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A String theory made E-Z

  1. Sep 22, 2016 #1
    Move over, M- theory and F-theory!

    A brief review of E theory
    Peter West
    (Submitted on 22 Sep 2016)
    I begin with some memories of Abdus Salam who was my PhD supervisor. After reviewing the theory of non-linear realisations and Kac-Moody algebras, I explain how to construct the non-linear realisation based on the Kac-Moody algebra E11 and its vector representation. I explain how this field theory leads to dynamical equations which contain an infinite number of fields defined on a space time with an infinite number of coordinates. I then show that these unique dynamical equations, when truncated to low level fields and the usual coordinates of space time, lead to precisely the equations of motion of eleven dimensional supergravity theory. By taking different group decompositions of E11 we find all the maximal supergravity theories, including the gauged maximal supergravities, and as a result the non-linear realisation should be thought of as a unified theory that is the low energy effective action for type II strings and branes. These results essentially confirm the E11 conjecture given many years ago.

    Non-abelian Z-theory: Berends-Giele recursion for the α′-expansion of disk integrals
    Carlos R. Mafra, Oliver Schlotterer
    (Submitted on 22 Sep 2016)
    We present a recursive method to calculate the α′-expansion of disk integrals arising in tree-level scattering of open strings which resembles the approach of Berends and Giele to gluon amplitudes. Following an earlier interpretation of disk integrals as doubly partial amplitudes of an effective theory of scalars dubbed as Z-theory, we pinpoint the equation of motion of Z-theory from the Berends-Giele recursion for its tree amplitudes. A computer implementation of this method including explicit results for the recursion up to order α′7 is made available on the website this http URL
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  3. Sep 22, 2016 #2


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    Are the E and Z related?

    But E is older than F, isn't it?
  4. Sep 23, 2016 #3
    The connection is the SU(N) nonlinear sigma model, which for N=2 describes the pions, and for N=3 also includes kaons and eta meson. The classic understanding of this theory is that it results from chiral symmetry breaking in QCD with N flavors. The chiral symmetry SU(N)L x SU(N)R breaks to SU(N)diagonal, the pions etc are the Goldstone bosons, and they realize the broken symmetries nonlinearly. Peter West proposes that the fundamental symmetry of M theory is E11 and that it too is realized nonlinearly, in a way that acts on spacetime and fields together.

    Meanwhile, today people are studying the double copy construction of graviton amplitudes from gauge boson amplitudes, that derives from the analogous relation between closed and open strings. The double copy construction requires that the gauge theory amplitudes satisfy special properties (color-kinematic duality, BCJ relations). The string theory origin of this is now being uncovered. Specifically, tree-level open string amplitudes can be written as a product of gauge amplitudes and amplitudes of a scalar field theory, dubbed Z-theory, with a BCJ property. The simplest case of Z-theory turns out to be the U(N) nonlinear sigma model, which is just the SU(N) theory with an extra U(1) factor.
  5. Sep 24, 2016 #4

    Urs Schreiber

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    Not sure. F-theory originates around 1996 with
    while "E-theory" (if it is to be called this way now) originates only around 2001 with
    • Peter West, "##E_{11}## and M theory", Class. Quant. Grav., 18:4443–4460, 2001. (arXiv:hep-th/0104081)
    The latter has a precursor in
    but that would still be 2 years after F-theory, it seems.
  6. Sep 26, 2016 #5

    Urs Schreiber

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    The derivation of the equations of motion of supergravities in the article is a review of
    • Alexander G. Tumanov, Peter West,
      "##E_{11}## must be a symmetry of strings and branes",
      Physics Letters B Volume 759, 10 August 2016, Pages 663–671
    • Alexander G. Tumanov, Peter West,
      "##E_{11} in ##11d##",
      Physics Letters B Volume 758, 10 July 2016, Pages 278–285
    I have trouble extracting the exact algorithm that is being used. It seems that an ##E_{11} \ltimes l_{1}## valued connection on ##l_1## is considered (in analogy to an ##SO(d-1,1) \ltimes \mathbb{R}^{d-1,1}##-valued Poincare connection on ##\mathbb{R}^{d-1,1}##) and then they look for any equations on this that are invariant under global ##E_{11}##-symmetry and local ##I_c(E_{11})## symmetry. The equations of motion for the various maximal supergravity theories are claimed to be shown to be such (to low order in levels of ##E_{11}##). Is the claim that these are the unique such equations?

    It is noteworthy that there are no fermions in this picture. The sugra equations are purely bosonic.
  7. Oct 4, 2016 #6
  8. Dec 18, 2016 #7
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