Research Interest of Grigory Vartanov

      Publication 1: Supersymmetric dualities beyond the conformal window (URL)
      Publication 2: Elliptic hypergeometry of supersymmetric dualities (URL)
      Publication 3: Infrared Safe Observables in ${\cal N}=4$ Super Yang-Mills Theory (URL)

    URL of Research: http://www.aei.mpg.de/~vartanov/RP.pdf

Statement of Interest:


  About 15 years ago Seiberg showed that there is electric-magnetic duality for N=1 SYM theories. There were a lot of papers showing new dualities for different gauge groups but there is no still an algorithm for finding duals for theories. Recently there was a paper by Romelsberger where there is an algorithm for counting chiral primaries in N=1 supersymmetric theories. This index is given in terms of the elliptic hypergeometric integrals. According to Spiridonov’s papers there are a lot of transformation for this kind of integrals which gives non-trivial dualities for N=1 supersymmetric theories. Also there is an interesting question of equality for t’Hooft anomaly matching from field theory side and the balancing condition for integrals from mathematical point of view. There is an application of the theory of elliptic hypergeometry and for quiver N=2 supersymmetric theories the index for which can be obtained by applying the Bailey tree algortihm.