W gravity, N=2 strings and (2+2) SU*(infinity) Yang-Mills instantons

Castro, Carlos

doi:10.1063/1.530500

W gravity, N=2 strings and (2+2) SU*(infinity) Yang-Mills instantons

Carlos Castro
(
- IAEC, Austin
)

Aug, 1993

10 pages

Published in:

J.Math.Phys. 35 (1994) 3013-3024

e-Print:

hep-th/9308102 [hep-th]

DOI:

10.1063/1.530500

Report number:

IAEC-8-93

View in:

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Abstract: (desy)

We conjecture that

W

gravity can be interpreted as the gauge theory of

\phi

diffeomorphisms in the space of dimensionally-reduced

D=2+2

SU~*(\infty)

Yang-Mills instantons. These

\phi

diffeomorphisms preserve a volume-three form and are those which furnish the correspondence between the dimensionally-reduced Plebanski equation and the KP equation in

(1+2)

dimensions. A supersymmetric extension furnishes super-

W

gravity. The Super-Plebanski equation generates self-dual complexified super gravitational backgrounds (SDSG) in terms of the super-Plebanski second heavenly form. Since the latter equation yields

N=1D=4SDSG

complexified backgrounds associated with the complexified-cotangent space of the Riemannian surface,

(T~*\Sigma)~c

, required in the formulation of

SU~*(\infty)

complexified Self-Dual Yang-Mills theory, (SDYM ); it naturally follows that the recently constructed

D=2+2N=4

SDSYM theory- as the consistent background of the open

N=2

superstring- can be embedded into the

N=1SU~*(\infty)

complexified Self-Dual-Super-Yang-Mills (SDSYM) in

D=3+3

dimensions. This is achieved after using a generalization of self-duality for

D>4

. We finally comment on the the plausible relationship between the geometry of

N=2

strings and the moduli of

SU~*(\infty)

complexified SDSYM in

3+3

dimensions.

gravitation
gauge field theory: W(N)
string model
gauge field theory: SU(infinity)
field equations: instanton
dimension: 4
dimension: 6
duality

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