1,423 research outputs found
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.
Discrete Information from CHL Black Holes
AdS_2/CFT_1 correspondence predicts that the logarithm of a Z_N twisted index
over states carrying a fixed set of charges grows as 1/N times the entropy of
the black hole carrying the same set of charges. In this paper we verify this
explicitly by calculating the microscopic Z_N twisted index for a class of
states in the CHL models. This demonstrates that black holes carry more
information about the microstates than just the total degeneracy.Comment: LaTeX file, 24 pages; v2: references adde
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
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
No entropy enigmas for N=4 dyons
We explain why multi-centered black hole configurations where at least one of
the centers is a large black hole do not contribute to the indexed degeneracies
in theories with N=4 supersymmetry. This is a consequence of the fact that such
configurations, although supersymmetric, belong to long supermultiplets. As a
result, there is no entropy enigma in N=4 theories, unlike in N=2 theories.Comment: 14 page
BKM Lie superalgebra for the Z_5 orbifolded CHL string
We study the Z_5-orbifolding of the CHL string theory by explicitly
constructing the modular form tilde{Phi}_2 generating the degeneracies of the
1/4-BPS states in the theory. Since the additive seed for the sum form is a
weak Jacobi form in this case, a mismatch is found between the modular forms
generated from the additive lift and the product form derived from threshold
corrections. We also construct the BKM Lie superalgebra, tilde{G}_5,
corresponding to the modular form tilde{Delta}_1 (Z) = tilde{Phi}_2 (Z)^{1/2}
which happens to be a hyperbolic algebra. This is the first occurrence of a
hyperbolic BKM Lie superalgebra. We also study the walls of marginal stability
of this theory in detail, and extend the arithmetic structure found by Cheng
and Dabholkar for the N=1,2,3 orbifoldings to the N=4,5 and 6 models, all of
which have an infinite number of walls in the fundamental domain. We find that
analogous to the Stern-Brocot tree, which generated the intercepts of the walls
on the real line, the intercepts for the N >3 cases are generated by linear
recurrence relations. Using the correspondence between the walls of marginal
stability and the walls of the Weyl chamber of the corresponding BKM Lie
superalgebra, we propose the Cartan matrices for the BKM Lie superalgebras
corresponding to the N=5 and 6 models.Comment: 30 pages, 2 figure
All states stand to save electricity were Indian Standard Time to be advanced
Earlier estimates of electricity savings from advancing
Indian Standard Time (IST) to GMT + 6:00 using
regional load curves provided encouraging results of
savings during evenings. This persuaded us to undertake
this more accurate study involving 13 states that
account for 85% of India’s annual electricity consumption.
As we expected, the savings obtained were higher than estimates from the five electrical regions of the country. Although advancing IST would benefit the northeastern and eastern regions, there is an apprehension that later dawns may inconvenience people in the north and northwest. In response we present data on postponement of the latest winter dawns in state capitals. We also report on the flattening of load curves in the six highest electricity consuming states and discuss how this affects the
results
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
Counting all dyons in N =4 string theory
For dyons in heterotic string theory compactified on a six-torus, with
electric charge vector Q and magnetic charge vector P, the positive integer I =
g.c.d.(Q \wedge P) is an invariant of the U-duality group. We propose the
microscopic theory for computing the spectrum of all dyons for all values of I,
generalizing earlier results that exist only for the simplest case of I=1. Our
derivation uses a combination of arguments from duality, 4d-5d lift, and a
careful analysis of fermionic zero modes. The resulting degeneracy agrees with
the black hole degeneracy for large charges and with the degeneracy of
field-theory dyons for small charges. It naturally satisfies several physical
requirements including integrality and duality invariance. As a byproduct, we
also derive the microscopic (0,4) superconformal field theory relevant for
computing the spectrum of five-dimensional Strominger-Vafa black holes in ALE
backgrounds and count the resulting degeneracies
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