587 research outputs found
Dressing and Wrapping
We prove that the validity of the recently proposed dressed, asymptotic Bethe
ansatz for the planar AdS/CFT system is indeed limited at weak coupling by
operator wrapping effects. This is done by comparing the Bethe ansatz
predictions for the four-loop anomalous dimension of finite-spin twist-two
operators to BFKL constraints from high-energy scattering amplitudes in N=4
gauge theory. We find disagreement, which means that the ansatz breaks down for
length-two operators at four-loop order. Our method supplies precision tools
for multiple all-loop tests of the veracity of any yet-to-be constructed set of
exact spectral equations. Finally we present a conjecture for the exact
four-loop anomalous dimension of the family of twist-two operators, which
includes the Konishi field.Comment: 20 pages, 2 tables, no figures; v2: references added, conjecture on
exact four-loop twist-two result state
The grieving adolescent
the purpose of this paper is to explore the developmental issues of adolescents related to their conception of death, as well as the stages of the grieving process. Intervention strategies for school counselors to use with adolescents will also be examined
Harmonic R matrices for scattering amplitudes and spectral regularization
Planar N=4 supersymmetric Yang-Mills theory appears to be integrable. While this allows one to find this theory's exact spectrum, integrability has hitherto been of no direct use for scattering amplitudes. To remedy this, we deform all scattering amplitudes by a spectral parameter. The deformed tree-level four-point function turns out to be essentially the one-loop R matrix of the integrable N=4 spin chain satisfying the Yang-Baxter equation. Deformed on-shell three-point functions yield novel three-leg R matrices satisfying bootstrap equations. Finally, we supply initial evidence that the spectral parameter might find its use as a novel symmetry-respecting regulator replacing dimensional regularization. Its physical meaning is a local deformation of particle helicity, a fact which might be useful for a much larger class of nonintegrable four-dimensional field theories. © 2013 American Physical Society
Spectral parameters for scattering amplitudes in N=4 super Yang-Mills theory
Planar N= 4 Super Yang-Mills theory appears to be a quantum integrable four-dimensional conformal theory. This has been used to find equations believed to describe its exact spectrum of anomalous dimensions. Integrability seemingly also extends to the planar space-time scattering amplitudes of the N= 4 model, which show strong signs of Yangian invariance. However, in contradistinction to the spectral problem, this has not yet led to equations determining the exact amplitudes. We propose that the missing element is the spectral parameter, ubiquitous in integrable models. We show that it may indeed be included into recent on-shell approaches to scattering amplitude integrands, providing a natural deformation of the latter. Under some constraints, Yangian symmetry is preserved. Finally we speculate that the spectral parameter might also be the regulator of choice for controlling the infrared divergences appearing when integrating the integrands in exactly four dimensions. © 2014 The Author(s)
Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM
We present the perturbative Yangian symmetry at next-to-leading order in the
su(2|1) sector of planar N=4 SYM. Just like the ordinary symmetry generators,
the bi-local Yangian charges receive corrections acting on several neighboring
sites. We confirm that the bi-local Yangian charges satisfy the necessary
conditions: they transform in the adjoint of su(2|1), they commute with the
dilatation generator, and they satisfy the Serre relations. This proves that
the sector is integrable at two loops.Comment: 13 pages, v2: minor correction
Aspects of Integrability in N =4 SYM
Various recently developed connections between supersymmetric Yang-Mills
theories in four dimensions and two dimensional integrable systems serve as
crucial ingredients in improving our understanding of the AdS/CFT
correspondence. In this review, we highlight some connections between
superconformal four dimensional Yang-Mills theory and various integrable
systems. In particular, we focus on the role of Yangian symmetries in studying
the gauge theory dual of closed string excitations. We also briefly review how
the gauge theory connects to Calogero models and open quantum spin chains
through the study of the gauge theory duals of D3 branes and open strings
ending on them. This invited review, written for Modern Physics Letters-A, is
based on a seminar given at the Institute of Advanced Study, Princeton.Comment: Invited brief review for Mod. Phys. Lett. A based on a talk at I.A.S,
Princeto
How to foster Sustainable Continuous Improvement: A cause-effect relations map of Lean soft practices
The instanton contributions to Yang-Mills theory on the torus: localization, Wilson loops and the perturbative expansion
The instanton contributions to the partition function and to homologically
trivial Wilson loops for a U(N) Yang-Mills theory on a torus are
analyzed. An exact expression for the partition function is obtained as a sum
of contributions localized around the classical solutions of Yang-Mills
equations, that appear according to the general classification of Atiyah and
Bott. Explicit expressions for the exact Wilson loop averages are obtained when
N=2, N=3. For general the contribution of the zero-instanton sector has
been carefully derived in the decompactification limit, reproducing the sum of
the perturbative series on the plane, in which the light-cone gauge Yang-Mills
propagator is prescribed according to Wu-Mandelstam-Leibbrandt (WML). Agreement
with the results coming from is therefore obtained, confirming the truly
perturbative nature of the WML computations.Comment: 28 pages, revtex, no figure
On the Maximum Crossing Number
Research about crossings is typically about minimization. In this paper, we
consider \emph{maximizing} the number of crossings over all possible ways to
draw a given graph in the plane. Alpert et al. [Electron. J. Combin., 2009]
conjectured that any graph has a \emph{convex} straight-line drawing, e.g., a
drawing with vertices in convex position, that maximizes the number of edge
crossings. We disprove this conjecture by constructing a planar graph on twelve
vertices that allows a non-convex drawing with more crossings than any convex
one. Bald et al. [Proc. COCOON, 2016] showed that it is NP-hard to compute the
maximum number of crossings of a geometric graph and that the weighted
geometric case is NP-hard to approximate. We strengthen these results by
showing hardness of approximation even for the unweighted geometric case and
prove that the unweighted topological case is NP-hard.Comment: 16 pages, 5 figure
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