paper

Four Dimensional String/String/String Triality

arXiv:hep-th/9508094 · doi:10.1016/0550-3213(95)00555-2

Abstract

In six spacetime dimensions, the heterotic string is dual to a Type string. On further toroidal compactification to four spacetime dimensions, the heterotic string acquires an $SL(2,\BbbZ)_S$ strong/weak coupling duality and an $SL(2,\BbbZ)_T \times SL(2,\BbbZ)_U$ target space duality acting on the dilaton/axion, complex Kahler form and the complex structure fields respectively. Strong/weak duality in interchanges the roles of and in yielding a Type string with fields . This suggests the existence of a third string (whose six-dimensional interpretation is more obscure) that interchanges the roles of and . It corresponds in fact to a Type string with fields leading to a four-dimensional string/string/string triality. Since $SL(2,\BbbZ)_S$ is perturbative for the Type string, this triality implies -duality for the heterotic string and thus fills a gap left by duality. For all three strings the total symmetry is $SL(2,\BbbZ)_S \times O(6,22;\BbbZ)_{TU}$. The $O(6,22;\BbbZ)$ is {\it perturbative} for the heterotic string but contains the conjectured {\it non-perturbative} $SL(2,\BbbZ)_X$, where is the complex scalar of the Type string. Thus four-dimensional triality also provides a (post-compactification) justification for this conjecture. We interpret the Bogomol'nyi spectrum from all three points of view. In particular we generalize the Sen-Schwarz formula for short multiplets to include intermediate multiplets also and discuss the corresponding black hole spectrum both for the theory and for a truncated ---- symmetric theory. Just as the first two strings are described by the four-dimensional {\it elementary} and {\it dual solitonic} solutions, so the

36 pages, Latex, 2 figures, some references changed, minor changes in formulas and tables; to appear in Nucl. Phys. B

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