Loop formulation of the supersymmetric nonlinear O(N) sigma model

Steinhauer, Kyle; Wenger, Urs (20 November 2014). Loop formulation of the supersymmetric nonlinear O(N) sigma model. PoS - proceedings of science, LATTICE2013(092). Scuola Internazionale Superiore di Studi Avanzati SISSA

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We derive the fermion loop formulation for the supersymmetric nonlinear O(N) sigma model by performing a hopping expansion using Wilson fermions. In this formulation the fermionic contribution to the partition function becomes a sum over all possible closed non-oriented fermion loop configurations. The interaction between the bosonic and fermionic degrees of freedom is encoded in the constraints arising from the supersymmetry and induces flavour changing fermion loops. For N ≥ 3 this leads to fermion loops which are no longer self-avoiding and hence to a potential sign problem. Since we use Wilson fermions the bare mass needs to be tuned to the chiral point. For N = 2 we determine the critical point and present boson and fermion masses in the critical regime.

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