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Register a new userVanishing superconformal indices and the chiral symmetry breaking
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Added by
Vyacheslav P. Spiridonov
Publication date
2014
fields
Physics
and research's language is
English
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Superconformal indices of 4d N=1 SYM theories with SU(N) and SP(2N) gauge groups are investigated for N_f=N and N_f=N+1 flavors, respectively. These indices vanish for generic values of the flavor fugacities. However, for a singular submanifold of fugacities they behave like the Dirac delta functions and describe the chiral symmetry breaking phenomenon. Similar picture holds for partition functions of 3d supersymmetric field theories with the chiral symmetry breaking.
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Solvability of the ubiquitous quantum harmonic oscillator relies on a spectrum generating osp(1|2) superconformal symmetry. We study the problem of constructing all quantum mechanical models with a hidden osp(1|2) symmetry on a given space of states. This problem stems from interacting higher spin models coupled to gravity. In one dimension, we show that the solution to this problem is the Plyushchay family of quantum mechanical models with hidden superconformal symmetry obtained by viewing the harmonic oscillator as a one dimensional Dirac system, so that Grassmann parity equals wavefunction parity. These models--both oscillator and particle-like--realize all possible unitary irreducible representations of osp(1|2).
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