26 research outputs found
The ALE Partition Functions of M-String Orbifolds
The ALE partition functions of a 6d (1,0) SCFT are interesting observables
which are able to detect the global structure of the SCFT. They are defined to
be the equivariant partition functions of the SCFT on a background with the
topology of a two-dimensional torus times an ALE singularity. In this work, we
compute the ALE partition functions of M-string orbifold SCFTs, extending our
previous results for the M-string SCFTs. Via geometric engineering, our results
about ALE partition functions are connected to the theory of higher-rank
Donaldson-Thomas invariants for resolutions of elliptic Calabi-Yau threefold
singularities. We predict that their generating functions satisfy interesting
modular properties. The partition functions receive contributions from BPS
strings probing the ALE singularity, whose worldsheet theories we determine via
a chain of string dualities. For this class of backgrounds the BPS strings'
worldsheet theories become relative field theories that are sensitive to
discrete data generalizing to 6d the familiar choices of flat connections at
infinity for instantons on ALE spaces. A novel feature we observe in the case
of M-string orbifold SCFTs, which does not arise for the M-string SCFT, is the
existence of frozen BPS strings which are pinned at the orbifold singularity
and carry fractional instanton charge with respect to the 6d gauge fields.Comment: 69 page
The ALE Partition Functions of M-Strings
We compute the equivariant partition function of the six-dimensional M-string
SCFTs on a background with the topology of a product of a two-dimensional torus
and an ALE singularity. We determine the result by exploiting BPS strings
probing the singularity, whose worldvolume theories we determine via a chain of
string dualities. A distinguished feature we observe is that for this class of
background the BPS strings' worldsheet theories become relative field theories
that are sensitive to finer discrete data generalizing to 6d the familiar
choices of flat connections at infinity for instantons on ALE spaces. We test
our proposal against a conjectural 6d N = (1,0) generalization of the Nekrasov
master formula, as well as against known results on ALE partition functions in
four dimensions.Comment: 44 page
Hidden exceptional symmetry in the pure spinor superstring
The pure spinor formulation of superstring theory includes an interacting
sector of central charge , which can be realized as a curved
system on the cone over the orthogonal Grassmannian
. We find that the spectrum of the system
organizes into representations of the affine
algebra at level , whose subalgebra encodes the rotational and ghost symmetries of the
system. As a consequence, the pure spinor partition function decomposes as a
sum of affine characters. We interpret this as an instance of
a more general pattern of enhancements in curved systems, which
also includes the cases and ,
corresponding to target spaces that are cones over the complex Grassmannian
and the complex Cayley plane . We identify
these curved systems with the chiral algebras of certain
CFTs arising from twisted compactification of 4d SCFTs
on .Comment: 8 pages, 1 figure; v2: added references, minor update
Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
We apply the modular approach to computing the topological string partition
function on non-compact elliptically fibered Calabi-Yau 3-folds with higher
Kodaira singularities in the fiber. The approach consists in making an ansatz
for the partition function at given base degree, exact in all fiber classes to
arbitrary order and to all genus, in terms of a rational function of weak
Jacobi forms. Our results yield, at given base degree, the elliptic genus of
the corresponding non-critical 6d string, and thus the associated BPS
invariants of the 6d theory. The required elliptic indices are determined from
the chiral anomaly 4-form of the 2d worldsheet theories, or the 8-form of the
corresponding 6d theories, and completely fix the holomorphic anomaly equation
constraining the partition function. We introduce subrings of the known rings
of Weyl invariant Jacobi forms which are adapted to the additional symmetries
of the partition function, making its computation feasible to low base wrapping
number. In contradistinction to the case of simpler singularities, generic
vanishing conditions on BPS numbers are no longer sufficient to fix the modular
ansatz at arbitrary base wrapping degree. We show that to low degree, imposing
exact vanishing conditions does suffice, and conjecture this to be the case
generally.Comment: 67 pages; v2 typos corrected, references adde
Holomorphic Anomalies, Fourfolds and Fluxes
We investigate holomorphic anomalies of partition functions underlying string
compactifications on Calabi-Yau fourfolds with background fluxes. For elliptic
fourfolds the partition functions have an alternative interpretation as
elliptic genera of N=1 supersymmetric string theories in four dimensions, or as
generating functions for relative Gromov-Witten invariants of fourfolds with
fluxes. We derive the holomorphic anomaly equations by starting from the BCOV
formalism of topological strings, and translating them into geometrical terms.
The result can be recast into modular and elliptic anomaly equations. As a new
feature, as compared to threefolds, we find an extra contribution which is
given by a gravitational descendant invariant. This leads to linear terms in
the anomaly equations, which support an algebra of derivatives mapping between
partition functions of the various flux sectors. These geometric features are
mirrored by certain properties of quasi-Jacobi forms. We also offer an
interpretation of the physics from the viewpoint of the worldsheet theory.Comment: 64 pages, 4 figure
Maximum black-hole spin from quasi-circular binary mergers
Black holes of mass M must have a spin angular momentum S below the Kerr
limit chi = S/M^2 < 1, but whether astrophysical black holes can attain this
limiting spin depends on their accretion history. Gas accretion from a thin
disk limits the black-hole spin to chi_gas < 0.9980 +- 0.0002, as
electromagnetic radiation from this disk with retrograde angular momentum is
preferentially absorbed by the black hole. Extrapolation of
numerical-relativity simulations of equal-mass binary black-hole mergers to
maximum initial spins suggests these mergers yield a maximum spin chi_eq <
0.95. Here we show that for smaller mass ratios q = m/M << 1, the superradiant
extraction of angular momentum from the larger black hole imposes a fundamental
limit chi_lim < 0.9979 +- 0.0001 on the final black-hole spin even in the
test-particle limit q -> 0 of binary black-hole mergers. The nearly equal
values of chi_gas and chi_lim imply that measurement of supermassive black-hole
spins cannot distinguish a black hole built by gas accretion from one assembled
by the gravitational inspiral of a disk of compact stellar remnants. We also
show how superradiant scattering alters the mass and spin predicted by models
derived from extrapolating test-particle mergers to finite mass ratios.Comment: final version accepted in PRD, new Fig.4 and discussio