Field Theory of Open and Closed Strings with Discrete Target Space

Abstract

We study a $U(N)$-invariant vector+matrix chain with the color structure of a lattice gauge theory with quarks and interpret it as a theory of open andclosed strings with target space $\mathbb{Z}$. The string field theory is constructed as a quasiclassical expansion for the Wilson loops and lines in this model. In a particular parametrization this is a theory of two scalar massless fields defined in the half-space $\{x\in \mathbb{Z},\tau >0\}$. The extra dimension $\tau$ is related to the longitudinal mode of the strings. The topology-changing string interactions are described by a local potential. The closed string interaction is nonzero only at boundary $\tau =0$ while the open string interaction falls exponentially with $\tau$.

15 pages, harvmac. no figures; some typos corrected and a reference added

References in corpus (8)

• Matrix Model Calculations beyond the Spherical Limit
• Multicritical Phases of the O(n) Model on a Random Lattice
• Strings with Discrete Target Space
• Gauge Invariant Matrix Model for the Â-D-Ê Closed Strings
• Loop Gas Model for Open Strings
• Open String Theory in 1+1 Dimensions
• From 1-matrix model to Kontsevich model
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Cited by in corpus (12)

• The Annular Report on Non-Critical String Theory
• The Small Scale Structure of Space-Time: A Bibliographical Review
• Boundary Ground Ring in 2D String Theory
• The Two-point Function of c=-2 Matter Coupled to 2D Quantum Gravity
• LOOP SPACE HAMILTONIAN FOR $c\le 1$ OPEN STRINGS
• Feynman rules for string field theories with discrete target space
• Symmetry in the Topological Phase of String Theory
• Algebraic Structure in 0<c<1 Open-Closed String Field Theories
• Stochastic Quantization Approach for Causal Dynamical Triangulation String Field Theory
• Causal dynamical triangulation for non-critical open-closed string field theory
• Causal dynamical triangulation of a 3D tensor model
• CDT open-closed surface field theory of a 3D tensor-matrix model