Classical Matrix sine-Gordon Theory

Details Classical Matrix sine-Gordon Theory Classical Matrix sine-Gordon Theory

1995-05-03

arxiv.org/abs/hep-th/9505017v1

Nucl.Phys. B458 (1996) 327-354

Physics

High Energy Physics

High Energy Physics - Theory

25 pages, 6 Postscript figures

Scientific paper

10.1016/0550-3213(95)00539-0

The matrix sine-Gordon theory, a matrix generalization of the well-known sine-Gordon theory, is studied. In particular, the $A_{3}$-generalization where fields take value in $SU(2)$ describes integrable deformations of conformal field theory corresponding to the coset $SU(2) \times SU(2) /SU(2)$. Various classical aspects of the matrix sine-Gordon theory are addressed. We find exact solutions, solitons and breathers which generalize those of the sine-Gordon theory with internal degrees of freedom, by applying the Zakharov-Shabat dressing method and explain their physical properties. Infinite current conservation laws and the B\"{a}cklund transformation of the theory are obtained from the zero curvature formalism of the equation of motion. From the B\"{a}cklund transformation, we also derive exact solutions as well as a nonlinear superposition principle by making use of the Bianchi's permutability theorem.

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