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Random graph gauge theories as toy models for non-perturbative string theories

Thomas Filk

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We present simple models which exhibit some of the remarkable features expected to hold for the as yet unknown non-perturbative formulation of string theories. Among these are: (a) the absence of a background or embedding space for the full theory; (b) perturbative ground states (local minima of the action) having the characteristics of spaces of different dimension; (c) duality transformations between large- and small-coupling expansions; and (d) perturbative excitations of these ground states which can be interpreted as string worldsheets or p-brane worldvolumes. In this context we formulate gauge theories on arbitrary graphs and speculate concerning actions for graphs which in a continuum and/or thermodynamic limit might be related to the Einstein-Hilbert action.


PACS

11.25.Sq Nonperturbative techniques; string field theory

11.25.Tq Gauge/string duality

11.15.-q Gauge field theories

MSC

81T30 String and superstring theories; other extended objects (e.g., branes) (See also 83E30)

81T13 Yang-Mills and other gauge theories (See also 53C07, 58E15)

Subjects

Particle physics and field theory

Dates

Issue 23 (7 December 2000)

Received 11 June 2000



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