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Register a new userSimulations of a supersymmetry inspired model on a fuzzy sphere
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Authors
Wolfgang Bietenholz
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We present a numerical study of a two dimensional model of the Wess-Zumino type. We formulate this model on a sphere, where the fields are expanded in spherical harmonics. The sphere becomes fuzzy by a truncation in the angular momenta. This leads to a finite set of degrees of freedom without explicitly breaking the space symmetries. The corresponding field theory is expressed in terms of a matrix model, which can be simulated. We present first numerical results for the phase structure of a variant of this model on a fuzzy sphere. The prospect to restore exact supersymmetry in certain limits is under investigation.
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We regularise the 3d lambda phi^4 model by discretising the Euclidean time and representing the spatial part on a fuzzy sphere. The latter involves a truncated expansion of the field in spherical harmonics. This yields a numerically tractable formulation, which constitutes an unconventional alternative to the lattice. In contrast to the 2d version, the radius R plays an independent r^{o}le. We explore the phase diagram in terms of R and the cutoff, as well as the parameters m^2 and lambda. Thus we identify the phases of disorder, uniform order and non-uniform order. We compare the result to the phase diagrams of the 3d model on a non-commutative torus, and of the 2d model on a fuzzy sphere. Our data at strong coupling reproduce accurately the behaviour of a matrix chain, which corresponds to the c=1-model in string theory. This observation enables a conjecture about the thermodynamic limit.
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