814 research outputs found
BPS black holes, the Hesse potential, and the topological string
The Hesse potential is constructed for a class of four-dimensional N=2
supersymmetric effective actions with S- and T-duality by performing the
relevant Legendre transform by iteration. It is a function of fields that
transform under duality according to an arithmetic subgroup of the classical
dualities reflecting the monodromies of the underlying string compactification.
These transformations are not subject to corrections, unlike the
transformations of the fields that appear in the effective action which are
affected by the presence of higher-derivative couplings. The class of actions
that are considered includes those of the FHSV and the STU model. We also
consider heterotic N=4 supersymmetric compactifications. The Hesse potential,
which is equal to the free energy function for BPS black holes, is manifestly
duality invariant. Generically it can be expanded in terms of powers of the
modulus that represents the inverse topological string coupling constant,
, and its complex conjugate. The terms depending holomorphically on
are expected to correspond to the topological string partition function and
this expectation is explicitly verified in two cases. Terms proportional to
mixed powers of and are in principle present.Comment: 28 pages, LaTeX, added comment
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
Nernst branes in gauged supergravity
We study static black brane solutions in the context of N = 2 U(1) gauged
supergravity in four dimensions. Using the formalism of first-order flow
equations, we construct novel extremal black brane solutions including examples
of Nernst branes, i.e. extremal black brane solutions with vanishing entropy
density. We also discuss a class of non-extremal generalizations which is
captured by the first-order formalism.Comment: 44 pages, 3 figures, v2: added appendix B and references, minor
typographic changes, v3: added some clarifying remarks, version 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
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
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
Flux compactification on smooth, compact three-dimensional toric varieties
Three-dimensional smooth, compact toric varieties (SCTV), when viewed as real
six-dimensional manifolds, can admit G-structures rendering them suitable for
internal manifolds in supersymmetric flux compactifications. We develop
techniques which allow us to systematically construct G-structures on SCTV and
read off their torsion classes. We illustrate our methods with explicit
examples, one of which consists of an infinite class of toric CP^1 bundles. We
give a self-contained review of the relevant concepts from toric geometry, in
particular the subject of the classification of SCTV in dimensions less or
equal to 3. Our results open up the possibility for a systematic construction
and study of supersymmetric flux vacua based on SCTV.Comment: 27 pages, 10 figures; v2: references, minor typos & improvement
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
BPS black holes in N=2 D=4 gauged supergravities
We construct and analyze BPS black hole solutions in gauged N=2, D=4
supergravity with charged hypermultiplets. A class of solutions can be found
through spontaneous symmetry breaking in vacua that preserve maximal
supersymmetry. The resulting black holes do not carry any hair for the scalars.
We demonstrate this with explicit examples of both asymptotically flat and
anti-de Sitter black holes. Next, we analyze the BPS conditions for
asymptotically flat black holes with scalar hair and spherical or axial
symmetry. We find solutions only in cases when the metric contains ripples and
the vector multiplet scalars become ghost-like. We give explicit examples that
can be analyzed numerically. Finally, we comment on a way to circumvent the
ghost-problem by introducing also fermionic hair.Comment: 40 pages, 2 figures; v2 references added; v3 minor changes, published
versio
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