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SUMMARY:Shota Komatsu (IAS)
DTSTART:20200515T130000Z
DTEND:20200515T150000Z
DTSTAMP:20260423T022717Z
UID:LIJC/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/LIJC/2/">Wil
 son loops as matrix product states</a>\nby Shota Komatsu (IAS) as part of 
 London Integrability Journal Club\n\n\nAbstract\nIn his paper in 1979\, Po
 lyakov envisaged a possibility of reformulating the gauge theory as a Prin
 cipal Chiral Model defined on a space of loops and discussed "the loop-spa
 ce integrability". This idea\, together with a closely related idea of the
  loop equation\, led to numerous important results in matrix models and 2d
  gauge theories\, but its application to four-dimensional gauge theories h
 ad only limited success. Now\, after 50 years\, we have a concrete example
  of integrable four-dimensional gauge theory\, N=4 SYM. However integrabil
 ity in N=4 SYM is formulated mostly in terms of local operators\, although
  important progress has been made in constructing the Yangian for the Wils
 on loops. In this talk\, I will present a framework which would bridge the
 se two distant notions of integrabililty. The key player in the story is a
  correlation function of a local operator and the Wilson loop. I reformula
 te the gauge-theory computation of this observable as an overlap between a
 n energy eigenstate of a spin chain and a matrix product state (MPS). Unli
 ke standard MPS's discussed in the literature\, our MPS has infinite bond 
 dimensions in order to accommodate infinite dimensionality of the space of
  loops. It provides an "intertwiner" between integrable structures of the 
 local operators and the Wilson loops\, and in particular implies the exist
 ence of a special set of deformations of the Wilson loop which satisfy the
  QQ-relation. I will also explain how to formulate a nonperturbative boots
 trap program based on the results obtained in this framework and compute t
 he correlator of the circular BPS Wilson loop and general non-BPS operator
 s at finite coupling\, emphasizing the relation to and the difference from
  other observables that were computed by a similar approach.\n
LOCATION:https://researchseminars.org/talk/LIJC/2/
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