It is observed that the classical part of the partition function associated with the mappings from a genus-g Reimann surface Σg to an "almost complex" target space T2d is equal to that related to the mappings Σd to T2g. The classical part related to the mappings from a genus-2g Reimann surface Σ2g described by a "real" period matrix, to a target space Td is equal to the classical part related to mappings from Σ2g to Tg. Some physical consequences of these mathematical identities are discusses.
|Original language||American English|
|Number of pages||6|
|Journal||Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics|
|State||Published - 13 Apr 1989|
Bibliographical noteFunding Information:
One imagination capturing feature of string theory is that a string moving in a target space which contains one circular dimension cannot distinguish if the radius of that circle is R or 1/2R \[1 \]. This duality generalizes to both bosonic and heterotic strings in any d-dimensional toroidal compactification \[2 \]. For the closed oriented bosonic string it takes, geometrically, the following form. Given the pair (G, B), where G is a positive definite symmetric constant background metric, and B is an antisymmetric constant background, one defines the "parameter matrix" D= G+B. Under the duality transformation D is transformed to 1/D. Some mathematical properties and physical consequences of this transformation were discussed in ref. \[3 \]. In ref. \[4 \] a different type of transformation, termed triality, was found in the c= 2 case. It related a string projected from a certain world-sheet torus into a certain 2-dimensional toroidal background to a string projected from a different world-sheet torus into a different background. In this note it is shown that there exists a more general relation between pairs (Z, T), where E denotes the world-sheet and T denotes the target space. It is shown that the classical part of the partition function describing pairs (Z, T) is related to the classical part of the pair (T, ~). The classical part of the pairs (Z, T) and (T, Z) is manifestly identical if the following conditions are satisfied. Either the target space is "al- Work supported in part by the Israeli Academy of Science and by the BSF - American Israeli Bi-National Science Foundation.