Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gross-Neveu Models, Nonlinear Dirac Equations, Surfaces and Strings   Recent studies of the thermodynamic phase diagrams of the Gross-Neveu model
(GN2), and its chiral cousin, the NJL2 model, have shown that there are phases
with inhomogeneous crystalline condensates. These (static) condensates can be
found analytically because the relevant Hartree-Fock and gap equations can be
reduced to the nonlinear Schr\"odinger equation, whose deformations are
governed by the mKdV and AKNS integrable hierarchies, respectively. Recently,
Thies et al have shown that time-dependent Hartree-Fock solutions describing
baryon scattering in the massless GN2 model satisfy the Sinh-Gordon equation,
and can be mapped directly to classical string solutions in AdS3. Here we
propose a geometric perspective for this result, based on the generalized
Weierstrass spinor representation for the embedding of 2d surfaces into 3d
spaces, which explains why these well-known integrable systems underlie these
various Gross-Neveu gap equations, and why there should be a connection to
classical string theory solutions. This geometric viewpoint may be useful for
higher dimensional models, where the relevant integrable hierarchies include
the Davey-Stewartson and Novikov-Veselov systems.

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The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
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The categories of this paper are: econ
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
10
The categories of this paper are: q-bio