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Conformal invariance of the full Leigh-Strassler deformation of N=4 SYM

Conformal invariance of the full Leigh-Strassler deformation of N=4 SYM. Alexander Zhiboedov Moscow State University, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research. Work with L. Bork, D. Kazakov, G. Vartanov (paper in preparation).

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Conformal invariance of the full Leigh-Strassler deformation of N=4 SYM

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  1. Conformal invariance of the full Leigh-Strassler deformation of N=4 SYM Alexander Zhiboedov Moscow State University, Bogoliubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research Work with L. Bork, D. Kazakov, G. Vartanov (paper in preparation)

  2. Introduction. The full Leigh-Strassler deformation. LS hep-th/9503121 M hep-th/9711200 GKP hep-th/9802109 W hep-th/9803131 Addition Lunin, Maldacena hep-th/0502086 Kulaxizi hep-th/0612160 Zanon et al. Whether the theory is conformal on quantum level? Sokatchev et al. KB hep-th/0706.4245

  3. R-symmetry. • R-symmetry. 2. global symmetry 3. cyclic permutation 3. cyclic permutation 4. 4. Symmetries of β-deformed theory and the full LS deformation β-deformed full LS 2. global symmetry

  4. Necessary properties of the theory to be conformal NZSV 83 Order by order in PT The topology of diagrams and structure of vertexes is the same in LS and N=4 theories. Thus, we are looking at difference between these theories. Remember that conformal invariance = finiteness can be achieved using two fold expansion Kazakov ‘85

  5. New notations. 1-loop condition. Let’s redefine our notations Zanon et al. ‘06

  6. Four-loop conformal condition in the planar limit Conformal and finite condition

  7. Three-loop conformal condition in the non-planar limit Conformal and finite condition

  8. Particularly is exactly superconformal in the planar limit Unitary equivalent points in moduli space of the LS theory We have done non-trivial check of our calculations and found exact agreement

  9. Is exactly superconformal in the planar limit??? Is exactly superconformal in the planar limit!!! Looking for new solutions in the planar limit Zanon et al. hep-th/0507282 Bork, Kazakov, Vartanov, Z (paper in preparation)

  10. Conclusion • We have found conditions of conformal invariance and finiteness of the full Leigh-Strassler deformation of N=4 SYM • - up to four loops in the planar limit • - up to three loops in the non-planar limit • Investigating obtained results we have found family of solutions which we suppose to be exactly conformal in the planar limit

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