Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings - High Energy Physics - TheoryReport as inadecuate




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Abstract: Recent studies of the thermodynamic phase diagrams of the Gross-Neveu modelGN2, and its chiral cousin, the NJL2 model, have shown that there are phaseswith inhomogeneous crystalline condensates. These static condensates can befound analytically because the relevant Hartree-Fock and gap equations can bereduced to the nonlinear Schr\-odinger equation, whose deformations aregoverned by the mKdV and AKNS integrable hierarchies, respectively. Recently,Thies et al have shown that time-dependent Hartree-Fock solutions describingbaryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation,and can be mapped directly to classical string solutions in AdS3. Here wepropose a geometric perspective for this result, based on the generalizedWeierstrass spinor representation for the embedding of 2d surfaces into 3dspaces, which explains why these well-known integrable systems underlie thesevarious Gross-Neveu gap equations, and why there should be a connection toclassical string theory solutions. This geometric viewpoint may be useful forhigher dimensional models, where the relevant integrable hierarchies includethe Davey-Stewartson and Novikov-Veselov systems.



Author: Gokce Basar, Gerald V. Dunne

Source: https://arxiv.org/







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