Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: "Anomaly" in n=infinity Alday-Maldacena Duality for Wavy Circle   If the Alday-Maldacena version of string/gauge duality is formulated as an
equivalence between double loop and area integrals a la arXiv: 0708.1625, then
this pure geometric relation can be tested for various choices of n-side
polygons. The simplest possibility arises at n=infinity, with polygon
substituted by an arbitrary continuous curve. If the curve is a circle, the
minimal surface problem is exactly solvable. If it infinitesimally deviates
from a circle, then the duality relation can be studied by expanding in powers
of a small parameter. In the first approximation the Nambu-Goto (NG) equations
can be linearized, and the peculiar NG Laplacian plays the central role. Making
use of explicit zero-modes of this operator (NG-harmonic functions), we
investigate the geometric duality in the lowest orders for small deformations
of arbitrary shape lying in the plane of the original circle. We find a
surprisingly strong dependence of the minimal area on regularization procedure
affecting "the boundary terms" in minimal area. If these terms are totally
omitted, the remaining piece is regularization independent, but still differs
by simple numerical factors like 4 from the double-loop integral which
represents the BDS formula so that we stop short from the first non-trivial
confirmation of the Alday-Maldacena duality. This confirms the earlier-found
discrepancy for two parallel lines at n=infinity, but demonstrates that it
actually affects only a finite number (out of infinitely many) of parameters in
the functional dependence on the shape of the boundary, and the duality is only
slightly violated, which allows one to call this violation an anomaly.

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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: physics
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
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The categories of this paper are: alg-geom
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph