120,466 research outputs found
The low energy expansion of the one-loop type II superstring amplitude
The one-loop four-graviton amplitude in either of the type II superstring
theories is expanded in powers of the external momenta up to and including
terms of order s^4 log s R^4, where R^4 denotes a specific contraction of four
linearized Weyl tensors and s is a Mandelstam invariant. Terms in this series
are obtained by integrating powers of the two-dimensional scalar field theory
propagator over the toroidal world-sheet as well as the moduli of the torus.
The values of these coefficients match expectations based on duality relations
between string theory and eleven-dimensional supergravity.Comment: harvmac (b), 25 pages, 3 eps figures. v2: Factors of 2 corrected.
Conclusion unchange
Homology representations arising from the half cube, II
In a previous work (arXiv:0806.1503v2), we defined a family of subcomplexes
of the -dimensional half cube by removing the interiors of all half cube
shaped faces of dimension at least , and we proved that the homology of such
a subcomplex is concentrated in degree . This homology group supports a
natural action of the Coxeter group of type . In this paper, we
explicitly determine the characters (over ) of these homology
representations, which turn out to be multiplicity free. Regarded as
representations of the symmetric group by restriction, the homology
representations turn out to be direct sums of certain representations induced
from parabolic subgroups. The latter representations of \sym_n agree (over
) with the representations of \sym_n on the -nd homology of
the complement of the -equal real hyperplane arrangement.Comment: 19 pages AMSTeX. One figure. The Conjecture in the previous version
is now a Theorem. This research was supported by NSF grant DMS-090576
On rank functions for heaps
Motivated by work of Stembridge, we study rank functions for Viennot's heaps
of pieces. We produce a simple and sufficient criterion for a heap to be a
ranked poset and apply the results to the heaps arising from fully commutative
words in Coxeter groups.Comment: 18 pages AMSTeX, 3 figure
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