647 research outputs found
Resummation of Threshold, Low- and High-Energy Expansions for Heavy-Quark Correlators
With the help of the Mellin-Barnes transform, we show how to simultaneously
resum the expansion of a heavy-quark correlator around q^2=0 (low-energy), q^2=
4 m^2 (threshold, where m is the quark mass) and q^2=-\infty (high-energy) in a
systematic way. We exemplify the method for the perturbative vector correlator
at O(alpha_s^2) and O(alpha_s^3). We show that the coefficients, Omega(n), of
the Taylor expansion of the vacuum polarization function in terms of the
conformal variable \omega admit, for large n, an expansion in powers of 1/n (up
to logarithms of n) that we can calculate exactly. This large-n expansion has a
sign-alternating component given by the logarithms of the OPE, and a fixed-sign
component given by the logarithms of the threshold expansion in the external
momentum q^2.Comment: 27 pages, 8 figures. We fix typos in Eqs. (18), (27), (55) and (56).
Results unchange
Frobenius Splittings
We give a gentle introduction to Frobenius splittings. Then we recall a few
results that have been obtained with the method.Comment: 21 pages, typos correcte
Cohomology for Frobenius kernels of
Let be the -th Frobenius kernels of the group scheme
defined over an algebraically field of characteristic . In this paper we
give for a complete description of the cohomology groups for
. We also prove that the reduced cohomology ring
\opH^\bullet((SL_2)_r,k)_{\red} is Cohen-Macaulay. Geometrically, we show for
each that the maximal ideal spectrum of the cohomology ring for
is homeomorphic to the fiber product G\times_B\fraku^r. Finally,
we adapt our calculations to obtain analogous results for the cohomology of
higher Frobenius-Luzstig kernels of quantized enveloping algebras of type
.Comment: published version; a section for the case p=2 is adde
The large N limit of M2-branes on Lens spaces
We study the matrix model for N M2-branes wrapping a Lens space L(p,1) =
S^3/Z_p. This arises from localization of the partition function of the ABJM
theory, and has some novel features compared with the case of a three-sphere,
including a sum over flat connections and a potential that depends
non-trivially on p. We study the matrix model both numerically and analytically
in the large N limit, finding that a certain family of p flat connections give
an equal dominant contribution. At large N we find the same eigenvalue
distribution for all p, and show that the free energy is simply 1/p times the
free energy on a three-sphere, in agreement with gravity dual expectations.Comment: 28 pages, 4 figure
Steinberg modules and Donkin pairs
We prove that in positive characteristic a module with good filtration for a
group of type E6 restricts to a module with good filtration for a subgroup of
type F4. (Recall that a filtration of a module for a semisimple algebraic group
is called good if its layers are dual Weyl modules.) Our result confirms a
conjecture of Brundan for one more case. The method relies on the canonical
Frobenius splittings of Mathieu. Next we settle the remaining cases, in
characteristic not 2, with a computer-aided variation on the old method of
Donkin.Comment: 16 pages; proof of Brundan's conjecture adde
Estimating Affective Taste Experience Using Combined Implicit Behavioral and Neurophysiological Measures
We trained a model to distinguish an extreme high arousal, unpleasant drink from regular drinks based on a range of implicit behavioral and physiological responses to naturalistic tasting. The trained model predicted arousal ratings of regular drinks, highlighting the possibility to estimate affective experience without having to rely on subjective ratings.</p
Gravitational mechanisms to self-tune the cosmological constant: obstructions and ways forward
Gravitational models of self-tuning are those in which vacuum energy has no observable effect on spacetime curvature, even though it is a priori unsuppressed below the cut-off. We complement Weinberg's no go theorem by studying field theoretic completions of self-adjustment allowing for broken translations as well as other generalisations, and identify new obstructions. Our analysis uses a very general Källén-Lehmann spectral representation of the exchange amplitude for conserved sources of energy-momentum and exploits unitarity and Lorentz invariance to show that a transition from self-tuning of long wavelength sources to near General Relativity on shorter scales is generically not possible. We search for novel ways around our obstructions and highlight two interesting possibilities. The first is an example of a unitary field configuration on anti-de Sitter space with the desired transition from self-tuning to GR. A second example is motivated by vacuumenergy sequestering
Orientifolds and the Refined Topological String
We study refined topological string theory in the presence of orientifolds by
counting second-quantized BPS states in M-theory. This leads us to propose a
new integrality condition for both refined and unrefined topological strings
when orientifolds are present. We define the SO(2N) refined Chern-Simons theory
which computes refined open string amplitudes for branes wrapping Seifert
three-manifolds. We use the SO(2N) refined Chern-Simons theory to compute new
invariants of torus knots that generalize the Kauffman polynomials. At large N,
the SO(2N) refined Chern-Simons theory on the three-sphere is dual to refined
topological strings on an orientifold of the resolved conifold, generalizing
the Gopakumar-Sinha-Vafa duality. Finally, we use the (2,0) theory to define
and solve refined Chern-Simons theory for all ADE gauge groups
5-dim Superconformal Index with Enhanced En Global Symmetry
The five-dimensional supersymmetric gauge theory with Sp(N)
gauge group and SO(2N_f) flavor symmetry describes the physics on N D4-branes
with D8-branes on top of a single O8 orientifold plane in Type I' theory.
This theory is known to be superconformal at the strong coupling limit with the
enhanced global symmetry for . In this work we calculate
the superconformal index on for the Sp(1) gauge theory by the
localization method and confirm such enhancement of the global symmetry at the
superconformal limit for to a few leading orders in the chemical
potential. Both perturbative and (anti)instanton contributions are present in
this calculation. For cases some issues related the pole structure of
the instanton calculation could not be resolved and here we could provide only
some suggestive answer for the leading contributions to the index. For the
Sp(N) case, similar issues related to the pole structure appear.Comment: 70 pages, references added, published versio
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