8,130 research outputs found
Wall Crossing, Quivers and Crystals
We study the spectrum of BPS D-branes on a Calabi-Yau manifold using the 0+1
dimensional quiver gauge theory that describes the dynamics of the branes at
low energies. The results of Kontsevich and Soibelman predict how the
degeneracies change. We argue that Seiberg dualities of the quiver gauge
theories, which change the basis of BPS states, correspond to crossing the
"walls of the second kind." There is a large class of examples, including local
del Pezzo surfaces, where the BPS degeneracies of quivers corresponding to one
D6 brane bound to arbitrary numbers of D4, D2 and D0 branes are counted by
melting crystal configurations. We show that the melting crystals that arise
are a discretization of the Calabi-Yau geometry. The shape of the crystal is
determined by the Calabi-Yau geometry and the background B-field, and its
microscopic structure by the quiver Q. We prove that the BPS degeneracies
computed from Q and Q' are related by the Kontsevich Soibelman formula, using a
geometric realization of the Seiberg duality in the crystal. We also show that,
in the limit of infinite B-field, the combinatorics of crystals arising from
the quivers becomes that of the topological vertex. We thus re-derive the
Gromov-Witten/Donaldson-Thomas correspondence
Supersymmetry and the LHC Inverse Problem
Given experimental evidence at the LHC for physics beyond the standard model,
how can we determine the nature of the underlying theory? We initiate an
approach to studying the "inverse map" from the space of LHC signatures to the
parameter space of theoretical models within the context of low-energy
supersymmetry, using 1808 LHC observables including essentially all those
suggested in the literature and a 15 dimensional parametrization of the
supersymmetric standard model. We show that the inverse map of a point in
signature space consists of a number of isolated islands in parameter space,
indicating the existence of "degeneracies"--qualitatively different models with
the same LHC signatures. The degeneracies have simple physical
characterizations, largely reflecting discrete ambiguities in electroweak-ino
spectrum, accompanied by small adjustments for the remaining soft parameters.
The number of degeneracies falls in the range 1<d<100, depending on whether or
not sleptons are copiously produced in cascade decays. This number is large
enough to represent a clear challenge but small enough to encourage looking for
new observables that can further break the degeneracies and determine at the
LHC most of the SUSY physics we care about. Degeneracies occur because
signatures are not independent, and our approach allows testing of any new
signature for its independence. Our methods can also be applied to any other
theory of physics beyond the standard model, allowing one to study how model
footprints differ in signature space and to test ways of distinguishing
qualitatively different possibilities for new physics at the LHC.Comment: 55 pages, 30 figure
The integrable quantum group invariant A_{2n-1}^(2) and D_{n+1}^(2) open spin chains
A family of A_{2n}^(2) integrable open spin chains with U_q(C_n) symmetry was
recently identified in arXiv:1702.01482. We identify here in a similar way a
family of A_{2n-1}^(2) integrable open spin chains with U_q(D_n) symmetry, and
two families of D_{n+1}^(2) integrable open spin chains with U_q(B_n) symmetry.
We discuss the consequences of these symmetries for the degeneracies and
multiplicities of the spectrum. We propose Bethe ansatz solutions for two of
these models, whose completeness we check numerically for small values of n and
chain length N. We find formulas for the Dynkin labels in terms of the numbers
of Bethe roots of each type, which are useful for determining the corresponding
degeneracies. In an appendix, we briefly consider D_{n+1}^(2) chains with other
integrable boundary conditions, which do not have quantum group symmetry.Comment: 47 pages; v2: two references added and minor change
Cosmic Complementarity: Joint Parameter Estimation from CMB Experiments and Redshift Surveys
We study the ability of future CMB anisotropy experiments and redshift
surveys to constrain a thirteen-dimensional parameterization of the adiabatic
cold dark matter model. Each alone is unable to determine all parameters to
high accuracy. However, considered together, one data set resolves the
difficulties of the other, allowing certain degenerate parameters to be
determined with far greater precision. We treat in detail the degeneracies
involving the classical cosmological parameters, massive neutrinos,
tensor-scalar ratio, bias, and reionization optical depth as well as how
redshift surveys can resolve them. We discuss the opportunities for internal
and external consistency checks on these measurements. Previous papers on
parameter estimation have generally treated smaller parameter spaces; in direct
comparisons to these works, we tend to find weaker constraints and suggest
numerical explanations for the discrepancies.Comment: Submitted to ApJ. LaTeX, 20 pages, emulateapj.sty and
onecolfloat.sty. Minor errors in Table 8 corrected; reference adde
K-causality and degenerate spacetimes
The causal relation was introduced by Sorkin and Woolgar to extend the
standard causal analysis of spacetimes to those that are only . Most
of their results also hold true in the case of spacetimes with degeneracies. In
this paper we seek to examine explicitly in the case of Lorentzian
topology changing Morse spacetimes containing isolated degeneracies. We first
demonstrate some interesting features of this relation in globally Lorentzian
spacetimes. In particular, we show that is robust and that it coincides
with the Seifert relation when the spacetime is stably causal. Moreover, the
Hawking and Sachs characterisation of causal continuity translates into a
natural expression in terms of for general spacetimes. We then examine
in topology changing Morse spacetimes both with and without the
degeneracies and find further characterisations of causal continuity.Comment: Latex, 23 pages, 4 figure
- …