99 research outputs found
Classical theta constants vs. lattice theta series, and super string partition functions
Recently, various possible expressions for the vacuum-to-vacuum superstring
amplitudes has been proposed at genus . To compare the different
proposals, here we will present a careful analysis of the comparison between
the two main technical tools adopted to realize the proposals: the classical
theta constants and the lattice theta series. We compute the relevant Fourier
coefficients in order to relate the two spaces. We will prove the equivalence
up to genus 4. In genus five we will show that the solutions are equivalent
modulo the Schottky form and coincide if we impose the vanishing of the
cosmological constant.Comment: 21 page
Eluding SUSY at every genus on stable closed string vacua
In closed string vacua, ergodicity of unipotent flows provide a key for
relating vacuum stability to the UV behavior of spectra and interactions.
Infrared finiteness at all genera in perturbation theory can be rephrased in
terms of cancelations involving only tree-level closed strings scattering
amplitudes. This provides quantitative results on the allowed deviations from
supersymmetry on perturbative stable vacua. From a mathematical perspective,
diagrammatic relations involving closed string amplitudes suggest a relevance
of unipotent flows dynamics for the Schottky problem and for the construction
of the superstring measure.Comment: v2, 17 pages, 8 figures, typos corrected, new figure added with 3
modular images of long horocycles,(obtained with Mathematica
Equidistribution Rates, Closed String Amplitudes, and the Riemann Hypothesis
We study asymptotic relations connecting unipotent averages of
automorphic forms to their integrals over the moduli space
of principally polarized abelian varieties. We obtain reformulations of the
Riemann hypothesis as a class of problems concerning the computation of the
equidistribution convergence rate in those asymptotic relations. We discuss
applications of our results to closed string amplitudes. Remarkably, the
Riemann hypothesis can be rephrased in terms of ultraviolet relations occurring
in perturbative closed string theory.Comment: 15 page
Supersymmetric AdS_4 black holes and attractors
Using the general recipe given in arXiv:0804.0009, where all timelike
supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian
vector multiplets were classified, we construct the first examples of genuine
supersymmetric black holes in AdS_4 with nonconstant scalar fields. This is
done for various choices of the prepotential, amongst others for the STU model.
These solutions permit to study the BPS attractor flow in AdS. We also
determine the most general supersymmetric static near-horizon geometry and
obtain the attractor equations in gauged supergravity. As a general feature we
find the presence of flat directions in the black hole potential, i.e.,
generically the values of the moduli on the horizon are not completely
specified by the charges. For one of the considered prepotentials, the
resulting moduli space is determined explicitely. Still, in all cases, we find
that the black hole entropy depends only on the charges, in agreement with the
attractor mechanism.Comment: 25 pages, uses JHEP3.cl
Rotating BPS black holes in matter-coupled AdS(4) supergravity
Using the general recipe given in arXiv:0804.0009, where all timelike
supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian
vector multiplets were classified, we construct genuine rotating supersymmetric
black holes in AdS(4) with nonconstant scalar fields. This is done for the
SU(1,1)/U(1) model with prepotential F=-iX^0X^1. In the static case, the black
holes are uplifted to eleven dimensions, and generalize the solution found in
hep-th/0105250 corresponding to membranes wrapping holomorphic curves in a
Calabi-Yau five-fold. The constructed rotating black holes preserve one quarter
of the supersymmetry, whereas their near-horizon geometry is one half BPS.
Moreover, for constant scalars, we generalize (a supersymmetric subclass of)
the Plebanski-Demianski solution of cosmological Einstein-Maxwell theory to an
arbitrary number of vector multiplets. Remarkably, the latter turns out to be
related to the dimensionally reduced gravitational Chern-Simons action.Comment: 23 pages, uses JHEP3.cl
Extending the Belavin-Knizhnik "wonderful formula" by the characterization of the Jacobian
A long-standing question in string theory is to find the explicit expression
of the bosonic measure, a crucial issue also in determining the superstring
measure. Such a measure was known up to genus three. Belavin and Knizhnik
conjectured an expression for genus four which has been proved in the framework
of the recently introduced vector-valued Teichmueller modular forms. It turns
out that for g>3 the bosonic measure is expressed in terms of such forms. In
particular, the genus four Belavin-Knizhnik "wonderful formula" has a
remarkable extension to arbitrary genus whose structure is deeply related to
the characterization of the Jacobian locus. Furthermore, it turns out that the
bosonic string measure has an elegant geometrical interpretation as generating
the quadrics in P^{g-1} characterizing the Riemann surface. All this leads to
identify forms on the Siegel upper half-space that, if certain conditions
related to the characterization of the Jacobian are satisfied, express the
bosonic measure as a multiresidue in the Siegel upper half-space. We also
suggest that it may exist a super analog on the super Siegel half-space.Comment: 15 pages. Typos corrected, refs. and comments adde
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Preface
Preface - The second International Conference on Mathematical Modeling in Physical Sciences (IC-MSQUARE) took place at Prague, Czech Republic, from Sunday 1 September to Thursday 5 September 2013
All the timelike supersymmetric solutions of all ungauged d=4 supergravities
We determine the form of all timelike supersymmetric solutions of all N
greater or equal than 2, d=4 ungauged supergravities, for N less or equal than
4 coupled to vector supermultiplets, using the $Usp(n+1,n+1)-symmetric
formulation of Andrianopoli, D'Auria and Ferrara and the spinor-bilinears
method, while preserving the global symmetries of the theories all the way. As
previously conjectured in the literature, the supersymmetric solutions are
always associated to a truncation to an N=2 theory that may include
hypermultiplets, although fields which are eliminated in the truncations can
have non-trivial values, as is required by the preservation of the global
symmetry of the theories. The solutions are determined by a number of
independent functions, harmonic in transverse space, which is twice the number
of vector fields of the theory (n+1). The transverse space is flat if an only
if the would-be hyperscalars of the associated N=2 truncation are trivial.Comment: v3: Some changes in the introduction. Version to be published in JHE
On BPS bounds in D=4 N=2 gauged supergravity II: general matter couplings and black hole masses
We continue the analysis of BPS bounds started in arXiv:1110.2688, extending
it to the full class of N=2 gauged supergravity theories with arbitrary vector
and hypermultiplets. We derive the general form of the asymptotic charges for
asymptotically flat (M_4), anti-de Sitter (AdS_4), and magnetic anti-de Sitter
(mAdS_4) spacetimes. Some particular examples from black hole physics are given
to explicitly demonstrate how AdS and mAdS masses differ when solutions with
non-trivial scalar profiles are considered.Comment: 21 pages; v2 added reference, published version; v3 minor correction
Generalized Attractors in Five-Dimensional Gauged Supergravity
In this paper we study generalized attractors in N=2 gauged supergravity
theory in five dimensions coupled to arbitrary number of hyper, vector and
tensor multiplets. We look for attractor solutions with constant anholonomy
coefficients. By analyzing the equations of motion we derive the attractor
potential. We further show that the generalized attractor potential can be
obtained from the fermionic shifts. We study some simple examples and show that
constant anholonomy gives rise to homogeneous black branes in five dimensions.Comment: 30 pages, no figures,V3 minor revisions, to appear in JHE
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