262,021 research outputs found
Asymptotic Euler-Maclaurin formula over lattice polytopes
An asymptotic expansion formula of Riemann sums over lattice polytopes is
given. The formula is an asymptotic form of the local Euler-Maclaurin formula
due to Berline-Vergne. The proof given here for Delzant lattice polytopes is
independent of the local Euler-Maclaurin formula. But we use it for general
lattice polytopes. As corollaries, an explicit formula for each term in the
expansion over Delzant polytopes in two dimension and an explicit formula for
the third term of the expansion for Delzant polytopes in arbitrary dimension
are given. Moreover, some uniqueness results are given.Comment: 35 pages. Results in the previous version are generalized to lattice
polytopes. Some further results are added. The title is changed. The
organization is changed to clarify the discussion
Off-shell renormalization in the presence of dimension 6 derivative operators. I. General theory
The consistent recursive subtraction of UV divergences order by order in the
loop expansion for spontaneously broken effective field theories with
dimension-6 derivative operators is presented for an Abelian gauge group. We
solve the Slavnov-Taylor identity to all orders in the loop expansion by
homotopy techniques and a suitable choice of invariant field coordinates (named
bleached variables) for the linearly realized gauge group. This allows one to
disentangle the gauge-invariant contributions to off-shell 1-PI amplitudes from
those associated with the gauge-fixing and (generalized) non-polynomial field
redefinitions (that do appear already at one loop). The tools presented can be
easily generalized to the non-Abelian case.Comment: 37 pages, 3 figures; updated version to match the published on
Bremsstrahlung function, leading Luscher correction at weak coupling and localization
We discuss the near BPS expansion of the generalized cusp anomalous dimension
with L units of R-charge. Integrability provides an exact solution, obtained by
solving a general TBA equation in the appropriate limit: we propose here an
alternative method based on supersymmetric localization. The basic idea is to
relate the computation to the vacuum expectation value of certain 1/8 BPS
Wilson loops with local operator insertions along the contour. These
observables localize on a two-dimensional gauge theory on S^2, opening the
possibility of exact calculations. As a test of our proposal, we reproduce the
leading Luscher correction at weak coupling to the generalized cusp anomalous
dimension. This result is also checked against a genuine Feynman diagram
approach in N=4 Super Yang-Mills theory.Comment: 25 pages, 6 figures. References added and typos correcte
Extremal Charged Black Holes with a Twisted Extra Dimension
We construct odd-dimensional extremal charged black hole solutions with a
twisted S^1 as an extra dimension on generalized Euclidean Taub-NUT spaces.
There exists a null hypersurface where an expansion for an outgoing null
geodesic congruence vanishes, then these spacetimes look like black holes. We
show that the metrics admit C^0 extension across the horizon, but some
components of Riemann curvature diverge there if the dimension is higher than
five. The singularity is not much strong so that an observer along a free-fall
geodesic can traverse the horizon. We also show solutions with a positive
cosmological constant.Comment: 21 pages, no figure, v2 added reference
A note on -saturated o-minimal expansions of real closed fields
We give necessary and sufficient conditions for a polynomially bounded
o-minimal expansion of a real closed field (in a language of arbitrary
cardinality) to be -saturated. The conditions are in terms of
the value group, residue field, and pseudo- Cauchy sequences of the natural
valuation on the real closed field. This is achieved by an analysis of types,
leading to the trichotomy. Our characterization provides a construction method
for saturated models, using fields of generalized power series.Comment: Key words and phrases. natural valuation, value group, residue field,
pseudo- Cauchy sequences, polynomially bounded o-minimal expansion of a real
closed field, definable closure, dimension, saturation. To appear in Algebra
and Logic volume 54 Issue 5 November 201
Strong-coupling expansion for the Hubbard model in arbitrary dimension using slave bosons
A strong-coupling expansion for the antiferromagnetic phase of the Hubbard
model is derived in the framework of the slave-boson mean-field approximation.
The expansion can be obtained in terms of moments of the density of states of
freely hopping electrons on a lattice, which in turn are obtained for
hypercubic lattices in arbitrary dimension. The expansion is given for the case
of half-filling and for the energy up to fifth order in the ratio of hopping
integral over on-site interaction , but can straightforwardly be
generalized to the non-half-filled case and be extended to higher orders in
. For the energy the expansion is found to have an accuracy of better than
for . A comparison is given with an earlier perturbation
expansion based on the Linear Spin Wave approximation and with a similar
expansion based on the Hartree-Fock approximation. The case of an infinite
number of spatial dimensions is discussed.Comment: 12 pages, LaTeX2e, to be published in Phys. Rev.
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