679 research outputs found
Simplicial vs. Continuum String Theory and Loop Equations
We derive loop equations in a scalar matrix field theory. We discuss their
solutions in terms of simplicial string theory -- the theory describing
embeddings of two--dimensional simplicial complexes into the space--time of the
matrix field theory. This relation between the loop equations and the
simplicial string theory gives further arguments that favor one of the
statements of the paper hep-th/0407018. The statement is that there is an
equivalence between the partition function of the simplicial string theory and
the functional integral in a continuum string theory -- the theory describing
embeddings of smooth two--dimensional world--sheets into the space--time of the
matrix field theory in question.Comment: 6 page
Towards the Theory of Non--Abelian Tensor Fields I
We present a triangulation--independent area--ordering prescription which
naturally generalizes the well known path ordering one. For such a prescription
it is natural that the two--form ``connection'' should carry three ``color''
indices rather than two as it is in the case of the ordinary one--form gauge
connection. To define the prescription in question we have to define how to
{\it exponentiate} a matrix with three indices. The definition uses the fusion
rule structure constants.Comment: 22 pages, 18 figure
Expansion in Feynman Graphs as Simplicial String Theory
We show that the series expansion of quantum field theory in the Feynman
diagrams can be explicitly mapped on the partition function of the simplicial
string theory -- the theory describing embeddings of the two--dimensional
simplicial complexes into the space--time of the field theory. The summation
over two--dimensional geometries in this theory is obtained from the summation
over the Feynman diagrams and the integration over the Schwinger parameters of
the propagators. We discuss the meaning of the obtained relation and derive the
one--dimensional analog of the simplicial theory on the example of the free
relativistic particle.Comment: Latex, 11pp, Minor mintakes are correcte
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