Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Renormalization group flows and continual Lie algebras   We study the renormalization group flows of two-dimensional metrics in sigma
models and demonstrate that they provide a continual analogue of the Toda field
equations based on the infinite dimensional algebra G(d/dt;1). The resulting
Toda field equation is a non-linear generalization of the heat equation, which
is integrable in target space and shares the same dissipative properties in
time. We provide the general solution of the renormalization group flows in
terms of free fields, via Backlund transformations, and present some simple
examples that illustrate the validity of their formal power series expansion in
terms of algebraic data. We study in detail the sausage model that arises as
geometric deformation of the O(3) sigma model, and give a new interpretation to
its ultra-violet limit by gluing together two copies of Witten's
two-dimensional black hole in the asymptotic region. We also provide some new
solutions that describe the renormalization group flow of negatively curved
spaces in different patches, which look like a cane in the infra-red region.
Finally, we revisit the transition of a flat cone C/Z_n to the plane, as
another special solution, and note that tachyon condensation in closed string
theory exhibits a hidden relation to the infinite dimensional algebra G(d/dt;1)
in the regime of gravity. Its exponential growth holds the key for the
construction of conserved currents and their systematic interpretation in
string theory, but they still remain unknown.

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The categories of this paper are: chem-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: dg-ga
3
The categories of this paper are: physics
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The categories of this paper are: cmp-lg
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: ao-sci
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin
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The categories of this paper are: math
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The categories of this paper are: nlin