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Contest: The most interesting article of the day: Pioline + Waldron

  1. Apr 4, 2004 #1
    This message is meant to start a new format of the postings on
    sci.physics.strings. Everyone is invited to answer the question "What was
    the most interesting paper on hep-th, hep-ph, or gr-qc today?"

    My answer for the night of April 4th is the paper by Pioline and Waldron

    The Automorphic Membrane

    It is a part of their efforts to determine the identity of "M" - which
    means the non-perturbative generalization of a string, relevant for
    M-theory (much like a string is fundamental in perturbative string

    There are various interesting terms in the effective action of M-theory
    (on tori), namely the R^4 terms (R is the curvature tensor), and their
    calculation is analogous to various calculations in string theory.
    Perturbative terms as well as toroidal membrane instantons contribute much
    like the worldsheet instantons in string theory would contribute to a
    similar process perturbatively.

    It has been possible to isolate the coefficient of the R^4 term for
    M-theory on T^3 (by a combination of perturbative calculations and duality
    arguments), and Pioline and Waldron study the modular forms - more
    precisely the theta series and automorphic forms - that manifestly respect
    the enhanced exceptional U-duality groups such as E_{6(6)} (Z) which
    includes not only SL(3,Z) times SL(2,Z) (U-duality on T^3), but also
    another copy of SL(3,Z) that generalizes the modular invariance SL(2,Z)
    of a string to the case of membranes (of toroidal topology).

    The math is perhaps difficult, but very intriguing. Boris Pioline has also
    explained me various relations of these mathematical objects to the p-adic
    numbers and adels (which are some ordered composite objects made of many
    p-adic numbers). Well, this is where the next big conceptual discoveries
    about M-theory may hide. I am certainly among those who believe that a
    proper (generalized) geometric understanding of these crazy exceptional
    duality groups of M-theory may hide a key to reveal something very deep
    about string/M-theory, perhaps something that would allow us, at least in
    principle, study also the realistic backgrounds in a non-perturbative and
    complete fashion.

    Replies including disagreement welcome.

    Best regards
    E-mail: lumo@matfyz.cz fax: +1-617/496-0110 Web: http://lumo.matfyz.cz/
    eFax: +1-801/454-1858 work: +1-617/496-8199 home: +1-617/868-4487 (call)
  2. jcsd
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