675,576 research outputs found
Supersymmetric Wilson loops at two loops
We study the quantum properties of certain BPS Wilson loops in
supersymmetric Yang-Mills theory. They belong to a general family, introduced
recently, in which the addition of particular scalar couplings endows generic
loops on with a fraction of supersymmetry. When restricted to ,
their quantum average has been further conjectured to be exactly computed by
the matrix model governing the zero-instanton sector of YM on the sphere.
We perform a complete two-loop analysis on a class of cusped Wilson loops lying
on a two-dimensional sphere, finding perfect agreement with the conjecture. The
perturbative computation reproduces the matrix-model expectation through a
highly non-trivial interplay between ladder diagrams and self-energies/vertex
contributions, suggesting the existence of a localization procedure.Comment: 35 pages, 14 figures, typos corrected, references adde
Wilson Loops @ 3-Loops in Special Kinematics
We obtain a compact expression for the octagon MHV amplitude / Wilson loop at
3 loops in planar N=4 SYM and in special 2d kinematics in terms of 7 unfixed
coefficients. We do this by making use of the cyclic and parity symmetry of the
amplitude/Wilson loop and its behaviour in the soft/collinear limits as well as
in the leading term in the expansion away from this limit. We also make a
natural and quite general assumption about the functional form of the result,
namely that it should consist of weight 6 polylogarithms whose symbol consists
of basic cross-ratios only (and not functions thereof). We also describe the
uplift of this result to 10 points.Comment: 26 pages. Typos correcte
Cosmic Loops
This paper explores a special kind of loop of grounding: cosmic loops. A cosmic loop is a loop that intuitively requires us to go "around" the entire universe to come back to the original ground. After describing several kinds of cosmic loop scenarios, I will discuss what we can learn from these scenarios about constraints on grounding; the conceivability of cosmic loops; the possibility of cosmic loops; and the prospects for salvaging local reflexivity, asymmetry and transitivity of grounding in a world containing a cosmic loop of ground. The considerations raised in this paper also bear on what we should think about relations that are meant to support grounding relations: in particular, revisions to theories of the part-whole relation are discussed
Cheban loops
Left Cheban loops are loops that satisfy the identity x(xy.z) = yx.xz. Right
Cheban loops satisfy the mirror identity {(z.yx)x = zx.xy}. Loops that are both
left and right Cheban are called Cheban loops. Cheban loops can also be
characterized as those loops that satisfy the identity x(xy.z) = (y.zx)x. These
loops were introduced in Cheban, A. M. Loops with identities of length four and
of rank three. II. (Russian) General algebra and discrete geometry, pp.
117-120, 164, "Shtiintsa", Kishinev, 1980. Here we initiate a study of their
structural properties. Left Cheban loops are left conjugacy closed. Cheban
loops are weak inverse property, power associative, conjugacy closed loops;
they are centrally nilpotent of class at most two.Comment: 6 page
Algebraic properties of some varieties of central loops
Isotopes of C-loops with unique non-identity squares are shown to be both
C-loops and A-loops. The relationship between C-loops and Steiner loops is
further studied. Central loops with the weak and cross inverse properties are
also investigated. C-loops are found to be Osborn loops if every element in
them are squares.Comment: 20 page
Three lectures on automorphic loops
These notes accompany a series of three lectures on automorphic loops to be
delivered by the author at Workshops Loops '15 (Ohrid, Macedonia, 2015).
Automorphic loops are loops in which all inner mappings are automorphisms.
The first paper on automorphic loops appeared in 1956 and there has been a
surge of interest in the topic since 2010. The purpose of these notes is to
introduce the methods used in the study of automorphic loops to a wider
audience of researchers working in nonassociative mathematics.
In the first lecture we establish basic properties of automorphic loops
(flexibility, power-associativity and the antiautomorphic inverse property) and
discuss relations of automorphic loops to Moufang loops.
In the second lecture we expand on ideas of Glauberman and investigate the
associated operation and similar concepts,
using a more modern approach of twisted subgroups. We establish many structural
results for commutative and general automorphic loops, including the Odd Order
Theorem.
In the last lecture we look at enumeration and constructions of automorphic
loops. We show that there are no nonassociative simple automorphic loops of
order less than , we study commutative automorphic loops of order
and , and introduce two general constructions of automorphic loops.
The material is newly organized and sometimes new, shorter proofs are given
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