1,559 research outputs found
Second Quantized Mathieu Moonshine
We study the second quantized version of the twisted twining genera of
generalized Mathieu moonshine, and prove that they give rise to Siegel modular
forms with infinite product representations. Most of these forms are expected
to have an interpretation as twisted partition functions counting 1/4 BPS dyons
in type II superstring theory on K3\times T^2 or in heterotic CHL-models. We
show that all these Siegel modular forms, independently of their possible
physical interpretation, satisfy an "S-duality" transformation and a
"wall-crossing formula". The latter reproduces all the eta-products of an older
version of generalized Mathieu moonshine proposed by Mason in the '90s.
Surprisingly, some of the Siegel modular forms we find coincide with the
multiplicative (Borcherds) lifts of Jacobi forms in umbral moonshine.Comment: 91 pages. Theorem 5.3 added; presentation improved, comments and
explanations adde
Dualities in CHL-Models
We define a very general class of CHL-models associated with any string
theory (bosonic or supersymmetric) compactified on an internal CFT C x T^d. We
take the orbifold by a pair (g,\delta), where g is a (possibly non-geometric)
symmetry of C and \delta is a translation along T^d. We analyze the T-dualities
of these models and show that in general they contain Atkin-Lehner type
symmetries. This generalizes our previous work on N=4 CHL-models based on
heterotic string theory on T^6 or type II on K3 x T^2, as well as the
`monstrous' CHL-models based on a compactification of heterotic string theory
on the Frenkel-Lepowsky-Meurman CFT V^{\natural}.Comment: 18 page
Fricke S-duality in CHL models
We consider four dimensional CHL models with sixteen spacetime
supersymmetries obtained from orbifolds of type IIA superstring on K3 x T^2 by
a Z_N symmetry acting (possibly) non-geometrically on K3. We show that most of
these models (in particular, for geometric symmetries) are self-dual under a
weak-strong duality acting on the heterotic axio-dilaton modulus S by a "Fricke
involution" S --> -1/NS. This is a novel symmetry of CHL models that lies
outside of the standard SL(2,Z)-symmetry of the parent theory, heterotic
strings on T^6. For self-dual models this implies that the lattice of purely
electric charges is N-modular, i.e. isometric to its dual up to a rescaling of
its quadratic form by N. We verify this prediction by determining the lattices
of electric and magnetic charges in all relevant examples. We also calculate
certain BPS-saturated couplings and verify that they are invariant under the
Fricke S-duality. For CHL models that are not self-dual, the strong coupling
limit is dual to type IIA compactified on T^6/Z_N, for some Z_N-symmetry
preserving half of the spacetime supersymmetries.Comment: 56 pages, 3 figures; v3: some minor mistakes correcte
Coxeter group structure of cosmological billiards on compact spatial manifolds
We present a systematic study of the cosmological billiard structures of
Einstein-p-form systems in which all spatial directions are compactified on a
manifold of nontrivial topology. This is achieved for all maximally oxidised
theories associated with split real forms, for all possible compactifications
as defined by the de Rham cohomology of the internal manifold. In each case, we
study the Coxeter group that controls the dynamics for energy scales below the
Planck scale as well as the relevant billiard region. We compare and contrast
them with the Weyl group and fundamental domain that emerge from the general
BKL analysis. For generic topologies we find a variety of possibilities: (i)
The group may or may not be a simplex Coxeter group; (ii) The billiard region
may or may not be a fundamental domain. When it is not a fundamental domain, it
can be described as a sequence of pairwise adjacent chambers, known as a
gallery, and the reflections in the billiard walls provide a non-standard
presentation of the Coxeter group. We find that it is only when the Coxeter
group is a simplex Coxeter group, and the billiard region is a fundamental
domain, that there is a correspondence between billiard walls and simple roots
of a Kac-Moody algebra, as in the general BKL analysis. For each
compactification we also determine whether or not the resulting theory exhibits
chaotic dynamics.Comment: 51 pages. Typos corrected. References added. Submitted for
publicatio
Fourier expansions of Kac-Moody Eisenstein series and degenerate Whittaker vectors
Motivated by string theory scattering amplitudes that are invariant under a
discrete U-duality, we study Fourier coefficients of Eisenstein series on
Kac-Moody groups. In particular, we analyse the Eisenstein series on ,
and corresponding to certain degenerate principal
series at the values s=3/2 and s=5/2 that were studied in 1204.3043. We show
that these Eisenstein series have very simple Fourier coefficients as expected
for their role as supersymmetric contributions to the higher derivative
couplings and coming from 1/2-BPS and 1/4-BPS
instantons, respectively. This suggests that there exist minimal and
next-to-minimal unipotent automorphic representations of the associated
Kac-Moody groups to which these special Eisenstein series are attached. We also
provide complete explicit expressions for degenerate Whittaker vectors of
minimal Eisenstein series on , and that have not
appeared in the literature before.Comment: 62 pages. Journal versio
Monstrous BPS-Algebras and the Superstring Origin of Moonshine
We provide a physics derivation of Monstrous moonshine. We show that the
McKay-Thompson series , , can be interpreted as
supersymmetric indices counting spacetime BPS-states in certain heterotic
string models. The invariance groups of these series arise naturally as
spacetime T-duality groups and their genus zero property descends from the
behaviour of these heterotic models in suitable decompactification limits. We
also show that the space of BPS-states forms a module for the Monstrous Lie
algebras , constructed by Borcherds and Carnahan. We argue that
arise in the heterotic models as algebras of spontaneously
broken gauge symmetries, whose generators are in exact correspondence with
BPS-states. This gives an interpretation as a kind of
BPS-algebra.Comment: 73 pages, with results summarized in introduction. v2: added a
discussion about coupling to gravity (section 3.3), additional references,
minor corrections and improvement
BPS Algebras, Genus Zero, and the Heterotic Monster
In this note, we expand on some technical issues raised in \cite{PPV} by the
authors, as well as providing a friendly introduction to and summary of our
previous work. We construct a set of heterotic string compactifications to 0+1
dimensions intimately related to the Monstrous moonshine module of Frenkel,
Lepowsky, and Meurman (and orbifolds thereof). Using this model, we review our
physical interpretation of the genus zero property of Monstrous moonshine.
Furthermore, we show that the space of (second-quantized) BPS-states forms a
module over the Monstrous Lie algebras ---some of the first and
most prominent examples of Generalized Kac-Moody algebras---constructed by
Borcherds and Carnahan. In particular, we clarify the structure of the module
present in the second-quantized string theory. We also sketch a proof of our
methods in the language of vertex operator algebras, for the interested
mathematician.Comment: 19 pages, 2 figure
Political Competition and Economic Performance: Theory and Evidence from the United States
We formulate a model to explain why the lack of political competition may stifle economic performance and use the United States as a testing ground for the model’s predictions, exploiting the 1965 Voting Rights Act which helped break the near monpoly on political power of the Democrats in southern states. We find statistically robust evidence that changes in political competition have quantitatively important effects on state income growth, state policies, and quality of Governors. By our bottom-line estimate, the increase in political competition triggered by the Voting Rights Act raised long-run per capita income in the average affected state by about 20 percent.US south; voting restrictions; political competition; economic growth
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