Infinite-component field theory and the Veneziano model

It is shown how w∞, w1+∞ gauge field theory actions in 2D emerge directly from 4D gravity. Strings and membranes actions in 2D and 3D originate as well from 4D Einstein gravity after recurring to the nonlinear connection formalism of Lagrange–Finsler and Hamilton–Cartan spaces. Quantum gravity in 3D can be described by a W∞ matrix model in D = 1 that can be solved exactly via the collective field theory method. We describe why a quantization of 4D gravity could be attained via a 2D quantum W∞ gauge theory coupled to an infinite-component scalar-multiplet. A proof that noncritical W∞ (super)strings are devoid of BRST anomalies in dimensions D = 27(D = 11), respectively, follows and which coincide with the critical (super)membrane dimensions D = 27(D = 11). We establish the correspondence between the states associated with the quasifinite highest weights irreducible representations of W∞, [Formula: see text] algebras and the quantum states of the continuous Toda molecule. Schrödinger-like quantum mechanics wave functional equations are derived and solutions are found in the zeroth-order approximation. Since higher-conformal spin W∞ symmetries are very relevant in the study of 2DW∞ gravity, the quantum Hall effect, large N QCD, strings, membranes, … it is warranted to explore further the interplay among all these theories.

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Infinite-component fields as a basis for a finite quantum field theory

Physics Letters B ◽

10.1016/0370-2693(88)91617-6 ◽

1988 ◽

Vol 206 (3) ◽

pp. 499-502 ◽

Cited By ~ 5

Author(s):

J.W. Moffat

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Quantum Field ◽

Infinite Component

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SCHIZOSYMMETRY: A NEW PARADIGM FOR SUPERFIELD EXPANSIONS

Modern Physics Letters A ◽

10.1142/s0217732394002173 ◽

1994 ◽

Vol 09 (25) ◽

pp. 2305-2313 ◽

Cited By ~ 3

Author(s):

R. DELBOURGO ◽

P.D. JARVIS ◽

ROLAND C. WARNER

Keyword(s):

Field Theory ◽

Quantum Field Theory ◽

Model Building ◽

Space Time ◽

Unified Model ◽

Quantum Field ◽

New Paradigm ◽

Field Transformation ◽

Component Field ◽

Symmetry Generators

A new principle of ‘schizosymmetry’ is proposed for interpreting superfield expansions over Grassmann parameters in quantum field theory. Symmetry generators T phys , determining component field transformation properties, are allowed to depend on the grading via T phys =Tℙ e +T′ℙ o , where ℙ e and ℙ o are the projections onto even and odd components in the Grassmann coordinates, respectively, and T and T′ correspond to different representations. Examples are given for both internal and space-time schizosymmetry. In the latter case, superfield expansions have components with both integer and half-integer spin. A program for the Lagrangian realization of schizosymmetry, including unified model building, is outlined.

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