discriminant states can be accounted for as two centered black holes. Thus
after the contribution to the index from the two centered black holes is
subtracted from the total microscopic index, the index for states with negative
discriminant vanishes even for finite values of charges, in agreement with the
results from the black hole side. Bound state metamorphosis -- which requires
us to identify certain apparently different two centered configurations
according to a specific set of rules -- plays a crucial role in this analysis.
We also generalize these results to a class of CHL string theories.Comment: LaTeX file, 32 pages; v2: reference added; v3: added new section 3.
Perturbative tests of non-perturbative counting
We observe that a class of quarter-BPS dyons in N=4 theories with charge
vector (Q, P) and with nontrivial values of the arithmetic duality invariant I
:= gcd (Q wedge P) are nonperturbative in one frame but perturbative in another
frame. This observation suggests a test of the recently computed
nonperturbative partition functions for dyons with nontrivial values of the
arithmetic invariant. For all values of I, we show that the nonperturbative
counting yields vanishing indexed degeneracy for this class of states
everywhere in the moduli space in precise agreement with the perturbative
result.Comment: 10 pages, 0 figure
Analytic Lifshitz black holes in higher dimensions
We generalize the four-dimensional R^2-corrected z=3/2 Lifshitz black hole to
a two-parameter family of black hole solutions for any dynamical exponent z and
for any dimension D. For a particular relation between the parameters, we find
the first example of an extremal Lifshitz black hole. An asymptotically
Lifshitz black hole with a logarithmic decay is also exhibited for a specific
critical exponent depending on the dimension. We extend this analysis to the
more general quadratic curvature corrections for which we present three new
families of higher-dimensional D>=5 analytic Lifshitz black holes for generic
z. One of these higher-dimensional families contains as critical limits the z=3
three-dimensional Lifshitz black hole and a new z=6 four-dimensional black
hole. The variety of analytic solutions presented here encourages to explore
these gravity models within the context of non-relativistic holographic
correspondence.Comment: 14 page
Logarithmic Corrections to Extremal Black Hole Entropy from Quantum Entropy Function
We evaluate the one loop determinant of matter multiplet fields of N=4
supergravity in the near horizon geometry of quarter BPS black holes, and use
it to calculate logarithmic corrections to the entropy of these black holes
using the quantum entropy function formalism. We show that even though
individual fields give non-vanishing logarithmic contribution to the entropy,
the net contribution from all the fields in the matter multiplet vanishes. Thus
logarithmic corrections to the entropy of quarter BPS black holes, if present,
must be independent of the number of matter multiplet fields in the theory.
This is consistent with the microscopic results. During our analysis we also
determine the complete spectrum of small fluctuations of matter multiplet
fields in the near horizon geometry.Comment: LaTeX file, 52 pages; v2: minor corrections, references 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
Wall-crossing of D4-D2-D0 and flop of the conifold
We discuss the wall-crossing of the BPS bound states of a non-compact
holomorphic D4-brane with D2 and D0-branes on the conifold. We use the
Kontsevich-Soibelman wall-crossing formula and analyze the BPS degeneracy in
various chambers. In particular we obtain a relation between BPS degeneracies
in two limiting attractor chambers related by a flop transition. Our result is
consistent with known results and predicts BPS degeneracies in all chambers.Comment: 15 pages, 4 figures; v2: typos corrected; v3: minor changes, a
reference added, version to be published in JHE
A Twist in the Dyon Partition Function
In four dimensional string theories with N=4 and N=8 supersymmetries one can
often define twisted index in a subspace of the moduli space which captures
additional information on the partition function than the ones contained in the
usual helicity trace index. We compute several such indices in type IIB string
theory on K3 x T^2 and T^6, and find that they share many properties with the
usual helicity trace index that captures the spectrum of quarter BPS states in
N=4 supersymmetric string theories. In particular the partition function is a
modular form of a subgroup of Sp(2,Z) and the jumps across the walls of
marginal stability are controlled by the residues at the poles of the partition
function. However for large charges the logarithm of this index grows as 1/n
times the entropy of a black hole carrying the same charges where n is the
order of the symmetry generator that is used to define the twisted index. We
provide a macroscopic explanation of this phenomenon using quantum entropy
function formalism. The leading saddle point corresponding to the attractor
geometry fails to contribute to the twisted index, but a Z_n orbifold of the
attractor geometry produces the desired contribution.Comment: LaTeX file, 35 pages; v2: references adde
Lifshitz black holes in string theory
We provide the first black hole solutions with Lifshitz asymptotics found in
string theory. These are expected to be dual to models enjoying anisotropic
scale invariance with dynamical exponent z=2 at finite temperature. We employ a
consistent truncation of type IIB supergravity to four dimensions with an
arbitrary 5-dimensional Einstein manifold times a circle as internal geometry.
New interesting features are found that significantly differ from previous
results in phenomenological models. In particular, small black holes are shown
to be thermodynamically unstable, analogously to the usual AdS-Schwarzschild
black holes, and extremality is never reached. This signals a possible
Hawking-Page like phase transition at low temperatures.Comment: 19 pages, 7 figures. v2 references adde
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